Beam Axles - Front, Rear or both. [Archive]

oz_olly

12-19-2009, 04:18 AM

Hey Rob,

Thanks for the interest. It's a shame Z has moved on from the forums these days because I am sure he would love to be in on the discussion. I am planning to give him a call over the coming weeks to give him an update on how it all went.

The decision to go with beam axles was based around a few different ideas. The first was that we had a very inexperienced team this year (75% first timers) so we needed something easy to understand and easier to manufacture with less reliance on getting the chassis really pick up points really accurate. The other idea was from a higher level, looking at FSAE as a cool project management problem. If we could design a car that maybe has C level performance but we have an A level team that develops and extracts the performance out of the C level car then we may be on to something. We are a small university with few people willing to volunteer their time for something like FSAE, so our goals have to be set appropriately. Unfortunately we didn't get much development time this year as we didn't finish the build until very late. I believe if we had of gone for a bells and whistles design we wouldn't have made it and our program probably would have been cancelled. So enough of the back ground more about the why...

Compared to the conventional double wishbone car, our car requires far fewer accurate pick up points. A double wishbone car with direct actuating dampers requires 24 pickup points, our car requires 10 (four on the front and 6 on the rear). This significantly increased the ease of manufacture on the chassis.

The beam axle suspension is also relatively easy to understand. We don't have to worry about the scrub vs camber change compromise. We can use castor in the front for increase cornering camber. Camber at the rear is shim adjustable as our drive train is sprung. You can set a static camber and then what you lose is due to compliance. It was quite easy to determine the roll centres for roll stiffness calculations and you can physically touch the roll centre if you are so inclined. Bump/roll steer on the front has not been measured yet but by placing the steering rack on the unsprung it was significantly reduced from what it may have been.

The big downside seems to be that disturbing one wheel sympathetically disturbs the other dependant wheel. It will change the vertical load and camber of the opposite wheel thereby changing either lateral or longitudinal force. Although if you have a fairly stiff antiroll bar on an independent suspension car, hitting a single wheel bump will also affect the vertical load on the opposite wheel.

I would like to take this concept further and see just how much we could simplify it. One of the things we are looking to test is a spool, we ran one in 2007 when our overcomplicated gear drive failed. The car didn’t accumulate many test miles so I am not in a position to make a very informed decision at this point. If we did run a spool and it looked to be successful then I would most certainly take a look at a solid axle like the one Buffalo has. I am a strong believer that a really simple car, well executed, using nicely machined parts in the right places has a real chance of being very successful. Sure in absolute performance terms it may be hard to beat a team like Stuttgart or Delft or UWA etc without the high levels of performance those designs may be capable of. The one thing I am sure of is that we could never pull off a car of that technical magnitude in one year let alone two. Our best chance of being really successful is to build the best C or B level performance car we can with a solid understanding of vehicle dynamics and test it, test it, test it, make it fast and then test it some more.
We are currently running a rack and pinion steering on the front unsprung but we are going to look to change that to a go-kart style for reduced unsprung mass and further simplicity/lower cost. One other benefit I forgot to mention before was the reduction in the number of spherical bearings required. Our design requires 27 in total (not including ARB) where as previous designs have required 40. So that in itself is a pretty decent saving. Looking at Rob’s design, I think he would need fewer again.

My biggest concern with the beam axles at this stage is compliance. I don’t think it is a show stopper though as it can be fixed through revised mechanical and structural design. I have also had time to think about how I would constrain the suspension in FEA modelling differently to how I did it. Constraining the model more realistically should help to target the causes of compliance.

Cheers

Olly

ACME Racing
UNSW@ADFA

rjwoods77

12-22-2009, 10:34 AM

Olly,

Just a side note did you see Eric Bana in the movie "Love the Beast". Such a good movie. Nothing will ever be as good as "Dust to Glory" but it was up there

Do you have Erik Zapletals contact info. I have and old phone number but I was hoping to latch onto an email I could contact him at since I am thinking about building a z bar suspension for my 1982 Toyota Starlet.

jonty

12-23-2009, 06:15 AM

Olly,

I'm an ex Team bath Racing Member from 2006. Funny you should mention beam axles - myself and an extreamly well respected special builder are currently developing the latest mallock racing car to use a de dion style rear end. However instead of using a a de dion tube we are using a space frame. The reasons.... well the gentleman that is helping me has in the past built 6 racing cars all around the beam axle principle. Two cars of which competed in F3.

Email me on jonty_hair@yahoo.co.uk, send me some photos of your car and we'll discuss further!

Remember the minute you put a roll bar on an independent suspension car it becomes dependant - also how big are the bumps on a race track???

rjwoods77

12-23-2009, 04:20 PM

Just thought I should mention that Satchel links work on dedion rear ends. It is in my opinion one of the best all around link configurations for beam axles/dedions.

oz_olly

04-11-2010, 02:12 AM

The section below comes from the March 2010 issue of 'Chassis Newsletter' by Mark Ortiz:

DE DION TUBE DESIGN AND LOCATION

Question:I am trying to decide on the arrangement to locate a DeDion axle in an autocross car that has a transverse engine/transmission directly in front of the axle. I plan to use a watts link for lateral location. Single trailing arms on each side with a third central link does not seem appropriate because the transverse engine would dictate a very short center link.

I am considering parallel trailing arms on each side. However, I have seen applications that converge the arms on each side to a single front mount. It seems to me that in this situation there might be bending forces applied to the arms when one wheel rises and/or the other falls. Perhaps these are not significant because the axle will have quite limited vertical movement.

Which do you consider more appropriate, parallel arms or triangular arms converging to one front mount on each side?

Answer: The simple answer is to go with parallel arms. Converging arms or hairpin-style ones with a single pivot will bind in roll, unless the DeDion tube has a swivel in the middle.

A swivel in the middle complicates the DeDion tube, but this was actually a feature of many designs when DeDion suspension was popular in F1 cars – for example the Mercedes W154. That car used a tube assembly that was rigid in bending and tension/compression, but not in torsion, and single trailing arms, with outboard brakes. Lateral location was provided by a roller in a slot machined into the back of the differential housing.

The Rover 2000/3500TC used a tube that both swiveled and telescoped: it was rigid only in bending. Lateral location was then provided by fixed-length halfshafts, eliminating the need for any plunge accommodation at the shafts, and the need for any additional lateral locating mechanism. Single trailing arms were used, and brakes were inboard.

Both of these designs offer somewhat more than 100% camber recovery in roll (ignoring tire deflection), and a roll center a bit higher than the halfshafts or the roller.

The Mercedes design afforded very ample anti-lift in braking, due to the combination of outboard brakes and single trailing arms. The Rover design does not have comparable anti-lift, despite similar side-view geometry, because the brakes are inboard.

Either of these designs could also use four trailing links, and they wouldn't have to be parallel. With outboard brakes, that would permit having any desired anti-lift in braking, without significant bump steer, which is not possible with parallel trailing links.
---------------------------------------------

This seems fairly relevant to the discussion above and the type of De Dion we did on our car (bit of a bump too). The way we got around the kinematic binding which occurs with single pivot trailing arms was to use a torsionally flexible beam that was still fairly stiff in bending (a tube with a slit cut down the bending neutral axis.

Cheers

Olly
ACME Racing
UNSW@ADFA

oz_olly

11-10-2010, 02:34 AM

One of the perceived weaknesses of beam axles is lack of camber gain in roll. I would say the solution to that is fairly simple:

Use a front solid beam axle zero steering axis inclination and enough castor until you have the camber gain you want.

In the rear use a twist axle style beam. We did it using a de Dion style design. Depending where you place the trailing arm pivots and torsion section of the beam, you can design in a reasonable about of camber gain.

I would say the difficulty with beam axles is designing in enough installed stiffness in both camber, toe and hub to hub stiffness. Bump/roll steer can be an issue but there are definitely solutions available to reduce those effects. The unsprung mass can be quite high at 14.5kg for each corner (29kg total)on the front and 14kg in the rear. Our initial design was fairly conservative and I definitely didn't nail the load paths and material distribution first time around.

Hopefully the beam axle discussions can continue here and continue to grow. Many of the reasons that beam axles fell out of favour are no longer relevant for our application for example we haven't exactly been crippled by steering shimmy.

oz_olly

11-26-2010, 04:12 AM

I just spent the last week manufacturing a suspension compliance test rig to try and put some numbers to the compliance of our beam axle design. Photos of the rig are available at:

http: // s928. photobucket. com/albums/ad127/oz_olly/Suspension%20Compliance%20Test%20Rig/

(just remove the spaces)

The first picture shows the rig set up with the car to measure camber stiffness and the other pictures (taken during fabrication) show the set up for toe compliance. Notice the leaning tower of G clamps for good measure. I did some quick tests this afternoon just to make sure everything worked and it all seemed to go quite well. The angle results were only accurate to +-0.05 deg as I was using an electronic camber gauge. When I do the full set of tests I will use either linear pots or LVDTs to get better resolution.

My initial results are 285Nm/deg in camber with 1.6g*80kg*0.2413m giving a moment of 303Nm. So we lose 1.07 deg camber at 1.6g with 80kg static corner weight. That's much more compliance than I would like and I have a feeling the toe compliance is going to be worse but now that we have a way to measure it we can quantify improvements.

Cheers

oz_olly

11-30-2010, 02:44 AM

bump! My post above was delayed even though I broke the link.

thewoundedsoldier

11-30-2010, 02:56 AM

Pretty cool rig, but I don't approve of welding in shorts!

haha last year I got terrible sunburn like 9 times from welding in a tshirt. always too lazy to walk over and get the sleeves...

I would be very interested to see your results plotted between 0 and 2.5 degrees camber in both directions. I'd expect it to be non-linear and unpredictable, meaning a glitchy car.

I'm going to spend a little while setting up something similar for our solid beam axle rear end TR test.

Very impressive!

exFSAE

11-30-2010, 06:01 AM

Originally posted by oz_olly:
I just spent the last week manufacturing a suspension compliance test rig to try and put some numbers to the compliance of our beam axle design. Photos of the rig are available at:

http: // s928. photobucket. com/albums/ad127/oz_olly/Suspension%20Compliance%20Test%20Rig/

(just remove the spaces)

The first picture shows the rig set up with the car to measure camber stiffness and the other pictures (taken during fabrication) show the set up for toe compliance. Notice the leaning tower of G clamps for good measure. I did some quick tests this afternoon just to make sure everything worked and it all seemed to go quite well. The angle results were only accurate to +-0.05 deg as I was using an electronic camber gauge. When I do the full set of tests I will use either linear pots or LVDTs to get better resolution.

My initial results are 285Nm/deg in camber with 1.6g*80kg*0.2413m giving a moment of 303Nm. So we lose 1.07 deg camber at 1.6g with 80kg static corner weight. That's much more compliance than I would like and I have a feeling the toe compliance is going to be worse but now that we have a way to measure it we can quantify improvements.

Cheers

Kinda missing load transfer in there. When you're mid corner, let's assume the inside and outside tires are roughly operating at similar mu's. Might get to oh say 130kg on the outside... 130*9.8*1.6*0.241 = 490N-m. 1.7deg of camber compliance... yikes.

oz_olly

11-30-2010, 03:33 PM

Bugger you're right exFSAE. I just did those numbers really quickly. Thanks for finding my mistake when I was writing it I had that feeling that I'd forgotten something important. I'll rework the actual numbers taking into account weight transfer and post my results. The design that I currently have definitely has too much compliance so now that I have measured it I can set realistic design targets for the next iteration. It would be interesting to see some numbers from wishbone suspension FSAE cars. I guess for them the upright plays a big role provided the control arms are loaded in as close to tension compression as possible.

As for Woundesoldiers hypothesis of the compliance being highly non-linear, this is not the case. The moment vs displacement curve is quite linear. There is a bit of non-linearity in the low moment area as any slop in bearings etc gets taken up but then it is pretty straight. I'll post some graphs up when I take more measurements with dial guages to measure displacement.

MalcolmG

11-30-2010, 09:27 PM

Originally posted by oz_olly:
It would be interesting to see some numbers from wishbone suspension FSAE cars. I guess for them the upright plays a big role provided the control arms are loaded in as close to tension compression as possible.

...well, I did some camber compliance testing on our unsprung assembly (not including wheel) last year, and although I don't have the raw data on hand to check I did my calculations correctly (or what mass assumptions I based the numbers on), I came up with 0.27 degrees for the heavy end of the car at 1g lateral acceleration. I'll see if I can find my moment vs deflection numbers when I get home for a more useful comparison.

TheoD

12-21-2010, 03:57 PM

Brown University had solid axle cars from 97 to 2004. We started with a front solid axle controlled with a peg and slot, that used torsion bars for springs, and rear axle-stressed engine also with a peg and slot and regular shocks.
Over the years we developed the designs to use:
Solid front axle with "stressed" steering rack, controled with Mumford linkage and leading arms
DeDion rear controled with Mumford linkage and trailing arms.

We always used 10" rims during these years (F500 class) and original Mini transmition hardware for diff/ half axles etc

We placed 6th in 2000
and 10th in 2002

After that the newer team members wanted to follow the fashion of Independant suspension and have not performed at the same level...

The 3 main reasons were:
1) Simplicity of manufacturing cause of jigging etc
2) If the independant suspension is so stiffly built that in effect it acts as a solid axle, then what is the advantage? Forgoe the cost and difficulty of it all together...
3) Roll center at or below the pavement!

Desclaimer: This was 10 years ago and I was not the Chassis and suspension designer so I am very rusty on details.

rjwoods77

12-20-2011, 10:11 PM

TheoD,

I remember seeing one picture of one of your cars many years ago. Where can one find pics of these cars.

shark.ashwa

12-20-2011, 10:27 PM

Originally posted by rjwoods77:
TheoD,

I remember seeing one picture of one of your cars many years ago. Where can one find pics of these cars.

Rob,

Found it!
http://www.brown.edu/Departmen.../The_Past%21.html#12 (http://www.brown.edu/Departments/Engineering/Organizations/fsae/Media/Pages/The_Past%21.html#12)

but then there are only one or two! http://fsae.com/groupee_common/emoticons/icon_frown.gif

Sharath

oz_olly

12-21-2011, 03:11 AM

The more I think about beam axles, the more I think a carbon tube live rear axle could be a really good choice for a Formula SAE car. A single (large OD ~2.5in) off the shelf carbon tube with bearing surfaces (sleeves), sprocket and brake disc carriers and hubs all bonded on. The kinematics could be controlled using your favourite linkage system. Major compromises would be no differential, no camber and toe adjustment but I think the system could be made to be of similar unsprung mass to a good a-arm suspension and it would have quite low camber and toe compliance. The system I am thinking of would look similar to the Buffalo car from a few years ago.

Can anyone else dig up more pictures of that Brown car? When Z was talking about the brown go kart, was he really talking about the Brown go kart http://fsae.com/groupee_common/emoticons/icon_wink.gif

Cheers

Edit: Turns out I should read the other posts. Looks like Rob and I see almost eye to eye on this one. Also Z is right, when you take your design in another direction to the general trend you don't have much to copy but you are forced to think about it right from first principles and I think you potentially come out the other side with a deeper/better understanding.

mech5496

12-21-2011, 06:37 AM

Oz, thats what I meant with "polished up" beam concept... (http://fsae.com/eve/forums/a/tpc/f/125607348/m/54820131151?r=32420641151#32420641151) This could go on to CF 4-link bars, pushrods and (why not?) a monocoque, making an 140kg car likely...

rjwoods77

12-21-2011, 01:50 PM

Olly,

I am curious as to how you differ on what I described.

01-19-2012, 07:17 PM

A few weeks ago on the "suspension for spool" (http://fsae.com/eve/forums/a/tpc/f/125607348/m/54820131151) thread I said I would post a sketch of a Twin Beam-Wing concept. I think this is a more suitable thread, so here it is (warts and all http://fsae.com/groupee_common/emoticons/icon_smile.gif).

https://lh5.googleusercontent.com/-8ABMaKebyXs/Txtdpl2DZEI/AAAAAAAAAIs/fCJ-84VnwMc/s800/TwinBeamWing.jpg

(Edit: Made image bigger.)

Main features:

* This is an "aero above all" car. Everything else is there just to support the aero. I figure "drive on the ceiling" at less than maximum FSAE speeds (ie. DF=W at <100kph, (maybe <70kph?)). And more is possible!

* Aero is direct acting on the wheels, and easily adjustable for F/R balance via the flaps. Since wings are close to ground, and with wheels as skirts/end-plates, drag is low (no induced drag). The streamlined fuselage and wheel pods also lower drag for good economy.

* The aero centres of pressure are unlikely to be exactly above wheel axle lines, so some force acts on chassis through BJs causing some pitch/heave. This can be fixed by either; a) not worrying about it, b) reshaping the wings, or c) interconnecting the wings with two torsionally flexible spars running alongside the chassis and attached flexibly to the beams on their axle lines. Extending this last solution sideways gives a full width "live" undertray.

* The rest of the car is as simple and robust as possible, for quicker build and more testing. Chassis is mandatory roll-hoops/side-impact-structure plus a minimum of extra tubes. Direct acting springs can be soft because little aero load through them, and wheel cambers unaffected by body roll, pitch, or heave. So dampers also soft.

* If the beams look a bit bulky, then think of them as the main spars and ribs of the heavily loaded wings. Each beam-wing is attached to chassis at only four hard points, namely the 2x spring-dampers, 1x heavy duty ball-joint (say 12mm or 1/2"), and 1x low friction "peg and slot" for lateral control (using, say, 2 x 12mmID 6201 ball bearings). Jigging can be done with stringline and tape measure.

* Rear wheels are 10" diameter (x 8" wide), but fronts are smaller, maybe 8" diameter. Less is more! This is subject to finding appropriate tyres, maybe from off-road quad racers with knobs cut off. If necessary, fronts can be narrow 10" diameter. Note semi-circular panels in front wing that turn with the wheels.

* Steering is bevel-gearbox-&-pitman-arm, for less friction, backlash, weight, and cost than R&P+UJs, and better ackermann (two sinusoids to work with).

* "Necessary ballast" is Royal Enfield! Shown is the old style engine with the separate gearbox relocated to front of crankcase. Jawa or similar single also possible, either upright as shown, or laydown as discussed "Objectively" (http://fsae.com/eve/forums/a/tpc/f/125607348/m/824105905/p/3) elsewhere.

* Important note: the final drive chain as shown will give some anti-squat under power (good), but also some wedge (bad - less LR load, more RR). So OS out of left turns, US out of right turns. This can be fixed by moving engine sideways so chain is on car centreline (or, less desirable, move BJ so in-line with chain).

* A Rob Woods/UB style spool-axle is shown, but a live diff can also be fitted (this is the reason for the 4 x axle bearings). Also camber and toe can be made adjustable by using two half axles connected in the middle with CVs (or well greased splines).

* A De-Dion layout with chassis mounted diff is also possible (my preference). In this case only the 2 outer axle bearings are required, together with CV'd half-shafts. BUT, this requires different kinematic location of the beam-wing to the chassis or else too much pro-squat (I didn't have room to show this on sketch - it's only A4). De-Dion is structurally similar, just some relatively small (but important) kinematic changes, so can be done as bolt-on "option".

* Finally, a first year or "limited resource" team can do this car without the aero. Use a RE, B&S, or similar engine and you have a simple lightweight car that is quicker to build than the usual wishbones-and-pull/pushrods&rockers-everywhere cars. And, all other things equal, it will have high grip and benign handling because of soft springs with no camber change (not possible with normal independent suspensions).

Comments and criticisms welcome! http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

Buckingham

01-19-2012, 09:00 PM

Very interesting concept. Lots of good ideas.

Packaging an effective braking system on the front axle may be the most difficult challenge with such small wheels, especially if the intent is to have low scrub radius to minimize fore/aft wheel so that it packages well with the aero.

If the car has to compromise on tires in order to maximize aero, this does not bode well for the novice FSAE driver who "drives too fast in the slow corners and too slow in the fast corners"

Rex Chan

01-19-2012, 09:15 PM

Just wanna say: that's a beautiful sketch/drawing. How did you do it?

Nihal

01-19-2012, 09:39 PM

Z, what is constraining the rear axle laterally?

Pete Marsh

01-19-2012, 11:21 PM

@ Nihal - A ball joint at the front mount and a "peg and slot" at the back, labeled P&S and detailed in a break out.

Pencil sketching is becoming a lost art. They don't encourage it nearly enough. I'll bet you Z can do such a sketch 10 times faster than you can do it CAD, and it communicates the concept perfectly.

@Z - Are you sure your not sitting in on our tech team meetings some how??? Or maybe we are channeling you? Some of our guys do talk funny.
It turns out surface area trumps the "twin wing" concept by quite a bit, and a full floor is superior. At least according to our relatively inexperienced aero team. Did you see the photo from Aus comp of our floor sitting on the ground without the car? Huge surface area.
That, and our 1 piece (as in both sides) flexure lower A arms do/are pretty much what you have here, but with the addition of top arms etc providing semi independence and much larger load bases to provide camber and toe stiffness easier.
As a aero mounting platform it is really good. We can run amazingly low and not touch.

Pete

01-20-2012, 11:56 PM

Buckingham,

I have looked at brake packaging with zero offset steering in 8" wheels before and don't see any major problems. Essentially there is a lot of fresh air in standard 13", and even 10", wheels that doesn't have to be there.

I have suggested the 8"s partly because of the rear weight bias (~40F:60R), but mainly because I don't think any more is necessary. Smaller diameter means less weight, lower CG, less stresses on axle (shorter lever arm), so less weight again, and so on.

If, at the initial design concept stage, you start thinking "13" wheels", then you end up with a powered DOWN F3 car. If you start thinking "smallest possible wheels", then you end up with a powered UP go-kart. Normal power go-karts are quite fast.

The only problem I can think of is ready access to tyre information. No TTC data on 8"s (?), so the team has to do its own research...
~~~~~o0o~~~~~

Rex,

It's newsagent bought ball-point pen (black, medium point), white-out, and A4 paper. Smooth lines with a plastic ruler and ellipse/circle stencils, plus some freehand. Some pencil construction lines to begin with, then erased.
~~~~~o0o~~~~~

Nihal,

As Pete says it's a P&S same as at the front. This is really only suitable for the relatively dirt-free and short travel conditions of circuit racing. I wouldn't recommend it for production cars, and definitely not for off-road racing.
~~~~~o0o~~~~~

Pete,

Previously I have mostly suggested a full width live undertray. The Twin-Wing concept is to get people thinking about how easy it is to start with beam-axles, then add some (plywood?) skins to turn them into wings. Then add flaps, extend the chord, more flaps+++. Also, with this path the F/R aero balance should be easy to adjust.

Regarding camber and toe stiffness, I don't see any problem at all. In fact, better than wishbones. A beam takes the forces from the wheel bearings to the chassis via a one-piece shell-like structure (the beam) that can be closely aligned with the axis of the tyre's "force screw". With wishbones, these forces first go up and down the often flimsy upright, then through the small outer BJs' (with lots of local deformations such as the BJ bolt in shear), then through the wishbones, then again through more small BJ's at the chassis. It's a detail design thing, but I reckon a sloppy wishbone layout is much worse than an average beam.

I'd love to see more detailed pics of your car but at the moment I'm using a borrowed "box of grief" that randomly seizes up when on the web (averaging every ~10mins!). I'm in the process of upgrading (grrrrrrrrrrr http://fsae.com/groupee_common/emoticons/icon_mad.gif ).

BTW, I believe you run a similar steering layout? It's gives good geometry, eh? http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

mech5496

01-22-2012, 09:52 AM

First of all, Z, I hate you. Your overall skills (including drawing) and understanding is waaaay higher than anyone I know. Onto the topic...As I have mentioned in the other thread ("suspension for spool" or "objectively", do not remebmer) I made a quick CAD during Xmas vacation. There are a couple of things that trouble me with all that approach. First of all, in order to make space for a complete "live" undertray/underwing and the pick up points for the beam axles, you have to raise your CoG a fair amount. You could separate the chassis mounting points (having 2 BJ's per axle instead of one) but this leads to other problems (increased roll stiffness). [EDIT: Separate BJ's could allow lower chassis/component placement for a greater length, as the chassis should be upswept (higher) only at the "peg n' slot" mounting ponts, allowing for a not-so-higher CoG compared to double wishbone.] I have come to a solution using something between UWAM and ADFA concept, namely a single piece lower A-arm/beam and two conventional upper A-Arms, mounting on the beam as close to centerline as possible (for minimum camber compliance). With that configuration, you have constant road camber during pitch/heave/roll, but now I'm worried about single wheel bump... All in all, I do not know if it's worth the risk (and the higher CoG/unsprung) compared to the traditional solution we use for years now....

Warpspeed

01-22-2012, 07:12 PM

Quite a few different ways to skin a cat.

How about a pair of stiff rear trailing arms to control toe, and a rear truss to tie the tops and bottoms of the rear hub carriers together.
With the lateral location device of your choice.

A bit lighter than a monster DeDion beam, and should be potentially a lot stiffer.

Just another species of twist axle.
Dare to be different.

mech5496

01-23-2012, 02:13 AM

Tony, what you mean is something like this?

http://picasaweb.google.com/ma...#5339857270245922882 (http://picasaweb.google.com/mattales/2009CalPolyFSAEManufacturing?fgl=true&fgl=true&pli=1#5339857270245922882)

If I get it right, yes, but removing the rear live axle and interconnecting the hubs by something else. (another tube on the upper point like the one on the bottom points?). IMO this is only applicable in the rear suspension (you have a chassis in between at the front), and I wouldn't do that on the rear either... You have a perfectly stiff tube (the live axle) to interconnect the "hubs", why adding extra weight and complexity? Unless you want to run a chassis mounted diff instead... Your solution interpreted for the front suspension is what ADFA uses! There are almost limitless ways of building what essentially is a beam axle....

------------------------------------------------

On with my thoughts on Z's approach... Wheel pods for decreased drag are a great idea, but not sure if still applicable after UWAM being unable to use theirs on the FSAE-A 2011.

Wheels: I completely agree with you on the wheel choice, and basically this was our reasoning in choosing 10"; significant decrease in weight (unsprung), decreased rotational inertia of the wheel assembly, smaller complance due to smaller lever arm meaning even lower weight on both wheel and upright. Screw fancy CF 13" wheels; our wheel assembly with 8" wide tires weighed just shy of 4kg, we are trying to get below that figure for 2012. The main issue with 8" diameter wheels is neither packaging (we can fit 200mm rotors to our 10"s) nor tire data (eitherway they are not available for modern 10" Hoosier R25B tires yet). It is the lack of sticky 8" tires... I cannot imagine any commercially available tiire to be anywere close to grip levels as modern FSAE tires. So 10" for me (6" wide on the front, 8" on the rear if you worry about temperature distribution due to weight distribution).

Steering: I love the Pitman arm solution. Actually I've been looking into it after seeing in UWAM's car in 2008. By far the easiest way to achieve high Ackerman geometry (impossible with R&P), cut off a kg or two, and spare some 600 euros. I still have my doubts about the bevel gearbox; mainly because of backlash issues. Back in 2007 (my first year with the team) we were forced to use one, and it was completely rubbish, both in terms of backlash and weight. Maybe it was the fact that we used the fisrt off-the-shelf industrial gearbox we found...

Aero/kinematics: The main reasoning behind using such a suspension is (although IMHO it should not be) the possibility of "live aero". I think that this is also possible with a "conventional" double a-arm layout. The main gain here is increased grip during accel/braking. A double wishbone suspension can be designed for "optimizing" wheel camber during roll (FAP's close to CoG or infinitely stiff ARB's or high amounts of camber gain during bump, etc) and thus decreasing longtitudinal acceleration capability OR for "optimal" camber during longtitudinal accelerations (parallel A-arms or huge anti-dive/squat), and thus decreasing lateral acceleration capability. (NOTE: All of the above "solutions" to the "optimal" wheel camber have their side-effects). By using a beam axle suspension, wheels maintain their "optimal" camber during accel/braking (pitch) AND roll. In single wheel bump, IMO both solutions are equally bad regarding wheel cambers (unless you use parallel wishbones); in the axle solution though, the wheel loads are coupled, making things, ehm, more interesting.

Overall: Aero is equally feasible either in a wishbone on a beam axle solution, although in the latter the undertray could be lighter (using beams as aero-load bearing structures/part of the undertray), so I'll leave it outside. Pros.: Easier manufacturing (less pick-ups), possibility for lighter chassis, softer suspension setup, constant wheel cambers (increased accel./decel.) Cons.: Reaction of all suspension forces in 2 points per axle (need to be bulky->heavy), higher CoG by a fair amount, "coupled effect" on bump per axis, higher unsprung mass. Need to try a lapsim with the two main parameters (increased lontidual acceleration/higher CoG) and see what effect those have on laptimes.... Any thoughts?

EDIT: Look what I found on facebook...
http://a1.sphotos.ak.fbcdn.net...921323_4646679_n.jpg (http://a1.sphotos.ak.fbcdn.net/hphotos-ak-snc4/163607_1724953797107_1036247896_31921323_4646679_n .jpg)
Interesting, huh?! Not much like the one described here, but much resemblance in wheel choice (Z?), although 6" here...

Warpspeed

01-23-2012, 01:24 PM

Harry,

Here is a hugely massive example of a Lotus97 trailing arm SLA rear suspension.

http://www.theriens.com/lotus/97rightr.jpg

This is going to be quite good for control of toe and rear bump steer.

Now suppose you removed the SLA links and connected the four ball joints on the hub carriers together via a simple X frame.
That would hold the hub carriers parallel, equidistant, and vertical to the track, while still allowing some independence of wheel movement.

This has probably been done before somewhere (?) but If it has, I have never sen it.

mech5496

01-23-2012, 04:40 PM

I see...again IMO not applicable on the front. If you modify the design to allow steering, again you have not enough space, due to the fact that you occupy a significant space in height -the x-brace will have to be as high (approximately) as the upright... Unless you have a front axle forward of the bulkhead.

Warpspeed

01-23-2012, 05:37 PM

At the rear, the trailing arms could extend back past the axle centreline so that the X member cleared the diff and final drive. All fairly simple, just another form of twist axle.

It is all a lot more difficult to do at the front, because of a space conflict between anything that directly links the front wheels together, and the chassis.

With wide flat tires, and a smooth flat track, a light beam axle may be surprisingly effective.

01-23-2012, 08:01 PM

Harry,

At last, hate mail! Thanks, I must be making progress. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Regarding:

WHEEL PODS. The banning of UWA's wheel pods was a disgrace! Supposedly "against the spirit" of open wheelers? What crap. Look at the latest Indy cars. They are thoroughly "podded" at rear for reasons of safety and fuel efficiency. Welcome, FSAE, to the typically brain-dead officialdom of motorsport that immediately bans anything useful. (Mumble, mumble, "where in the rulebook???", mumble, mumble, "should be flogged!"... http://fsae.com/groupee_common/emoticons/icon_rolleyes.gif)
~~~o0o~~~

8" TYRES. This is a bit off-topic, but as agreed there is an advantage to smaller wheels. I guess the first team that finds out how big this advantage is, will be the first team that tries it (hint: off-road quad racing tyres for mud/clay can be very soft?).
~~~o0o~~~

STEERING. Production car R&Ps minimize backlash by using a spring loaded pad to push the "floating" end of the rack against the pinion. This increases friction (ie. between pad and rack), and is more difficult to do with a central pinion because of "rack-rattle" at its ends.

Backlash is easily minimized with bevel gears by allowing the "crown" gear and its shaft to slide vertically in its housing (ie. in cylindrical bronze bushes or needle bearings). A spring loaded pad pushes down on the centre of this shaft preloading the crown gear against the pinion with minimal frictional torque (because forces are at small radius).
~~~o0o~~~

CG HEIGHT & AERO. The major masses are the driver and engine/drivetrain. These can be mounted as low as possible, whilst also using a live aero-undertray, by cutting a hole in the undertray roughly the size of the rear half of the fuselage. The low rear fuselage floor, with low mounted driver's bum and engine, pokes down through this hole. A flexible membrane seals the gap between low rear floor and undertray to prevent negative pressure loss.

So, CG as low as possible.
~~~o0o~~~

CG HEIGHT & STRUCTURE. The Twin-Beam layout has, without a doubt, a lower CG than any current FSAE wishbone layout. Most of the structure (beams, BJs, P&Ss, chassis mounts for BJ/P&S) is as low as physically possible, ie. within 10cm of ground level! Only the wheel-hubs/bearings are at a "high" level (this is an advantage of smaller diameter wheels).

(Voice rising, face getting redder.) Not only do wishbone layouts have roughly half their structure significantly above axle height (ie. upper wishbone and upper half of upright), they also have a lot of heavy chassis structure up high (count number of chassis tubes going to upper wishbone mounts!). And then some genius decides to use pushrods leading to rockers and spring-dampers mounted as high as physically possible! On top of nose or engine!! Why???!!!

(Entering Full-Rant Mode.) What we have here is a lot of unimaginative drones who refuse to think rationally about their problem (eg. by considering CG height). They mindlessly copy pre-existing and bad designs, but are quite happy to pour their energies into long-winded but nonsensical justifications of their "optimisations"! "Oh, it gives us better access to the dampers..."

(Calming down, slowly.) The argument for wishbones over beams is similar to (actually somewhat worse than) the argument for bi-planes versus mono-planes in aeronautics. Sure bi-plane structures might, to a simpleton, be lighter and stiffer than mono-planes, but that doesn't make them better overall.

The major forces on an FSAE car go from ground-level wheelprints to low-as-possible chassis CG, so there are good structural reasons to position the members carrying these forces also low. A low CG is an added benefit.
~~~o0o~~~

CG HEIGHT & SUSPENSION MODES. I posted extensively about "coupled" suspension back in 2005, for example here (http://fsae.com/eve/forums/a/tpc/f/125607348/m/10310835721?r=32410118721#32410118721), but clearly this is a step too far for most FSAEers. (Incidentally, back in March 2000 Racecar Engineering I asked "How long will it be before racecar designers of the 21st century catch up to the steam tractor designers of the 19th century, and start designing racecars with a soft twist mode?" I note that 12 years later there is some talk about front-to-rear interconnected dampers in some high level race series. Geez, the Citroen 2CV, "the world's cheapest car", had better in 1939...)

Anyway, the relevant point here is that FSAE RACETRACKS HAVE NO BUMPS! Except for the rules, FSAE could be won with no suspension at all. Nevertheless, a bit of damped movement, say +/- 5mm, is useful in suppressing "bouncing on the tyres". And the right sort of soft Twist (=warp) mode makes it easier to have predictable LLTD for good handling, especially over slightly undulating ground.

The bottom line is that suspension Bounce (=heave) and Pitch modes only need very short travel. This is easily done with beams by having short travel (+/- 5mm) bump rubbers fitted at the mid-beam position. With these the chassis can be run very low with no scraping, so low CG, but there can still be plenty of wheel travel in Roll and Twist modes to keep the scrutineers happy. The soft Roll mode is, of course, no problem because no camber change, and the undertray doesn't scrape because it is beam mounted.

Z

Warpspeed

01-23-2012, 08:33 PM

Hehehe, I can just imagine the evil FASE organisers reading that "there are no bumps"....

And planning the next event at a BMX track.

01-23-2012, 09:14 PM

Harry,

The HyperProRacer in your link has a live spool axle at rear, and lateral swing arms at front. It is an attempt to make a safer superkart by providing much better driver protection (roll cage, belts, etc.). I talked to the builders at a recent autoshow - nice guys and I hope they have success with it.
~~~o0o~~~

Tony,

The type of twist-beam you describe is similar to that used on 1930's Mercedes GP cars. The beam must be torsionally flexible and have some means of lateral constraint (P&S on the M-B cars).

If, as you described, and on the M-B cars, the rear beam is behind the diff, then it has greater than 100% camber compensation. That is, during outward body roll the wheels lean into the corner.

Other variations have appeared over the years, such as an interconnected trailing-arm rear suspension on Volvo station wagons of about 20 years ago.

Z

PS. Back in 2005 I was suggesting that the organisers should deliberately put bumps on the tracks. They could then delete the mandatory +/- 1" suspension rule, and leave the decision up to the teams (good suspension would win). It will never happen.

PatClarke

01-24-2012, 02:03 AM

Quote Z 'The banning of UWA's wheel pods was a disgrace'!

Erik, the UWA pods were never banned!
Teams know that turbulence created by a rotating wheel creats drag and every year the rules committee get several enquiries about wheel pods, mudguards or similar.
The response is consistant. It has been determined that an 'open wheel' car is one where the entire wheel is visible in plan view.

The UWA team were asked to trim the pods a little so the wheels were not covered. They decided to remove the pods instead.

Pat

mech5496

01-24-2012, 03:06 AM

Originally posted by Z:
Anyway, the relevant point here is that FSAE RACETRACKS HAVE NO BUMPS!
Z

Go tell that to the FSG organisers... There are two points at the track where some cars catch some air for split seconds, making us feel a bot like WRC drivers (OK, exaggerating a bit but you get the point). Agreed that in a perfectly flat surface, double wishbones are no match for beam axles though... IMO beams could be lighter that double wishbones if polished up a bit, maybe a little heavier as actual structures but leading to a decreased overall weight (fewer mounting points -> "fewer" chassis needed to facilitate load transfers etc)

NickFavazzo

01-24-2012, 09:45 AM

A Little off topic but in reply to Pat, We were asked to modify or remove the wheel pods, we followed the rule to the letter it was written and determined that there are many teams who also break this rule, we did get a rule clarification (and upon checking, we were the WA team to speak to the rules committee about this), We as a team decided to design to every other definition of an open wheeler as we were under the impression that if we had to remove our conflicting part, other teams would also (ie rear wings pods etc) and it would not be done. We didn't jump up and down about it because it wasn't worth it, we didn't cut them up as they were part of a students ongoing work/thesis.

I personally don't see the problem in allowing/disallowing them, but I think if a rule is enforced it needs to be followed by all.

back on topic here;

@mech5496, we use a custom gearbox with a neat little aluminium casting after a few years of refinement it has been quite good to us, although at 2011 comp we had a few issues they can be prevented by finishing a job properly...

@Z the low mounting of the beam I imagine would be similar to the flexures we currently use, helps bring the CoM down, we already have the drivers "bumsert" lower than the flexure pickups (I think it may be the lowest part of the sprung..but don't quite me on that)

Bumps on track would be a fun and interesting experiment, similar to the wet skidpan...

(and we're still trying to find where you are hiding in our tech meetings Z.)

Zac

01-24-2012, 10:29 AM

8" TYRES. This is a bit off-topic, but as agreed there is an advantage to smaller wheels. I guess the first team that finds out how big this advantage is, will be the first team that tries it (hint: off-road quad racing tyres for mud/clay can be very soft?).

Is there a slick ATV race tire out there though? And will that be any lighter than a 10" or even a 13" FSAE tire?

All of the examples I've seen have been either very aggressive knobby patterns or at best something that looks like a traditional sprint car tire. In either case the loss of net footprint area and tread stiffness would be a disadvantage.

On top of that you're looking at heavier tread-caps and sidewalls (typical sports car tires are mono or dual-ply, an ATV tire is likely to have a 6 ply-rating) in general and are running a higher aspect ratio than what is currently seen on FSAE tires. I doubt you save any weight or inertia over a 10" or even a 13".

I'm not saying that a proper 8" tire couldn't be developed, just that I haven't seen anything that's close.

AxelRipper

01-24-2012, 10:57 AM

Originally posted by Zac:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">8" TYRES. This is a bit off-topic, but as agreed there is an advantage to smaller wheels. I guess the first team that finds out how big this advantage is, will be the first team that tries it (hint: off-road quad racing tyres for mud/clay can be very soft?).

Is there a slick ATV race tire out there though? And will that be any lighter than a 10" or even a 13" FSAE tire?

All of the examples I've seen have been either very aggressive knobby patterns or at best something that looks like a traditional sprint car tire. In either case the loss of net footprint area and tread stiffness would be a disadvantage.

On top of that you're looking at heavier tread-caps and sidewalls (typical sports car tires are mono or dual-ply, an ATV tire is likely to have a 6 ply-rating) in general and are running a higher aspect ratio than what is currently seen on FSAE tires. I doubt you save any weight or inertia over a 10" or even a 13".

I'm not saying that a proper 8" tire couldn't be developed, just that I haven't seen anything that's close. </div></BLOCKQUOTE>

I was looking around a while ago just to see if anyone had them. American Racing and Hoosier both make tires in 8" size for MiniCup cars. However, it looks like these tires are supposed to last a few races, or possibly even a season on those cars so the compounds are at the exact opposite end of the spectrum as FSAE tires (very hard instead of very soft).

Kirk Feldkamp

01-24-2012, 11:20 AM

Originally posted by AxelRipper:
American Racing and Hoosier both make tires in 8" size for MiniCup cars.

It's American Racer: http://www.americanraceronline...Track/mini-cups.html (http://www.americanraceronline.com/Asphalt-Track/mini-cups.html) They claim to have "softer" compounds.

Hoosier seems to only make that one very hard 8" MiniCup tire. http://www.hoosiertire.com/pdfs/speccat.pdf (page 5) Do we have any FSAE alums working at Hoosier that could convince them to do a run of R25B compound MiniCup tires?

What does it take to get new tires into the Tire Test Consortium queue? http://fsae.com/groupee_common/emoticons/icon_smile.gif

I'm sure to a lot of people using 8" wheels seems nuts. Perhaps as nuts as a 450 single seemed in 2005. Just because there hasn't been a simple, commercially available solution before doesn't mean it's not a smart approach to the FSAE problem!

mech5496

01-24-2012, 11:42 AM

Originally posted by Z:

The bottom line is that suspension Bounce (=heave) and Pitch modes only need very short travel. This is easily done with beams by having short travel (+/- 5mm) bump rubbers fitted at the mid-beam position. With these the chassis can be run very low with no scraping, so low CG, but there can still be plenty of wheel travel in Roll and Twist modes to keep the scrutineers happy. The soft Roll mode is, of course, no problem because no camber change, and the undertray doesn't scrape because it is beam mounted.

Z

Has anyone checked HOW the "minimum suspension travel" rule is measured? Usually the marshals push the car down with their foot (so suspension operates in bump) and visually check it. A solution such as the one described by Z above could not be acceptable then...Of course you could use scrutineering-specific rubber bumps and replace them for the race (suspension springs CAN be exchanged at any time and this is essentially a suspension "spring", but I do not know how the scrutinneers will feel about it; it is a bad way to get DQ. Anyone checked it with the rules yet? Instead of a rubber "spring" you could use a horizontally mounted spring/damper, actuated by a peg n slot driven bellcrank, thus having an adjustable (and dampened) heave/pitch spring...

Seriously, topics like this ARE the reason why I love the fsae forums. I would really like to have this convesation up personal with all of you, something like a design meeting with a drawing board somewhere in the room, but I'm afraid we would be discussing for days.... http://fsae.com/groupee_common/emoticons/icon_biggrin.gif

Kirk Feldkamp

01-24-2012, 02:51 PM

Have you talked to American Racer? If so, what information have you gotten about their MiniCup tires?

Splitting a 60 tire production run between a few teams wouldn't be that bad of a deal to put together. 15 sets is nothing! I think the current Hoosier MiniCup tires are only $60 each!!! I'm sure they've seen how much demand there is worldwide from FSAE, considering they seem to be out of 13" FSAE tires at least once a year. The only way to make something like this happen is to convince a company that it makes business ($$$) sense. The "passion project" approach will never work.

Kirk Feldkamp

01-24-2012, 03:52 PM

What were the other 8" asphalt racing tire manufacturers that you identified? My cursory search a few months back only found the two we've been talking about.

[sorry about the major thread hijack]

NickFavazzo

01-24-2012, 07:06 PM

I dont think the rules specify how exactly they are measured, you may need a clarification on this, putting different springs in to pass shouldnt be necessary, what if you run mega stiff springs, you can have the required trvel, but you don't use it, it would need to be proven another way..

Dash

01-24-2012, 07:47 PM

We ran into a design issue with our car two years ago, but didn't figure it out until about a week or two before competition. The kinematics our rear suspension made it incredibly stiff even with the softest springs we had ( its my fault, and I'll admit that ). Anyway, we definitely had the capability to move 2" kinematically, but in reality it only moved about 0.5" when you jumped hard on the rear end of the frame. Judges looked at me skeptically, but passed us through with no real issue.

mech5496

01-25-2012, 09:27 AM

Travel was always "measured" on our cars that way; a marshall jumping up and down on chassis...that's why I was wondering about the solution Z proposed.

Z, I was reading your thoughts on "damper histograms" thread, and I have a question... In a beam suspension like the one described here, why would anyone want any stiff mode? You could limit chassis roll by using stops, but again, why limiting pitch and roll? Besides geometric weight transfer caused by movement of the CoG while pitching/rolling(which isn't that much), I cannot think of anything obvious... Another thing is that by using beams, all the lateral forces are transferred to the chassis via 2 points for each axle (plus two for the dampers), so a fairly stiff bottom is all you need. The rest of the chassis could be really flimsy (besides crash structures) with no problems. Plus you can achieve a soft twist mode (while having harder pitch and roll modes) by making a chassis torsionally flexible....

SoonerJack

01-25-2012, 12:14 PM

It looks like a great idea.

But I'm not so sure about the aerodynamics.

So far we haven't seen any great aero-packages without wings that helped a lot.

e.g. Munich's car didn't seem faster through the undertray compared to a similar design from Stuttgart.

One thing I'm curious about is the "live" aero.

I couldn't find anything in all the aerodynamic papers online that said that live aero is so much better than a normal mounted aerodynamic.

I just read that the suspension can be softer but no other significant bonuses.

I guess it's good to have the force directly on the wheels but is that enough to change the whole layout of a car?

The design of the different wheel sizes is interessting. Maryland did it with 13inch and 10inch. Maybe this would help the concept too. The new 13inch Goodyear's should be pretty soft...

Cheers,

Jack

mech5496

01-25-2012, 12:27 PM

Jack,

Besides running softer suspension setup, which aids mechanical grip due to reduced tire load variation, and more direct aero load paths, it also has the advantage of being able to run the sides of the undertray extremely low, as its distance relative to the wheels is maintained. This in turn gives extremely good seal to the negative pressure developed by an undertray, and lots of downforce due to ground effect (remember sliding skirts or even better "double chassis" Lotus F1 cars?). On the negative side, live aero means added unsprung weight... IMO the main point here is not aero, as live undertrays are possible with double wishbone suspensions too, but purely (possible) kinematic/loadpath gains....

SoonerJack

01-25-2012, 01:29 PM

Thank you for your explanations.

I was just curious about this topic in the first place and thought it might be a good point to register and ask it right now http://fsae.com/groupee_common/emoticons/icon_smile.gif

I read Pat's column and saw that he sad ECU's aero wasn't that good as Monash's because it was chassis mounted not unsprung.

I can't see the huge advantage at the front wing for instance if it's mounted to the bellcranks or something like that..

Thanks again!

Rex Chan

01-25-2012, 07:40 PM

SoonerJack: I read in an older wings thread (called WINGS!), that sprung aero = stiffer springs = less mechanical grip at slow speeds (where downforce is less), so a slight problem. Unsprung aero would not have this issue.

If you've done some reading/research into direct aero, would you like to share on this thread? (or to my email/fb). In my quick Google searches, there wasn't much info. But I hadn't looked into SAE papers yet. The problem is that FSAE is one of the few classes of motorsport that allows direct aero, so not many people care about it.

01-25-2012, 08:25 PM

Harry,

You ask, "In a beam suspension like the one described here, why would anyone want any stiff mode?"

For circuit racing a lowest possible CG is beneficial. So it is good to have all the heavy bits close to the ground at all times (so not bouncing upwards over crests, etc.). Formula cars have most of the heavy bits spread along the centreline of the car, so it is beneficial to have stiff heave and pitch modes that "lock" the centreline down low (with, say, +/- 5mm of highly damped soft motion to suppress bouncing on the tyres). A saloon car also needs a stiff roll mode (with damped +/- 5mm) so the sides of the car can be low, but don't scrape during cornering.

The Z-bar layout in the Damper Histogram thread allows a completely soft twist mode (which gives consistent LLTD over uneven ground), while stiffening up heave and pitch, or heave and roll, or all three, as needed.
~~~o0o~~~

You say, "you can achieve a soft twist mode (while having harder pitch and roll modes) by making a chassis torsionally flexible...."

And, indeed, this was the way it was done in the early days of motorsport. Prior to about 1930 the production chassis were deliberately softened when they went racing, by removal of crossmembers. However, this required the right sort of engine mounts, etc., to get the right LLTD (eg. 2 bellhousing mounts at mid-chassis, and only 1 engine nose mount). Also the torsional chassis spring was undamped, except for "inertial damping" from loosely mounted fuel tank, driver, etc. A stiff chassis with damped twist-soft suspension works better.
~~~~~~~~~~~~~~o0o~~~~~~~~~~~~~~~

SoonerJack,

You say, "I couldn't find anything in all the aerodynamic papers online that said that live aero is so much better than a normal mounted aerodynamic. ... I just read that the suspension can be softer but no other significant bonuses."

Three main points here:

1. Live aero is usually banned as soon as anyone uses it (it is too good), so you are not going to find many papers about it.

2. Sprung aero requires stiff springs to minimize ride height changes at different speeds ('cos different DF). Given the "always low CG" argument above this isn't such a big problem because stiff "third springs", which control heave and pitch, can do both jobs. In fact, most such cars have a somewhat "active aero" in that the rear "third spring" is softer than the front, so the car's rake changes from tail-up at low speed (for more DF), to horizontal at high speed.

Nevertheless, these third springs are rarely properly damped, so the car "porpoises". So, in F1, Renault fitted front and rear inertial dampers of a similar type to those used on "the world's cheapest car" (Citroen 2CV), which cheaply fixed the problem. So the moron Max Mosely banned them, initially on grounds of "cost and safety" (!!!), and later because "they are movable aerodynamic devices"!!!!! Nowadays the cars have less effective, and more expensive, "inerters". Ah, progress at the cutting edge.... http://fsae.com/groupee_common/emoticons/icon_rolleyes.gif

3. The beams in the sketch make for easy mounting of the aero panels. Just attach wherever and however is most convenient. If attaching to bellcranks as you suggested, then several balljoint ended pull/pushrods, plus possibly more linkages, are required in just the right places...
~~~~~~~~~~~~~~~o0o~~~~~~~~~~~~~~~~~~

More miscellaneous ramblings:
~~~o0o~~~

8" TYRES. The HyperProRacer (http://www.hyperracer.com/hyper-racer/proracer/faq.html) mentioned earlier is one of the voices in the back of my head saying "13 inch is waaaay too big!". This link (http://www.hyperracer.com/hyper-racer/pro-news/news15_march11/news15_march.html) gives an interesting comparison of HPR with some other racecars, including an FSAE car. Maybe someone in Melbourne knows which FSAE car that was?

Anyway, the HPR is like a higher speed version of FSAE, but built to more liberal rules. It is 185kg (sturdy roll cage), Yamaha 450 single, spool-beam rear axle, good for 200+kph, and seems to do just fine on 6" go-kart tyres. Their rationale for the 6"s is to reduce running costs, which makes sense.

Even so, if I was starting today and had to be at FSAE comp in December, I would be designing for 10"s all round (wide rears, narrow fronts). Meanwhile, I'd put 8" rims on last year's car and go testing any 8" tyres I could find. Less is more! http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

ENGINE. The engine in the Twin-Beam sketch was supposed to be a Royal Enfield, based on info I found on various websites. It won't work as shown. I got parts of the old and new models mixed up...

But, funnily enough, the day after I posted the sketch I was tyre-kicking in a quad bike shop and guess what's sitting in the corner? Three old British bikes - a Norton twin, Matchless 500 single, and a Royal Enfield 500! (Old Z had a Matchless 500 engine that went in every "fun" vehicle he dreamt up. I clearly remember it NOT being a great success in the canoe (I was about 10). The first time the throttle was cracked open the propellor spun maybe five times one way, and the canoe did a half turn the other!)

So I had a good look at the RE, and I like it! If lots of REs were available, at the right price, then I would certainly consider one. The long term goal would be a turbo or supercharger (with standard CR~7:1), crank driven clutch and dog-neutral, then direct chain final drive ~5:1 (ie. ditch the gearbox).
~~~o0o~~~

WHEEL PODS. Pat, if there's nothing against it in the rulebook, then IT IS LEGAL. The moment officials start interpreting the rules according to their whims and fancies, honest law abiding citizens start disappearing in the middle of the night. Well, maybe not that quickly, but that's how it starts.

Z

mech5496

01-26-2012, 02:03 AM

Originally posted by Z:
Harry,

You ask, "In a beam suspension like the one described here, why would anyone want any stiff mode?"

For circuit racing a lowest possible CG is beneficial. So it is good to have all the heavy bits close to the ground at all times (so not bouncing upwards over crests, etc.). Formula cars have most of the heavy bits spread along the centreline of the car, so it is beneficial to have stiff heave and pitch modes that "lock" the centreline down low (with, say, +/- 5mm of highly damped soft motion to suppress bouncing on the tyres)....

...You say, "you can achieve a soft twist mode (while having harder pitch and roll modes) by making a chassis torsionally flexible...."

And, indeed, this was the way it was done in the early days of motorsport. Prior to about 1930 the production chassis were deliberately softened when they went racing, by removal of crossmembers. However, this required the right sort of engine mounts, etc., to get the right LLTD (eg. 2 bellhousing mounts at mid-chassis, and only 1 engine nose mount). Also the torsional chassis spring was undamped, except for "inertial damping" from loosely mounted fuel tank, driver, etc. A stiff chassis with damped twist-soft suspension works better....
Z

Thanks for the input Z! So, to my understanding you want a fairly stiff pitch/heave mode... You can achieve that with a heave/pitch spring and damper for each beam, mounted under the chassis and activated via bellcrank through the suspension vertical movement (bellcrank mounts at the peg n' slot position, so not activated during roll) and using very soft springs/dampers for all other modes. I still think a "soft" chassis as a good idea though, although "undampened", mainly because of the need of only a few mounting points as explained in my earlier post; you can just use the chassis as a part holder, cutting off significant weight. Or you can just use a longitudinal z-bar configuration!

Rex Chan

01-26-2012, 02:21 AM

Z: I know that both Swinburne Petrol 2010 and RMIT were at the Top Gear. I fb'd Stefan Millard, and it says he's at RMIT.

JWard

01-26-2012, 08:11 AM

Re adding this post back in as it's not so off topic i guess:

That HPR is a mean little machine! I do have to ask why they wouldn't use a 2T in it instead of that thumper. Is it just the bad rep the little 2T's have? Surely you could find a more powerful, and lighter 2T engine, that costs half as much for a full rebuild?

Only con i see is there being less engine options for electric start in 2T compared to 4T, and of course the stigma that comes along with them.

01-27-2012, 04:43 AM

JWard,

Your post IS on topic! (Put it back. http://fsae.com/groupee_common/emoticons/icon_smile.gif) The HPR has a beam rear axle so I think it is in keeping with Oz-Olly's original theme. It is also KISS, which was Olly's rationale for beams.

Unfortunately, I can't remember exactly how this rear beam is located, and haven't been able to find a good picture on the HPR website. FWIW, I think it has three longitudinal links (two lower, one upper central) and a panhard rod for lateral location. These connect between chassis and the oval shaped subframe (visible in some pics) that carries the spool axle. A single central monoshock S-D is used together with a fairly stiff ARB (to unload the inner wheel and thus reduce spool-induced U-S). If anyone knows better, please advise. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Regarding the four-stroke engine, I guess yes, it is there because of its "greenlyness" (and its sequential 'box).

Z

rjwoods77

01-29-2012, 11:10 PM

Z,

I like the design concept you proposed. Very interesting direction. I have some comments on your setup and further expansion of my double beam idea but want to ask a couple questions to pick your brain before I continue with those.

It seems that aero balance was the reasoning behind splitting the aero into front and rear underwings. I know that this was an issue with Herbs Adams wing car that they didn't have time/money to develop to its potential.

http://www.oldracingcars.com/I...America1983-1000.jpg (http://www.oldracingcars.com/Images/snyder/Escort-WaltBohren-RoadAmerica1983-1000.jpg)

http://i114.photobucket.com/al...t-1983-06-05-bg4.jpg (http://i114.photobucket.com/albums/n251/xxThe_Stickmanxx/Mosport-1983-06-05-bg4.jpg)

http://www.racingsportscars.co...0.jpg?dir=photo/1983 (http://www.racingsportscars.com/wm/photo/1983/WM_Mosport-1983-06-05-010.jpg?dir=photo/1983)

http://www.racingsportscars.co...aunton&wi=&mode=Null (http://www.racingsportscars.com/wm/photo/1983/WM_Lime_Rock-1983-07-04-010.jpg?dir=photo/1983&img=Lime_Rock-1983-07-04-010.jpg&txt=Mark%20Staunton&wi=&mode=Null)

Also minimizing individual movements of the suspension modes (i.e. interconnected suspension) to keep the aero consistent in general but especially if it was a single aero element connected to both beams as to keep from wraping/breaking said aero element in whatever form is most efficient.

From the lengthy descriptions of you "z-bar" concept topic it would seem to be a great answer to minimizing the suspension mode movements enough to allow a single piece aero element to survive. Could you discuss the application of an interconnected suspension in terms of benefiting a pure aero performance driven design.

Also in from that Z-bar concept discussion:

http://i16.photobucket.com/alb...ll/ZBARFSAEsmall.jpg (http://i16.photobucket.com/albums/b33/john-bucknell/ZBARFSAEsmall.jpg)

In my concept I wanted to use a front and rear mumford link. I can arrange the mumfrod rockers in such a way to connect a pair of torsion z bars front to rear by running the bars right under the drivers ass. This would make for a hybrid of the two diagrams that you drew up. My question to that is would the beam axles then act as an theoretically infinitely stiff "end-pair" leaf springs. Please discuss what and how that would would work if it did.

You claim that the dampening requirements for a "z-bar" suspension would only need to be in the slow speed range. F500 cars are mandated by rules to not run hydraulic dampers of any sorts. They are forced to run polymer pucks of dimensions set by the rules. Per my comparison of the brutally low tech F500 being at every disadvantage to a modern RIT FSAE car in the engine/cvt topic except transmission as I so espoused, and how razor thin close in actual track performance it was to RIT, it seems that non hydraulic damper has some merit. If an interconnected double beam could utilize polymer dampers it would easily cut 5000 dollars off the the cost report of a car to further push this concept path. Please comment on this.

http://novakar.com/

http://novakar.com/images/features_4.jpg

http://novakar.com/images/features_6.jpg

http://novakar.com/images/features_7.jpg

http://www.formula500.org/view...8b5583e47861cfdc2427 (http://www.formula500.org/viewtopic.php?p=25799&highlight=&sid=c17c2f55094f8b5583e47861cfdc2427)

http://sports.racer.net/chassi...vakar/elastomers.htm (http://sports.racer.net/chassis/novakar/elastomers.htm)

Also with my love affair of F500 cars I should note that in the SCCA rule book for their class they have rules that discuss how far up the front fairing pods are allowed to come to the top of the tire as to keep the car an open wheel car and not a closed body car. Since much of the FSAE rulebook looks to be copied straight from the SCCA rulebook I think the judges may end up using the same F500 rule in the future to avoid conflicts that UWA brought up.

rjwoods77

01-30-2012, 06:08 AM

A couple of addendums to the above post...

Z,

Could the A/B ratio in such a scheme I described be somehow used to balance front to rear aero forces conducted into the unsrpung mass through that interconnection?

The "F500 wheelpod" rule I mentioned in Rule 9.1.1.E.9.

http://cms.scca.com/documents/...updated%20August.pdf (http://cms.scca.com/documents/2011%20Tech/GCR-%20updated%20August.pdf)

I would like to hear the rational as to why this has to be an open wheel format and the purpose behind it. It seems that there should be freedom to decide if you want to pursue that or not. Allowing a closed body car would probably increase the finishing rate of cars just from not taking cones to fragile pieces. Teams should be allowed to justify the weight and expense of doing it versus not. CanAm in its weaker later series was Formula Atlantic tubs with aero bodies on them which the current IRL cars are practically doing now so if the intent is for post baccalaureate jobs then it would seem the current way to go it to allow such things.

http://www.electricdreams.com/...age/IMG_0535-600.jpg (http://www.electricdreams.com/Shop/myfiles/image/IMG_0535-600.jpg)

rrobb

01-30-2012, 06:23 AM

I would like to hear the rational as to why this has to be an open wheel format and the purpose behind it.

Fashion.

rjwoods77

01-30-2012, 06:37 AM

Well if it is fashion then we need to up our game to something along the lines of the Red Bull X2010 or the Camparo F1. Seems that when F1 engineers are asked if they had a clean sheet what would they do they say open wheel F1 car with fairings that make it not so open wheel.

http://en.wikipedia.org/wiki/Red_Bull_X2010

http://en.wikipedia.org/wiki/Caparo_T1

mech5496

01-30-2012, 08:42 AM

Rob Woods is back! Too many posts on one of your favorite topics and no reply in a week or so- I was just getting worried... F500's are so neat small and simple machines, that could make a hell of a "beginners car" in FSAE. (adopted to the rulebook) The only thing I doubt of is the CVT, and I doubt because I have never dealt with one, so in my mind they are just heavy, complicated, hard to work things that make your engine sound funny... http://fsae.com/groupee_common/emoticons/icon_biggrin.gif

rjwoods77

01-30-2012, 09:10 AM

I was out of town and busy after that. Check out this post and videos.

http://fsae.com/eve/forums/a/t...20489051#51220489051 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/824105905?r=51220489051#51220489051)

A F500 has a worse weight to power ratio, no hydraulic dampers only polymer pucks for springs AND dampening, 20 inches more minimum wheelbase, not allowed to run wings or tunnels so only really a diffuser and a 800lbs minimum weight and it ran within a couple tenths of RIT FSAE most recent car. They are terribly handicapped in every respect to a modern competitive FSAE car yet run times that are very close to competing for a win. It's ALL in the CVT. Imagine a 60 inch wheelbase(instead of 80 inch), 350lbs car (instead of 800), with a weight to power ration of 7:1 (instead of 10:1), suspension designed to integrate aero (instead of mandated suspension design), with a well tuned CVT and you can see how that would make up for a couple tenths and much much more. If you could integrate a polymer puck instead of hydraulic damper with spring you can save 5000 on the cost report. Ditch the diff and halfshafts for a solid axle and save an additional 3000. You can easily win cost and sales presentation. The possibilites for a cheaper yet more effective win are there because otherwise you wont be able to out resource (talent,funding,knowledge,facilites,etc.)a team like Oregon unless you are an elite few (maybe 20 teams).

mech5496

01-30-2012, 09:33 AM

Well, if you notice, I have commented a great deal in the above posted thread....http://fsae.com/groupee_common/emoticons/icon_biggrin.gif I did not say CVT's are no good (in fact I like your approach a lot) but I have not dealt with them even a little, so it's "black magic" to me, so no CVT for my car (as stated in the "objectively" thread, single cylinder with 3 gear transmission). I think I'm waaaaay offtopic now though!

rjwoods77

01-30-2012, 09:38 AM

I noticed Harry. Threw that one out to tie back to the other topic for the uninitiated.. They aren't all that big and scary. They are less complicated that learning a fuel injection system and that is something all teams have to go through.

Kirk Feldkamp

01-30-2012, 09:49 AM

Originally posted by rjwoods77:
I would like to hear the rationale as to why this has to be an open wheel format and the purpose behind it.

If it's anything like the rule about the restrictor location within the system, it's still there because they think it's both "challenging" and "for safety." I'm sure if you pressed the issue that you would get an earful about how allowing for a closed body would make it too easy to generate downforce and how that would somehow lead to the cars becoming too dangerous to drive. I got the same argument when I pressed the restrictor location thing. There was also a heavy dose of "tradition" thrown in when I pressed the restrictor issue (which I also thought was silly). I'm sure they would also feel the "formula" part of Formula SAE would be gone if they weren't completely open wheel cars anymore.

As long as there is a clearly defined spec, I think it's fine to do whatever they want. I hope that the rules committee will quickly address the apparent hole in the "open wheel" issue. The rules say something to that effect in the beginning, but then there's no written definition of what that actually means!

-Kirk

mech5496

01-30-2012, 09:57 AM

I know shit about fuel injection too...http://fsae.com/groupee_common/emoticons/icon_biggrin.gif You are right that this is part of learning though. The thing is that despite my "fear for the unknown", all current FSAE engines have gearboxes; a CVT is more extra weight. So, possible solutions:
1) Replace gears with axles, bolt CVT; straightforward but heavy
2) Machine a new crankcase with no GB and built-in CVT; hard on resources, easier for singles (ball-bearing bottom end, simpler lubrication, split stock crankcase)
3) Electric drive; far from simple, a bit heavy compared to singles, expensive, but lots of torque, direct drive, more powerful than any 4-cyl.

In fact we are going no3. this year (and this was a decision of our faculty which in first did not like). I know that this seems way off the "simple" way, but I assure you that our car is gonna be simple as hell; direct drive from the motor (no reduction), no torque vectoring so a simple powertrain, components and mainly batteries placed for minimum Iz. The thing is that I have a hard time convincing our faculty to go "low tech" (beam axles), especially now that we spend a lot of money to go "high tech" (electric)... The good thing is that I like this way so much, that I have already made tons of research on my own. Actually I will have some of our team members do some quantitative analysis on gains/losses on a "beam axle" car, but after the exam period is over, which I will post around here for reference (unless we decide to go that way after all...:P)

rjwoods77

01-30-2012, 10:03 AM

Funny you mention electric. I was thinking the other day how easy it would be to make a double beam car with a pancake motor in each wheel.

mech5496

01-30-2012, 10:07 AM

(Just edited above post). OR wou could make a 4WD electric car, benefiting from aggresive regenerative braking to cut down battery pack size and use a well-tuned torque vectoring system to aid vehicle dynamics... I will have my eyes open for Delft this year, they go 4WD and they cut down their battery pack about 13kg (per my calculations based on data about their new batteries), so it might get interesting!

02-01-2012, 03:44 AM

Some comments regarding:

AERO
=====

(Rob Woods quote)
"It seems that aero balance was the reasoning behind splitting the aero into front and rear underwings."

Rob,

Yes, the Twin Beam-Wing is intended to give maximum aero performance for minimum effort, which includes minimum understanding of aero. This means easy set up of, and stable, F/R balance. Hence the two wings with their separately adjustable flaps and downforce. There will be some inevitable interactions between the two wings, but hopefully easily managed. More downforce is possible (from full undertray) but that requires better aero understanding, especially regarding F/R balance.

IMO the Herb Adams' Catamaran-Wing-Car in your links likely suffered from excessive pitch sensitivity of total DF and F/R balance. Even with rigid suspension and a perfectly flat road any slight nose-down pitching, say from tyre squash, brings the nose splitter closer to the road, which creates a thoroughly "unsteady" flow condition, which first increases front DF, but then the suction travels further back ('cos unsteady), etc., all of which is a killer for predictable handling.

Incidentally, the smooth upper-body surface possible with the catamaran layout is not necessary for good aero DF (although maybe a small advantage for low drag). A wing can only have a maximum Cp=+1 on its pressure surface, while Cp<-10 is possible on the suction surface. A similar 10:1 ratio applies over the whole surfaces. Bottom line is that the top surface of a racecar is of little importance to DF, because all the action is underneath (with some qualifications http://fsae.com/groupee_common/emoticons/icon_smile.gif). A good example is military aircraft that have a dog's breakfast of bombs, missiles, fuel tanks, etc., stored on the pressure side of the wing, but rarely anything on the suction side.
~~~o0o~~~

The best way to deal with aero balance problems is via the aero design (ie. as noted above, even rigid suspension and flat roads can't fix some problems).

Nevertheless, you ask,
"Also minimizing individual movements of the suspension modes (i.e. interconnected suspension) to keep the aero consistent in general but especially if it was a single aero element...
Could you discuss the application of an interconnected suspension in terms of benefiting a pure aero performance driven design."

Conceptually, the best way to have a single rigid aero element and keep it at a consistent height and attitude above the road surface, is as shown at top left and right of the Z-Bar sketch (redisplayed below). This is perhaps best understood in the top right sketch where the diamond shaped structure (say the aero element) is positioned relative to the uneven road surface such that its two side-points are at the average height of the two side-pairs of wheelprints, and its two end-points are at the average height of the two end-pairs (axle-pairs) of wheelprints.

Strictly speaking, these sketches are over-constrained. The diamond structure only needs three of its corners attached to the mid-points of three of the "balance-beams" (or "averaging-lines") that interconnect the four wheels. This three-point support (like a tripod) controls the diamond's heave, pitch, and roll motions. The symmetry of the four point support helps with understanding, and is better structurally (better distribution of loads).

Many different practical implementations are possible, but something close to the top left sketch, though with lightweight and rigid Side-Pair-Balance-Beams instead of centre-pivot-leafsprings, and BJs instead of coils at the beam-axle centres, would work. The SPBBs could do double duty as beam-axle locators. The chassis would then sit on four soft coil springs arranged in a diamond pattern on the centres of the 2xBeam-Axle+2xSPBB substructure.

http://i16.photobucket.com/albums/b33/john-bucknell/ZBARFSAEsmall.jpg

(RW quote)
"Could the A/B ratio in such a scheme I described be somehow used to balance front to rear aero forces conducted into the unsrpung mass through that interconnection?

No. The resultant of the aero pressures (ie. the aero "force screw") is always equal and opposite to the resultant of its reactions from the four wheelprints. Any contrived linkage between these "equal and opposite" forces cannot change the F/R aero balance. However, the linkage can change the distribution of the front DF acting on the two front wheels, and hence necessarily also alter the distribution of DF acting on the two rear wheels.

This is similar to a given cornering force always giving the same total Lateral Load Transfer from one side to the other, although the distribution of this LLT between front and rear wheels can be varied.
~~~~~~~~~~~o0o~~~~~~~~~~~

SUSPENSION LINKAGES
====================

(RW quote)
"In my concept I wanted to use a front and rear mumford link ... to connect a pair of torsion z bars front to rear"

That could be done, BUT (!!!) it is important to remember that the ends of the Z-bars MUST BE bent in opposite directions (otherwise it is a U-bar). So, picturing an end view of the linkages, if the front Mumford rockers are in their "normal" orientation, then the rear rockers MUST BE upside down. This puts one set of rockers quite low down, and may cause problems with ground clearance. Some draft layouts would be necessary to see if it can all be fitted into the space available.

Note that for FSAE or F500, the lever arms at the ends of the Z-bars only have to be about 2" long to give adequate suspension travel. In terms of stresses, the Z-torsion bar could be about 1/2" diameter 4140 steel (x wheelbase length), or even thinner if using proper spring steel.
~~~o0o~~~

(RW quote)
"would the beam axles then act as an theoretically infinitely stiff "end-pair" leaf springs"

No. The Mumford link rigidly constrains axle-lateral-motion relative to its virtual RC, while offering no resistance to axle-roll about that point, or axle-bounce (=axle-heave). So you would have to add a central coil spring, between beam and chassis, to control axle-bounce. It is possible to control axle-bounce with non-linearities of the Z-bar lever arms (eg. by giving them rising rates), but that might introduce other problems (eg. non-linear LLTD).
~~~~~~~~~~o0o~~~~~~~~~~~

DAMPING
========

(RW quote)
"F500 cars are mandated by rules to not run hydraulic dampers of any sorts. They are forced to run polymer pucks ...
If an interconnected double beam could utilize polymer dampers it would easily cut 5000 dollars off the the cost report ...
Please comment..."

The main point I was making on the "Damper Histograms" thread was that the importance of dampers is highly over-rated. Expensive (eg. 4-way adjustable) dampers are "crutches" for badly designed suspensions, namely suspensions that have "stupid" springing. A moderately clever suspension, such as one with interconnected springs, can manage with very little damping.

A most important thing to know about damping is that IF the springing has a low rate, then the damping also only needs to be low. So, Critical-Damping ~ Sqrt(M.K), and thus for given mass M, lower stiffness K means less damping needed.

Modern racecars need lots of damping because of excessively stiff springs, a consequence of stupid spring layout, and aero loads through the springs. With aero direct to the wheels, and interconnected springing (which allows different rates for the different modes), the dampers can be very soft. Even with normal "spring-at-each-corner", but with beam-axles, the springs can be soft ('cos no camber change), so again the damping can be low.

I would go so far as to say that the Twin Beam concept would run adequately with old-style friction dampers. That is, just a small amount of frictional stick-slip "Coulomb damping" would be enough to suppress any resonant bouncing. Cheap mountain bike dampers would be more than enough. Internal hysteresis from polymer pucks may also be enough (depending on compound?).

One way to get a feel for this is as follows. Drop a well pumped up ball (soccer, basketball, etc.) from chest height onto a smooth hard surface. It will bounce almost back into your hands, and then keep bouncing for a long time. This is a curious oscillating system (zero rate spring for a long time while in the air, then variable rate spring for the almost negligible time while on the ground), which has very little damping.

Now drop the ball onto a surface with a few millimetres of water, or loose sand, covering it. The ball barely gets off the ground on its first bounce, and stops shortly thereafter. It only takes a little bit of energy dissipation (ie. damping) to kill the oscillation. This damping doesn't have to be in linear proportion to velocity (as per usual analysis), or even continuous.
~~~~~~~~~~o0o~~~~~~~~~~

SOFT TWIST MODE
================

I stress that the big advantage of both the Z-bar and Twin Beam concepts is that they allow the car to have a soft twist (=warp) mode.

The Z-Bar allows a completely soft twist mode, regardless of other suspension characteristics. In the case of the Twin Beam, both twist and roll modes have equal stiffness, and likewise heave and pitch. However, the fact that body heave, pitch and roll have no effect on wheel camber means the car can be soft in all four modes. This means only soft dampers are required, and also the handling balance is less affected by twist in the roadway.

By comparison, conventional suspension cars (ie. wishbones with spring-at-each-corner) are screwed. They must have stiff springs and thus also dampers, or else they suffer too much body-roll and thus camber change, or they must have stiff ARBs and thus LLTD changes over uneven ground, etc., etc.....
~~~o0o~~~

(Harry quote)
"The thing is that I have a hard time convincing our faculty to go "low tech" (beam axles)...
Actually I will have some of our team members do some quantitative analysis on gains/losses on a "beam axle" car..."

Harry,

From a rational analysis, and for a relatively smooth track, beam-axles are far better than a conventional suspension (as explained above).

The main disadvantages of beams are;

1. Small increase in unsprung mass. Of negligible importance on smooth tracks, and countered by the softer springing possible (stiffly sprung cars have unsprung-mass ~ total-mass!). Even in off-road racing there are many fast beam-axle trucks that suggest this can not be too big a disadvantage.

2. Fashion! If beams weren't around forever, and someone just invented them, then they would be heralded as the greatest advance in circuit racing, ever! (Well, that's the typical hype. http://fsae.com/groupee_common/emoticons/icon_smile.gif) For example, there have been many complicated "camber compensating" wishbone style suspensions that have been patented over the years, but mostly they do nothing more than what a beam does.

I really think that the argument is similar to bi-planes vs mono-planes in aeronautics, with current suspension designers insisting that "Bi-planes are clearly far superior. So much stiffer, lighter, more adjustable, blah, blah, blah..."
~~~~~~~~~~o0o~~~~~~~~~~

AERO RULES & WHEEL PODS
=========================

If ever there was a good example of the failed education system, mainly from the neglect of teaching Euclid, then this is it.

The FSAE aero rules were either written by someone who deliberately wanted to leave open the option of arbitrarily banning any car the judges didn't like, or else they were written by a complete imbecile!

(Quote from Rules.)
"ARTICLE 12: AERODYNAMIC DEVICES
B12.1 Aero Dynamics and Ground Effects - General
All aerodynamic devices must satisfy the following requirements:
B12.2 Location
B12.2.1 In plan view, no part of any aerodynamic device ... blah, blah, blah..."

What (TF!!!) is an "aerodynamic device"??? Nowhere in the rules can I find any attempt to DEFINE this crucial term!

Almost everything on, or even in, the car might be considered an "aerodynamic device". The wheels, engine, roll hoop, car's nose, driver's nose, etc., all have some aerodynamic effect. In F1 Max Mosely banned Renault's inertial dampers (a simple mass-spring inside a sealed container!) because they were "movable aerodynamic devices".

Really, someone needs a thorough arse-kicking..... http://fsae.com/groupee_common/emoticons/icon_mad.gif

And the craziest part of all this is that wheel pods improve both safety and fuel efficiency!
~~~o0o~~~

Enough for now. I've got to cool down after that last one...

Z

Warpspeed

02-01-2012, 02:13 PM

The main disadvantages of beams are;

1. Small increase in unsprung mass. Of negligible importance on smooth tracks, and countered by the softer springing possible (stiffly sprung cars have unsprung-mass ~ total-mass!). Even in off-road racing there are many fast beam-axle trucks that suggest this can not be too big a disadvantage.

If you weigh the wheels, tires, hubs, hub carriers, brakes, and driveshafts, the suspension location links usually end up being a very small fraction of the total final unsprung weight.
A beam axle does not have to be an actual beam, just some suitably light and rigid structure to perform that function.
I am not convinced that the increased unsprung weight argument is as bad as most people assume.

Loz

02-01-2012, 02:53 PM

The ADFA car had a full weight audit of the car and all components. I cant remember the figures exactly but the front unsprung was approximately 29kg and the rear 28kg. In comparison to previous ADFA cars with A-arms front and rear, this was only marginally heavier. And in comparison to sprung vs unsprung ratios, it was comparable with many other well performing cars running independent systems.

BMEP

02-01-2012, 02:54 PM

Z,
You are crazy. I like you

rjwoods77

02-02-2012, 09:17 AM

Z,

Thank you for the response. I am going to go ahead and model up my ideas with some decent detail. I am going to start referring to the Z-bar mumford link as the "Zumford Link". As for a rough idea of what that will be I am looking at modeling non parallel torsion bars (ala packard suspension)where the bars are closer together in the front and fan out toward the back. The mumford rockers will be of normal layout which means the are elevated a little bit above the lowest crossmember of the main roll hoop and bulkhead. The opposed lever arms will then sit directly under the rockers and connect into the point where the pullrods (i.e lateral force members) of the axle attach to those rockers. So the front lever arms pivot on the torsion bars inside of where the two pullrods attach to the rockers whereas in the rear they are on the outside of the pullrod attacheents.

02-03-2012, 05:15 AM

Rob,

Re: Z-Bar/Mumford Links
=======================

Oops, I didn't think my above answer through properly (under Suspension Linkages). http://fsae.com/groupee_common/emoticons/icon_frown.gif It won't work as stated!

In fact, the Z-bars will only provide anti-heave springing, and only one bar is needed, though two will double the stiffness.

The problem is that the Mumford outer diagonal links only provide "lateral" control of the beam (wrt the virtual RC), and they don't allow individual "vertical" control of each side of the beam.

However, you can still use two longitudinal Z-bars as you explained (closer together at the front than rear) and just connect them to the beams with short links. (Edit: These links must be more vertical than the Mumford diagonal links!) These two Z-bars will control body heave and roll motions.

Furthemore, you can fit a spring between one Mumford rocker and the chassis (resisting rotation of the rocker), and that will control axle-bounce at that end of the car (ie. this would be instead of a separate coil spring at axle centre). Doing same at front and rear gives body heave and pitch control.

Edit: Note that:
1. When the axle rolls wrt chassis, there is no movement of the Mumford rockers wrt chassis (ie. they could be welded solid to the chassis).
2. When the axle bounces (=heaves) wrt chassis, both rockers rotate equal amounts but in opposite directions wrt chassis (ie. they act as if they are two gears in mesh).

All this is proof that a picture is truly worth a thousand words!

Z

mech5496

02-04-2012, 05:48 AM

So you could have a heave/pitch spring attached to both mumford rockers....

rjwoods77

02-07-2012, 04:03 PM

Z,

I was just suggesting the Zumford Link as a lateral control of front and rear beam and z bar interconenction in one clever Chapmanesque device and not as a complete form of beam location. I was also looking to use said mechanism to tie into some sort of rotary damper to tie inline with the Mumford rocker pivot(s) such as a cush drive works on a motorcycle in order to eliminate any need for hydraulic dampers. A rotary way that a F500 achieves linearly. I realize that front and rear beam would still be unconstrained longitudinally. I started with "how do i z bar a double beam" without other layout concerns as my first "wouldn't it be cool if". I was under the impression that two z bars were needed but now if I understand correctly we only need one.

I started drawing and found there there are a couple driver/engine placement combinations in reference to wheelbase along with many different beam and beam control. Some of which were quite innovative and packaged neatly such as the one that places the rear beam 2.5 inches rearward of the main roll hoop while the engine lays underneath the drivers legs. This led me to have questions regarding these linkage arrangments along with what would be an ideal canvas to work with to later add aero.

I dig your concept but would like to explore some other possible methods to achieve the same effect. That being a double beam car with aero but with the addition of suspension interconnection to reduce expensive componentry and more effective platform for aero.

Please review these statements to make sure my understanding is correct. Assume A/B=1 for these and that lever arm A and B connect to the middle of the beams.

1) A beam connects each end pair together so only one z bar(as opposed to two in an IFS/IRS car)is needed because rotation of chassis to one beam is equally and oppositely reacted by the other beam to keep the chassis level. If I lift up on the LF by 1 unit then RF,LR,RR will push down by 1/4 unit which will effectively make a heave of 1/4 unit? ***One wheel lift skew effect***

2) A single spring/damper setup on the end pair beam will affect only the compression of that beam so the spring/damper on the rear is for acceleration squat and the front is for braking dive. Without these, if i lift up on LF and RF by 1 unit then LR,RR will push down by 1 unit which will effectively make a pitch/dive of 1 unit? ***End pair pitch effect without spring/damper***

3) A beam connects each end pair together so only one z bar(as opposed to two in an IFS/IRS car)is needed because rotation of chassis to one beam is equally and oppositely reacted by the other beam to keep the chassis level. If I lift up on LF,LR by 1 unit then RF,RR will push down by 1 unit which will effectively make a roll of 0 degrees? ***Side pair compression roll effect***

I read you correction. So if I ran a single z bar with lever arms that attached to a the beams in the center and run a spring/damper at each end again attached to the beams in the center I would be able to control all spring and dampening through the centerline of the car (spring damper mounts and torsion bar bushing mounts) and have my suspension interconnected? I like the symmetry and ease of this. Would there be any other good reason to run more than one z bar to pullrods coming off of ends of the beams. Beam bending from spring forces? Your comments of mumford rockers not doing anything in roll confuses me. You can see it move with one wheel bump (roll) in this video...

http://www.youtube.com/watch?v=jIiEV0DILBw

I am rather unfamiliar with aero requirements and wonder how that effects the freedom of design if the intent it to eventually put a single piece aero tray that has been claimed to offed the most downforce. Both designs have the minimum wheelbase of 60" and a track of 48" One has the beam axle 2.5" behind the main roll hoop plane and the other is 15". The crossbar for the main roll hoop is 1" ODx 24 inches wide and currently 3 inches to tube centerline from the ground (2.5" ground clearance) The rules madate how far the tunnels of the diffuser can go behind the rear axle. I have no idea the hows and why of how fast the tunnels grow but I was wondering if you or anyone could comment if that it doesnt leave enough room for future tray design versus the less choked up rear axle centerline.

02-07-2012, 08:37 PM

Rob,

As I said, a picture is truly worth a thousand words, and a simple sketching facility here would make all this much easier. http://fsae.com/groupee_common/emoticons/icon_rolleyes.gif

Nevertheless, let's start with the Mumford link, as shown in your link above. This has;
1. The "chassis".
2. "Two rockers" pivoting about longitudinal axles fixed to the chassis.
3. A "central link" connecting the two rockers, such that the rockers always rotate equal and opposite amounts wrt the chassis. Looking at this a different way, instead of this central link, each rocker could have gear teeth near the car centreline that mesh with the teeth of the other rocker. Structurally, the central link is probably better than teeth (less backlash, etc.), but for understanding it might be easier to imagine the two rockers as "geared" together.
3. "Two diagonal-links" going from the rockers out to the beam-axle ends.
4. The "beam-axle".

You say "Your comments of mumford rockers not doing anything in roll confuses me. You can see it move with one wheel bump (roll) in this video..."

What you are seeing is indeed "one wheel bump". But, importantly, the left-wheel-only-bump of say 2" equals axle-bounce of 1" (ie. both wheels up 1") plus axle-roll of 1" (ie. left up 1" and right down 1"). So what that video is showing is the rockers moving as a result of the axle-bounce of 1" (ie. the height the centre of the axle is moving wrt chassis).

To further clarify this (hopefully???), imagine the rockers welded solid to the chassis. Now there is a four-bar linkage consisting of the chassis, two diagonal-links, and the beam-axle. The beam-axle and chassis can only move wrt each other by rotating about the "Instant Centre" found at the intersection of the two diagonal-link centrelines (these being "n-lines", or lines of "no relative motion"). This IC is thus the "Kinematic Roll Centre" (for this simplified 2-D analysis).

So "no rocker motion" = "pure roll".

Now imagine the axle moving in pure bounce (both wheels up or down equal amounts). The diagonal-links pull equally on their respective rockers, and the rockers rotate equal amounts but in opposite directions ('cos geared together).

So if you want to provide a spring that controls ONLY axle-bounce, you can do so by resisting this rocker rotation. This could be your "some sort of rotary damper to tie inline with the Mumford rocker pivot(s) such as a cush drive works on a motorcycle", or any other arrangement that resists the rotation of the rockers. Note that you only have to control one rocker, because they are both linked together, but providing a torsion spring to both rockers spreads the load structurally, and may be neater (?).

All the above only refers to one end of the car (ie. front OR rear). But if you provide such an arrangement (ie. Mumford link with spring controlled rockers) to both ends of the car (F AND R), then you have control of body heave and pitch. This is similar to the "Z-Bar Sketch" top-left WITHOUT the two side "centre-pivot-leafsprings". So the "sprung-rocker-MLs" replace the "coils-at-beam-centres", plus providing lateral control, and perhaps being better structurally because less "beam bending".

BUT, you must still control the body's roll mode, without adding twist stiffness!

A single centreline Z-bar connected to the beam centres would ONLY add body heave stiffness/control. When I said "you only need one of these" (connected to the ML rockers) I meant that one bar adds heave stiffness, and the second just adds even more heave stiffness. Importantly, neither adds any roll stiffness/control (in fact, they add NO stiffness to ANY other mode).

So, YOU STILL NEED TWO LONGITUDINAL Z-BARS with their ends connected to the outer end of the beams (say, via short vertical links). These give body heave and roll control. The extra heave control is not really needed, but to get independent control of ONLY the roll mode takes a different mechanism, possibly more complicated.

There are other solutions possible (eg. "Balanced Suspension", which gives simple and completely independent control of all modes) but that is another very long (!) story, and not really necessary for the smooth tracks of FSAE and F500.
~~~~~o0o~~~~~

You say, "I realize that front and rear beam would still be unconstrained longitudinally."

Yes. But if (?) you want to use something like the side-pair Centre-Pivot-Leafsprings (= body heave/roll Z-bars) in the Z-Bar sketch (top-left), then these can be used for longitudinal control. Braking torque reaction of the axles would also be needed, but even this could be incorporated into the side-pair CPLs.

In fact, that top-left sketch, with peg-and-slots for lateral beam control, has a lot of potential for a very simple, smooth track, short wheelbase racecar.
~~~~~o0o~~~~~

You ask, "I am rather unfamiliar with aero requirements...
I have no idea the hows and why of how fast the tunnels grow but I was wondering if you or anyone could comment if that it doesnt leave enough room for future tray design versus the less choked up rear axle centerline."

From my point of view, tunnels are NOT necessary. A completely flat floor will work IF you "drive" it right. That is, a separate "flap", or "wing", or "aero surface", at the right distance from the rear edge of a flat floor will work just fine (like each wing on the Twin Beam Wing sketch). Similar "aero devices" at the front and side edges of the floor will make it work even better! This requires some original thinking, but there are huge gains possible. http://fsae.com/groupee_common/emoticons/icon_smile.gif

One aero requirement that should be met (I guess?) is that the aero surfaces should remain a reasonably constant distance from the road. Since the road is likely to have some small "twist" in it, I reckon it may be beneficial to let the periphery of the rectangular aero-undertray also twist with the road surface.

The Twin Beam Wing does this, in the sense that the two beam-wings follow any twist in the road. Likewise, the top-left Z-Bar sketch does this, if the aero-undertray periphery is fixed to the two beams and two side-pair CPLs.

(Edit:
Also, the top-right "Z-Bar" sketches (p4) show how the undertray can be divided into five rigid pieces and still conform well to a twisting road. The floor of the chassis forms the central diamond shaped piece, and four triangular corner pieces pivot off the edges of the central diamond to complete the rectangular undertray. The pivots (ie. hinges between diamond and corner pieces) can be low friction, so the whole undertray is very flexible and adds no twist stiffness to the suspension. This also makes accident repairs easier - just replace the damaged corner.
End Edit)

~~~~~o0o~~~~~

Apologies for all the capitals, but this forum definitely needs a simple sketching facility!

Z

Test Driver

02-08-2012, 09:35 AM

All,

A lot of what is being posted about interconnecting corners in varying manners has already been or is being done. However, it's being done hydraulically. Think UWA.

02-09-2012, 03:58 AM

TestDriver,

"Already been done"?

Let's not forget the "world's cheapest car", the Citroen 2CV, designed in the 1930s with very effective mechanical side-pair interconnection.

I am sure motorsport will catch up one day.....

(Not sure about Detroit. http://fsae.com/groupee_common/emoticons/icon_biggrin.gif)

Z

mech5496

02-09-2012, 07:55 AM

Z,

I'n not getting something here. You say "A single centreline Z-bar connected to the beam centres would ONLY add body heave stiffness/control." and "So, YOU STILL NEED TWO LONGITUDINAL Z-BARS with their ends connected to the outer end of the beams (say, via short vertical links). These give body heave and roll control. The extra heave control is not really needed..."

Let's say that the front axle bounces by 1" the rear goes down by 1". This to mu understanding represents a pitch motion (heave would be the other way round). When the front axle bounces by 1" the Z-bar would like to push the rear axle down by equal amount (if A=B). So how a Z-bar connecting front and rear axles contributes to heave/pitch stiffness? Am I missing something here?

As I see it we have two separate issues to be resolved:
1st is axle location both longitudinal and lateral.
2nd is control body movements. If you can incorporate lateral control to motion control or something, you end up with fewer parts->lighter. The real issue to me right now is which modes you want to control, why and how.
On a beam axle car I would not bother having some roll and pitch, as they do not affect tire path or tire loads that much. It might be upsetting for the driver a little, but I think that those modes should not be (very) stiff, they could be left somewhat soft.
The same applies with warp mode (as soft as it gets) and bounce (stiff enough for the chassis not to bottom out hard on axles; maybe rubber bumpstops?). Actually the only movement I would like to limit somehow is single wheel bump. Any thoughts on this?

02-09-2012, 10:31 PM

Harry,

You ask, "So how a [centreline] Z-bar connecting [centres of] front and rear axles contributes to heave/pitch stiffness?"

I think we have to start with a clearer description of what these "four-wheel-modes" mean. The following is not a rigorous definition (not enough space here) but hopefully it is of some help.
~~~~~o0o~~~~~~

Firstly, think of the car's body fixed in space (as the reference frame) and the four wheelprints moving in a generally vertical direction wrt the body. Importantly, we are not concerned with the horizontal (x,y) or rotational (Wx, Wy, Wz) constraints of the wheels or their uprights, which are a function of the control arms (beams, wishbones, whatever). We are only concerned with the approximately vertical (z) motion of the wheelprints, which is the function of the spring-dampers.

To specify the positions (heights) of the four wheelprints, wrt body, we need four numbers. The most obvious choice is LFz, RFz, LRz, and RRz (ie. the wheelprint "z" positions, or perhaps "altitudes" wrt car floorplane). A conventional "spring-at-each-corner" suspension follows this obvious approach and provides a single spring to control each of these numbers.

Now, the fact is that we have four infinities of choices as to how we specify these "four degrees of freedom" (wheelprint heights). I won't go through all these choices http://fsae.com/groupee_common/emoticons/icon_smile.gif , just the following "all-four-wheels" method.

Here we specify our four numbers thus:
1. Bounce mode, Bz = (LFz+RFz+LRz+RRz)/4. This is also called the "Heave" mode. As the equation suggests, this is the average height of all four wheels. We can picture this mode in motion as all four wheels moving up by an equal amount (or down for negative motion).
2. Pitch mode, Pz = ((LFz+RFz)/2-(LRz+RRz)/2)/2. In words, half the difference between the average front-pair and rear-pair heights. We picture this as the two front wheels moving up, and two rear wheels moving down, an equal amount.
3. Roll mode, Rz = ((LFz+LRz)/2-(RFz+RRz)/2)/2. Similar to Pitch mode, but turned 90 degrees.
4. Twist mode, Tz = ((LFz+RRz)/2-(RFz+LRz)/2)/2 (aka "Warp" mode). This time, half the difference between the average heights of diagonal pairs.

So, as an example consider a "single wheel bounce" of left-front wheel up four units (LFz = 4 inches, 4 cm, 4 whatever), and all other wheels at "zero".
1. Bz = (4+0+0+0)/4 = 1 unit.
2. Pz = ((4+0)/2-(0+0)/2)/2 =1 unit.
3. Rz = (likewise) = 1 unit.
4. Tz = (") = 1 unit.

This is saying that a single wheel bounce of LF up 4 units (with all other wheels at zero) is equal to (Bounce = all wheels up 1 unit) + (Pitch = fronts up 1, and rears down 1) + (Roll = lefts up 1, and rights down 1) + (Twist = LF and RR up 1, and RF and LR down 1).

I hope I'm not boring you, but a useful aspect of the above is that all the modes can be measured with simple linear dimensions (inches, metres), and angular measures for P, R, and T are not needed.
~~~~~o0o~~~~~

Anyway, back to your original question. I will redisplay the Z-bar sketch below because 1) it's free, 2) it is too much of a hassle to display another sketch (the sketching is easy, but then scanners, file xfers, Picassa web wanks, http://fsae.com/groupee_common/emoticons/icon_frown.gif ), and 3) hopefully it helps understanding.

Looking at the top-left of the sketch, picture only one "centre-pivot-leafspring" (= a "Z-bar") on the car centreline. Picture the ends of this leafspring as ball-jointed to the centres of the F & R beams. So now the chassis sits ONLY on the centre-pivot of this single centreline leafspring.

It should be apparent that NO Pitch, Roll, or Twist motions (as described above) can be transmitted FROM the wheelprints TO the chassis. So, the chassis responds ONLY to Bounce (=Heave) motions of the four wheelprints. So a centreline Z-bar is purely a Bounce mode spring. It does NOTHING MORE.

The above can be seen by noting that the height of the BJ at the centre of each beam provides an average of the heights of the beam's two wheelprints. The height of the centre-pivot of the leafspring then provides an average of these two averages. Thus the whole linkage (2 beams + CPL) provides an average height of all four wheelprint heights, and nothing more.

So, by INTERCONNECTING all four wheels, this linkage has SEPARATED the all-wheel Bounce mode from the other all-wheel modes (P, R, T). Similar (but a bit different http://fsae.com/groupee_common/emoticons/icon_smile.gif) linkages connecting all wheels can give separate, or "independent", control of each of the other modes.

See SAE paper 2000-01-3572 "Balanced Suspension" , or US Patent No. 6,702,265 (lapsed), for neat ways of doing this.

http://i16.photobucket.com/albums/b33/john-bucknell/ZBARFSAEsmall.jpg
~~~~~o0o~~~~~

You ask, "As I see it we have two separate issues to be resolved:
1st is axle location both longitudinal and lateral."

The Mumford Link does lateral control of a beam. My comments in earlier posts about "springing the rockers" would add axle-bounce control (but not axle-roll control). Personally, I do not think the ML is necessary for FSAE (it has too many parts for my taste), but it would work.
~~~~~o0o~~~~~

"2nd is control body movements....
The real issue to me right now is which modes you want to control, why and how."

As you say, with beam-axles it doesn't really matter how much the body moves, because the wheels always maintain the same camber. So Bounce, Pitch, and Roll can all be soft. For independent suspensions with little "camber recovery" (ie. long "virtual swing arms") it is beneficial to stiffen the Roll mode, but keep Bounce and Pitch soft (at least between limits, ie. bump stops). For sprung-aero cars the Bounce mode has to be stiff (to maintain constant ride height), but the Pitch mode can still be soft.

VERY IMPORTANTLY, in all cases there are huge advantages in having a completely soft twist mode (again, between bump stops that limit the range of twist).

It is truly astonishing that motorsports is the only sub-section of the "land vehicle" community that doesn't realise this! Even more incredible is that many of the people involved have been made aware of this, yet couldn't be bothered even thinking about it. Truly brain-dead!!! (Or just as likely, they have no need, or desire, to win!)
~~~~~o0o~~~~~

"Actually the only movement I would like to limit somehow is single wheel bump. Any thoughts on this?"

Why?

The big advantage of a soft Twist mode is that it allows the car to easily drive over large single wheel bumps.

Looking again at the example at the top of this post, if a car has rigid Bounce, Pitch, and Roll modes, and a completely soft Twist mode, then it can drive, even very slowly, over a 4" high single wheel bump with the car's CG only moving up 1", and the body only pitching 1" and rolling 1" (as defined earlier). (Picture top-left of Z-bar sketch with stiff leafs and coils, then look at top-right for the effect of a soft Twist mode.)

Most importantly, the soft Twist mode means no changes to the vertical wheel loads over bumps (not considering inertia). That is why almost everyone else bar the motorpsorts community uses it. (See Appendix of above-referenced SAE paper for examples.)

Z

mech5496

02-10-2012, 04:37 AM

Z,

First of all, thanks about all the info. Everything is put much much better than vehicle dynamics books I know and far easier to understand, so thank you (and I believe I speak for every member on the forum). I have already gone through the "balanced suspension" patent numerous times, and I have to admit it is more than interesting! (Actually I have a quite funny story behind that exact patent; have you ever heard about a Greek magazine called R&D? I bet you didn't, but they had a presentation on the "Zapletal suspension" back in 2006, so the first time I actually read it was when I was at highschool....)

Anyway, the reason I thought a stiffer single wheel bump will be beneficial is the camber change at both wheels, as well as gyroscopic phenomena of the axle while during this...but I assume the latter can be cured with fairly soft "springing" and relatively high damping. Plus, as you said, "the soft Twist mode means no changes to the vertical wheel loads over bumps". A quick calculation says that I would have a total of 2.3deg camber change for 2" single wheel bump (improbable in a FSAE track), so I suppose I could trade that off for all the above gains.

DougMilliken

02-10-2012, 06:19 AM

Originally posted by Z:
Here we specify our four numbers thus:
1. Bounce mode,...
2. Pitch mode,...
3. Roll mode,...
4. Twist mode,...(aka "Warp" mode).

This is how the control system software for the Lotus Active Suspension was configured, starting in the early 1980's. By the time they got done, they built something over 80 prototype vehicles with variants of the system--from F1 cars to large single-unit trucks (for Volvo, among others). I drove a light tank fitted with a variant of the system that greatly reduced pitching, when compared to normal tracked vehicles.
A search will turn up a number of pages with various descriptions. In typical racing (and "trade secret") style they did not do a lot of technical publishing. Most of the written documentation went to specific customers.

02-21-2012, 01:51 AM

Originally posted by mech5496:
Anyway, the reason I thought a stiffer single wheel bump will be beneficial is the camber change at both wheels, as well as gyroscopic phenomena of the axle...
...
A quick calculation says that I would have a total of 2.3deg camber change for 2" single wheel bump (improbable in a FSAE track)...

Harry,

It is worth considering how these "bumps" affect the suspension.
~~~o0o~~~

First of all, bumps can come as "mountains", or as "molehills", ie. big or small.

1. Let's say that "big" bumps have a smooth sinusoidal shape in horizontal directions (x and y), with a wavelength significantly longer than the car (so, say, 3++ metres). Sort of like longish waves, or "swells", on the ocean. Given the relatively low speeds of FSAE, a car driving over these "undulations" will not feel significant vertical accelerations of its wheelprints wrt body, so discussions about "unsprung weight" are frankly irrelevant. Likewise, gyroscopic forces are minimal, so changes in wheel inclination angle are not a problem.

However, these undulations will twist the four wheelprints out of a flat plain, and thus very adversely affect the wheel loads of a stiff twist-mode suspension (ie. most racecars). So, a soft twist-mode is a big benefit here. Furthermore, in this case the best camber angles for the tyres is relative to the road surface as drawn as a straight line through laterally paired wheelprints. So the camber change of a beam-axle is just what you want. http://fsae.com/groupee_common/emoticons/icon_smile.gif

2. On the other hand, what about short wavelength bumps (say, <~1m wavelength)? I call these "corrugations". Now the accelerations are more severe, and, together with gyroscopic effects, suggest a suspension with lightweight wheel assemblies and NO camber change during the frequent single wheel bumps.

Is the resulting "zero camber recovery" bad for cornering grip? Not really. The fact is that in this situation the wheels are rolling over ground that is constantly changing its relative "inclination" angle to the wheel. So for about half the time there is an effective positive camber angle, and the rest of the time there is an effective negative camber angle. If the bumps, or ruts, are short enough the wheel might have both positive and negative "camber" at the same time (ie. on either side)!

In this case I think worrying about tenths of a degree of "camber recovery" is pointless. However, a soft twist-mode (as well as soft all-other modes) is beneficial because it gives more constant vertical wheel load, and thus better all round grip.
~~~o0o~~~

To sum up:

1. For smooth "undulating" roads, like circuit racing and FSAE, the car benefits from a soft twist-mode, and wheels that are kept at a constant camber angle relative to a line drawn through lateral pairs of wheelprints. So, for example, use beam-axles, or lateral swing arms with a lateral Z-bar that minimizes "axle-bounce", but allows "axle-roll".

2. For harsh "corrugated" roads, like rallying and off-road racing, the car benefits from a soft twist-mode, and wheels that are kept at a constant camber angle relative to the body. So, for example, use leading and trailing arms, or, if you must use lateral wishbones, make them long, equal length, parallel, and horizontal at normal ride height.

Z

(Edit: It is instructive to draw a "map" of the type of bumps that ground vehicles drive over. On the the horizontal axis plot "Frequency" (Hz) as a log scale. On the vertical axis plot "Amplitude" (say, in metres) again as a log scale. Now, assuming sinusoidal bumps, the maximum vertical velocities and accelerations of the wheelprints are shown as two series of diagonal lines on the map (different slopes for V and A). FSAE is at the bottom-left of this map (along with forklifts, etc.), while desert racers are at the top-right.)

Tickers

02-21-2012, 06:31 AM

Z,

As much as I love the idea of a simple go-kart type FSAE car, I look at the sketches and ideas in this thread and wonder where the simplicity is!

Teams aren't just using wishbones and push/pullrods because that's what "real" single seaters use; they use them because they're easy to make. The parts are almost all built from simple materials (rods, tubes, plates etc) that are all small and manageable to fabricate.

Sure, there can be "interesting" handling characteristics if the geometry is poor, but the teams who only care about getting a car going can just weld up a few tubes (with the required rod ends in bending) and get out on track. Teams who know what they're doing can spend a while analysing the kinematics for decent geometry, with a large amount of existing resources to guide them.

The ideas here require large parts and assemblies that would need to be fabricated, either by machining (expensive for large parts) or casting (expensive for anything). Not only are the systems you're advocating likely to cost more to produce than a double-wishbone setup (which puts off the poor teams), they'll also put off the lazy teams as they'll have little to guide them, meaning they have to design the whole thing themselves!

A go-kart would be fantastic, but unfortunately we're required to have suspension. In trying to accommodate the requirements while avoiding double-wishbones in the name of "simplicity" I think you've done the opposite.

02-21-2012, 09:56 PM

Originally posted by Tickers:
... I look at the sketches and ideas in this thread and wonder where the simplicity is!
Tickers,

Groan!!! http://fsae.com/groupee_common/emoticons/icon_rolleyes.gif I have heard this line so many times before...

People do things in ridiculously complicated ways, and then say "Oh, it's not difficult at all!"

Why???

Because that's the way they have always done it! http://fsae.com/groupee_common/emoticons/icon_confused.gif
~~~o0o~~~

You say, "Teams [use wishbones] because they're easy to make."

And, The ideas here require large parts and assemblies that would need to be fabricated, either by machining (expensive for large parts) or casting (expensive for anything)....

I suspect that the above is just a leg-pull, but if not, then it is pure crap! http://fsae.com/groupee_common/emoticons/icon_smile.gif

I have been through the "easy to make" process of wishbones, and while I agree that it is a mind-numbingly boring and brainless job, that fact is that making all those little gubbins, fishmouths, gussets, etc., MULTIPLIED BY EIGHT, takes a long time.

The two beams I drew would be fabricated from a few lengths of tube and some sheet-steel gussets (no "machining large parts", or "casting" - where did that crap come from!!!). From past experience I reckon it would take about half the time of a full wishbone setup.

But the even bigger gain comes from the simpler chassis with its much smaller number of hardpoints. Only four of these hardpoints need to be accurately positioned, and they are all on the centreline of the chassis. So much easier than when hardpoints are scattered all over the place.
~~~o0o~~~

It never ceases to amaze me how fearful Homo Sapiens are of change. Even the young ones!

Any pissweak excuse to avoid change will do, "... have to design the whole thing themselves!".

Any FSAEers with testicles out there????? http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

mech5496

02-22-2012, 02:46 AM

Z, you have to admit there are terribly complicated ways to build a beam axle... Like the concept our team evaluates, which you might all see as long as we finish the manufacturing of our current car. Tickers, simple beams can be built very very cheaply and easily. Polished-up concepts to shave off some unsprung are a bit more complicated, but even if you say that it has the same complexity with a double wishbone setup, I'm pretty convinced there ARE performance gains in beam setups. You just have to think it as the whole system, not just the suspension... Right now you are staring at the tree, while missing the woods behind it....

whiltebeitel

02-24-2012, 02:40 AM

Originally posted by Z:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Tickers:
... I look at the sketches and ideas in this thread and wonder where the simplicity is!
Tickers,

Groan!!! http://fsae.com/groupee_common/emoticons/icon_rolleyes.gif I have heard this line so many times before...

People do things in ridiculously complicated ways, and then say "Oh, it's not difficult at all!"

Why???

Because that's the way they have always done it! http://fsae.com/groupee_common/emoticons/icon_confused.gif
~~~o0o~~~

You say, "Teams [use wishbones] because they're easy to make."

And, The ideas here require large parts and assemblies that would need to be fabricated, either by machining (expensive for large parts) or casting (expensive for anything)....

I suspect that the above is just a leg-pull, but if not, then it is pure crap! http://fsae.com/groupee_common/emoticons/icon_smile.gif

I have been through the "easy to make" process of wishbones, and while I agree that it is a mind-numbingly boring and brainless job, that fact is that making all those little gubbins, fishmouths, gussets, etc., MULTIPLIED BY EIGHT, takes a long time.

The two beams I drew would be fabricated from a few lengths of tube and some sheet-steel gussets (no "machining large parts", or "casting" - where did that crap come from!!!). From past experience I reckon it would take about half the time of a full wishbone setup.

But the even bigger gain comes from the simpler chassis with its much smaller number of hardpoints. Only four of these hardpoints need to be accurately positioned, and they are all on the centreline of the chassis. So much easier than when hardpoints are scattered all over the place.
~~~o0o~~~

It never ceases to amaze me how fearful Homo Sapiens are of change. Even the young ones!

Any pissweak excuse to avoid change will do, "... have to design the whole thing themselves!".

Any FSAEers with testicles out there????? http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z </div></BLOCKQUOTE>

Z, there is a limit to the steps in thickness of availible material for these giant leaf springs with big center pivots. I can cheaply buy coil springs in 5 lbf/in increments to tune my suspension, and a few click on the damper or a spin on my 5" long ARB blades. How does one tune this great big deal? A truckbed of leaves of spring steel?

Also, twist modes aside, there's a lot to be said about camber thrust and adjusting your suspension to give you the camber you need under roll to improve grip. Sidewalls are compliant, and often not to our advantage.

That said, this IS an interesting concept. They said rear steer could not work on the Thrust SCC, but some guy made it happen. Are you willing to help make it happen for a team, or just for a demonstration?

02-24-2012, 04:38 AM

(More groaning... "like trying to put brains into statues....", grooooaaan....) http://fsae.com/groupee_common/emoticons/icon_smile.gif

whiltebeitel,

You say, "there is a limit to the steps in thickness of availible material for these giant leaf springs..."

At the top-left of the sketch it says "Z-Bar Concept". I drew the "centre-pivot leafsprings" for those "imaginatively challenged" students who can't figure out how a torsional Z-bar works. The lateral CPLs shown at bottom-right are the sort of thing that an apprentice blacksmith could make without a second thought. But a bit too much for you??? (Mumble, mumble, "education system, grrrr...")
~~~o0o~~~

"How does one tune this great big deal?"

Top-right! ERMD (=LLTD) = B/A. http://fsae.com/groupee_common/emoticons/icon_rolleyes.gif

(Key point: By geometry NOT spring rate!)
~~~o0o~~~

Are you willing to help make it happen for a team, or just for a demonstration?"

Read the Appendix of the SAE paper referenced above (just above Z-bar Sketch this page). As explained there, twist-soft suspensions are by far the most common for real working vehicles. Motorsports is in a tiny minority that hasn't figured it out yet. (Braindead!!!!)

Z

whiltebeitel

02-24-2012, 01:52 PM

Originally posted by Z:
Read the Appendix of the SAE paper referenced above (just above Z-bar Sketch this page). As explained there, twist-soft suspensions are by far the most common for real working vehicles. Motorsports is in a tiny minority that hasn't figured it out yet. (Braindead!!!!)

Z

Any relation the the author?

It's a wonder more of your ideas have not caught on, with such a flowery personality and charm.

02-24-2012, 06:05 PM

Originally posted by coleasterling:
... but there comes a point when you have to actually make it and PROVE superiority.
coleasterling,

And for the Nth**n time, it is the most thoroughly proven concept in the ground vehicle industry!!!

Read the Appendix in the above paper, and then YOU PROVE to me how modern racecars (the odd ones out) are superior. http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

"... you're just that crazy old guy who yells about how dumb kids these days are..."

The crazy thing is that I feel like the teenager living in the Old Folks Home.

OFs "Have some tea and digestive biscuits Z."

Z "Aw, but I want to go out and play. You know, do something interesting..."

OFs "No, no, Z, don't put any sugar in your tea! You'll get too excited. Now you don't want to miss Bingo this afternoon. You know how much we all enjoy that..."
~~~~~~o0o~~~~~~

whiltebeitel,

Yes.

"flowery personality and charm"?

The OFs like it.

Z

Gruntguru

02-25-2012, 12:10 AM

Originally posted by Z:
ENGINE. The engine in the Twin-Beam sketch was supposed to be a Royal Enfield, based on info I found on various websites. It won't work as shown. I got parts of the old and new models mixed up...

But, funnily enough, the day after I posted the sketch I was tyre-kicking in a quad bike shop and guess what's sitting in the corner? Three old British bikes - a Norton twin, Matchless 500 single, and a Royal Enfield 500! (Old Z had a Matchless 500 engine that went in every "fun" vehicle he dreamt up. I clearly remember it NOT being a great success in the canoe (I was about 10). The first time the throttle was cracked open the propellor spun maybe five times one way, and the canoe did a half turn the other!)

So I had a good look at the RE, and I like it! If lots of REs were available, at the right price, then I would certainly consider one. The long term goal would be a turbo or supercharger (with standard CR~7:1), crank driven clutch and dog-neutral, then direct chain final drive ~5:1 (ie. ditch the gearbox).
Royal Enfield motorcycles are available new - made in India. http://www.enfieldmotorcycles.com/

Indian Institute of Technology Roorkee competed at FSAE Australasia in 2011 using this engine.

02-25-2012, 03:39 AM

Gruntguru,

Unfortunately RE have updated the engine so that it and the gearbox are now of unit construction. The advantage I saw in the old engine was the separate gearbox that could be relocated to the front of the crankcases, for better overall packaging.

Or better yet, the gearbox could just be deleted, then some variation of single or dual chain drive used. The RE turns slowly enough that a direct final drive is possible. Less is more!

The old style engine had air-cooling with big fins, 2 valve hemi-head, approximately square bore/stroke, roller main bearings but pressure fed slipper big-end, dry-sump with separate inernal scavenge and pressure pumps and internal oil tank, and a direct drive alternator. Not too far from what I would want in a bespoke FSAE engine.

Z

02-25-2012, 07:03 PM

Cole,

You say, "... I do have the opinion that your overall package is way out there for an FSAE car."

By "way out there" I guess you mean that you don't approve of it, and you think that it won't work?

Well, around the same time I was pushing the "brown go-kart" back in 2005, RMIT (with Geoff Pearson) built a car that was a step in that direction, and it was very successful. Quite a few more teams are now going in that direction (witness all the recent debate about "singles vs fours" that wasn't there in 2005).

However, the simple, lightweight single (with aero!) is still in the minority, so most FSAE students think that this approach is a "radical" step with lots of associated risks (eg. many think that they have to go "carbonfibre + titanium" to have a chance).

I am just trying to reassure these students that the KISS approach is in fact the easiest way to outright victory. (And please note, KISS does not mean mindlessly copying the unnecessarily complicated "standard" FSAE car.)
~~~o0o~~~

"....you've "already explained why" the single or two gear concept is better, but again, saying it and proving it are two different things. You speak these things like they are gospel when there are no results to back them up in FSAE."

Quote from Kevin Hayward in "Any way to objectively choose engine?" thread.
"Many cars in FSAE have done very well running the endurance in one gear. Even with heavy cars."

And, incidentally, Kev's old school, UWA, has successfully run soft twist-mode suspension for quite a few (?) years.
~~~o0o~~~

"... but dang those insults are getting old."

If you do something really stupid, and you are told that it is stupid, then it is only an insult if you refuse to believe that it is stupid.

A kick up the bum can be good for you. Thinking back, I wish I got a few more at certain times in my life. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

Gruntguru

02-25-2012, 08:17 PM

Love this thread. I have been advocating the single with aero and beams for a while. Now the "soft twist" concept has my attention but there are so many questions. For example - in the top left Z-Bar drawing, how would you adjust RMD? Adjustable side pivot location to change A/B would be a design challenge. Would fiddling the RCH's be sufficient? Perhaps an ARB at one end? And how to select the longitudinal location of the side pivots - at the CG? Slightly further back if running a spool?

These are some of the design challenges that would make teams wary of such a radical departure from "typical" FSAE layouts.

02-26-2012, 05:41 AM

Gruntguru,

The top-left Z-bar sketch was mainly intended just to explain the concept. In practice it could be done, but the RMD wouldn't be easily adjustable, so you would have to work that out first.

That's why I also did the bottom-right sketch with its longitudinal Z-bars. These are harder to understand, but they make it easier to adjust RMD, simply by adjusting relative A and B lengths.

One of the main advantages of beams is that they can run very soft springs, so the suspension is already reasonably twist-soft. However, to adjust ERMD you have to change springs, which can be time consuming, expensive (need lots of springs), hard to make fine adjustments, etc.

So if you have beams with longitudinal Z-bars (and perhaps soft central coils like in top-left sketch) you can more easily adjust RMD via the geometric change to A/B lengths, a relatively simple bit of mechanical detail design.

Also, I would suggest to start with a soft damper-at-each-corner. So if the Z-bars get too confusing you can scrap them and easily go back to a spring-at-each-corner (on the dampers).

Z

02-26-2012, 06:33 PM

I should also note that "Z-Bars" can be done "2CV style" (see 2CV pic somewhere? on these pages).

So let's say you are already running push/pullrods-and-rockers, and the pivot-axes of the rockers lie in a vertical-lateral plane. Now you can interconnect the pair of rockers (F&R) on each side of the car with a pullrod that acts as a Z-bar. Ie. when one wheel goes up, it pulls the rod, which forces the other wheel down.

Practically, the Z-bar-pullrod could be a ~4mm diameter cable with its ends wrapped around pulley sections on the rockers (like those machines in gyms). Somewhere along the length of cable would be fitted a compression spring, in the fashion of the springs used on tent ropes.

Importantly, the SPRING-RATE does NOT have any influence on handling balance via ERMD. The springs are there for comfort. The ERMD (=ELLTD) is determined soley by the geometry of the rocker arms (etc...), and is thus independent of bounce/pitch/roll motions of the car, and (importantly!) of twist in the roadway.

A system like this is the only justification for "rockers" that I can think of (ie. at least here the rockers are doing something useful!). Its practical implementation would be quite easy, being similar to current layouts, and allowing flexibility in the positioning of the Z-bar-pullrod/cable runs.

(Note also: Only three Z-bars total are required for sufficient control of the suspension of all four wheels. I'll let you students figure that out...)

Z

coleasterling

02-27-2012, 02:36 PM

Originally posted by Z:

"Many cars in FSAE have done very well running the endurance in one gear. Even with heavy cars."

And, incidentally, Kev's old school, UWA, has successfully run soft twist-mode suspension for quite a few (?) years.
Z

How are you defining "well" and "success" here? Doing well, by my definition, is putting down an endurance pace capable of giving your team an overall win. To my knowledge, no team running a single gear has been able do this. That certainly doesn't support your concept.

How successful is UWA? My definition of success is winning the competition. Not to mention, sure, UWA is soft-twist, but they are still nowhere close to your overall concept.

Gruntguru

02-27-2012, 04:06 PM

Originally posted by coleasterling:
How successful is UWA? My definition of success is winning the competition. Not to mention, sure, UWA is soft-twist, but they are still nowhere close to your overall concept.
-Cole
A pretty old list but I don't think WA's wins have been reversed.

Team Name # of Wins
Cornell University 9
University of Texas - Arlington 8
RMIT 4
Georgia Tech 3
University of Toronto 3
University of Wollongong 3
Texas A&M University 3
Sophia University 3
Graz University of Technology 2
USP São Carlos 2
University of Western Australia 2
University of Stuttgart 2
California State University - Pomona 1
Centro Univ. da FEI 1
Kanazawa University 1
Steven's Institute of Technology 1
University of Akron 1
University of Applied Sciences Graz 1
University of Houston 1
University of Maryland 1
University of Michigan - Ann Arbor 1
University of Texas - Austin 1
University of Wisconsin - Madison 1
Virginia Tech 1
Faculdade de Engenharia de Sorocaba 1

Pete Marsh

02-27-2012, 05:55 PM

I wasn't claiming they don't have any wins. It was a genuine question. The statement still stands, however. They build a car that is nothing like the beam-axle concept.

There has been one more win since then, and a few more if you are only looking at dynamic wins. Not the same concept sure, but many similar outcomes. Ours is more of an "add on" way of achieving soft twist.

We have run the system for a long time, even after the sponsorship went away in the GFC. So it must have something going for it. It has no advantage in the design event, and until a judge drives it, will remain extremely difficult to justify to them.

On the flip side, Stuttgart has a pretty good dynamics record too, with a pretty similar concept but with a stiff twist mode, and the FSG track is far from flat.

So, hard to tell if the soft twist is much of an advantage, but clearly UWA, and some stop watches, thinks so.

Pete

Will M

04-11-2012, 09:36 AM

Originally posted by Z:
A few weeks ago on the "suspension for spool" (http://fsae.com/eve/forums/a/tpc/f/125607348/m/54820131151) thread I said I would post a sketch of a Twin Beam-Wing concept. I think this is a more suitable thread, so here it is (warts and all http://fsae.com/groupee_common/emoticons/icon_smile.gif).

https://lh5.googleusercontent.com/-8ABMaKebyXs/Txtdpl2DZEI/AAAAAAAAAIs/fCJ-84VnwMc/s800/TwinBeamWing.jpg

(Edit: Made image bigger.)

Main features:

* This is an "aero above all" car. Everything else is there just to support the aero. I figure "drive on the ceiling" at less than maximum FSAE speeds (ie. DF=W at <100kph, (maybe <70kph?)). And more is possible!

* Aero is direct acting on the wheels, and easily adjustable for F/R balance via the flaps. Since wings are close to ground, and with wheels as skirts/end-plates, drag is low (no induced drag). The streamlined fuselage and wheel pods also lower drag for good economy.

* The aero centres of pressure are unlikely to be exactly above wheel axle lines, so some force acts on chassis through BJs causing some pitch/heave. This can be fixed by either; a) not worrying about it, b) reshaping the wings, or c) interconnecting the wings with two torsionally flexible spars running alongside the chassis and attached flexibly to the beams on their axle lines. Extending this last solution sideways gives a full width "live" undertray.

* Finally, a first year or "limited resource" team can do this car without the aero. Use a RE, B&S, or similar engine and you have a simple lightweight car that is quicker to build than the usual wishbones-and-pull/pushrods&rockers-everywhere cars. And, all other things equal, it will have high grip and benign handling because of soft springs with no camber change (not possible with normal independent suspensions).

Comments and criticisms welcome! http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

Z,

With the softer springs you should see more travel and I estimate from your drawing that a 2cm travel will cause about 2.5 degrees for caster change in the wheels and angle of attack for the aero (assuming the front and rear aren't linked). You might only see that much travel under heavy braking or hitting a bump and it might not make a big difference but it is another design consideration I wanted to point out.

mech5496

04-11-2012, 11:02 AM

How the hell did you figure that "2.5 degrees of caster change"?

Will M

04-11-2012, 03:28 PM

mech5496,

Unless I am completely not understanding the idea (I am not a suspension guy really) this should be right. Also I got the 45cm from Z's drawing.

William

http://s13.postimage.org/mfmip1r1j/001.jpg

04-12-2012, 06:35 AM

Originally posted by Will M:
I got the 45cm from Z's drawing.
William,

Actually, it is 50cm (lower right of picture).

Aerofoil AoA will only change about half your figure under extreme braking (even with +/-2cm F&R), but regardless of AoA the downforce can be kept fairly constant with the right profiles (ie. maintain a constant gap to ground). If the two main BJs are closer to centre of wheelbase (in side-view), then less AoA and castor change during pitch. Also there is quite a lot of anti-dive/lift in the kinematics, which lessens pitch under braking.

But the main point here is that you do NOT want to do a lot of braking or accelerating. Fast cornering, and a "constant speed car", is best! http://fsae.com/groupee_common/emoticons/icon_smile.gif

Also, the wings as shown are mainly for ease of construction. Just a "plywood" add-on to a simple beam-axle suspension suitable for a first year team. More advanced and powerful aero is hinted at in my quoted text in your first post.

Lastly, lots of castor change (+/-10+deg!) over bumps is NOT a problem. And FSAE tracks don't have bumps! http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

mech5496

04-12-2012, 07:22 AM

Actually you could have NO (or very limited) pitch under braking by designing a certain amount of anti-dive and using a dedicated pitch/heave "spring" and "damper" (a polymer puck could replace both), directly on the sliding mechanism, so it does not affect roll at all. What's more, what is so bad about a degree of caster change?!

Will M

04-12-2012, 08:47 PM

I am actually a big fan of this car architecture, I'm just trying it for possible weak areas. The main problem I see with dynamic caster change is if it went from positive to negative or the other way around that could be disconcerting for the driver. Caster change is not bad, like bump-steer it is a knob you can turn but you do have to think about it.

Z,

Also. If you were building one of these how much adjust-ability would you add? If the geometry was locked in the beam could be very stiff and light... Maybe two sets one adjustable and then a second fixed one...

William

04-14-2012, 05:06 AM

William,

"How much adjustability?

Good question. I didn't want to put too much detail into the earlier posts, but I'll briefly cover this important issue now. What follows applies to teams that are fairly new to racing, which is pretty much all FSAE teams, and certainly any that might try beam-axles (because very few examples to "learn from" (ie. copy http://fsae.com/groupee_common/emoticons/icon_smile.gif)).

The following also applies to any suspension type on smooth track circuit racing. So this is mainly about going fast around tarmac corners. Top of the list is most important, and less important further down.

Important Suspension Adjustments for Fast Cornering.
==============================================

1. Tyres - Type (carcass/compound), Size, Pressure, Rim Width.

2. Static Toe - to +/- one tenth degree.

3. Static Camber - to +/- one degree.

4. Front/Rear Roll Rates - ie. LLTD or ERMD (same things). Note Pitch/Heave rates are important for sprung-aero cars, but not considered in detail here.

5. Dampers - just enough to suppress resonant bouncing on above springs, or on the tyres.

6. Kinematics - RC heights, anti-pitch, camber recovery, etc.
~~~o0o~~~

Note that things like Ackermann and compliance are also very important in FSAE (in fact, close to top of list, depending on details), but will leave that for another time. Also a spectacular cock-up on something like Kinematics (say, severe rear bump toe-out) will push it to the top of list. And also not considering Z-bars (can be added later).

So from the above, and IMHO, the biggest gains come from lots of testing of different tyres, their hot pressures (anything from 0.5 bar (7psi) to 2+bar (30+psi) can be "optimal", depending on...), and also rim widths, which can make a big difference.

On the other hand, any kinematic issues can be covered by other adjustments (again, unless you truly stuff it up). A brief example is Formula Vee, which mandates Beetle suspension with ground level front RC and ~axle height rear RC, but corners as fast as any other similar single seater on same tyres (hint: high rear RC compensated by zero rear roll rate springing).
~~~o0o~~~

So for a beam-axle FSAE car I suggest the kinematics be non-adjustable, as in the sketch. That is, roll and pitch axes (strictly speaking, the beam's "cylindroid") as low as practical, which is just above floor level (to allow room for the brackets, bolts, etc.). (See note re: De-dion below.)

The spring-dampers can be direct acting as in sketch. LLTD adjusted by changing springs or, for fine adjustments, small changes to the angle or axle mounting points of the S-Ds might be used. Preferably do NOT use any ARBs, but if you must, then use only one (say, a stiff one at rear to compensate for a "spool" differential). Do not overcomplicate this! There are much bigger gains elsewhere. http://fsae.com/groupee_common/emoticons/icon_smile.gif

That leaves the two big ones on the suspension front, namely static Toe and Camber angles.
~~~o0o~~~

FRONT AXLE - Static Toe is easily adjusted via the steering tie rods. I suggest building one structurally efficient beam, then adjusting Camber and Castor (less important) at the king-pin. This is an opportunity for some good detail design, but even a crude overweight design won't cause too much harm here (as long as it doesn't break!).

REAR AXLE - More options here.

Live Spool, as one tube wheel-to-wheel. Here Toe and Camber are fixed at zero, but it is important to make everything stiff enough.

Live Spool, as two half axles with spline/CV at centre. This is the reason for the four bearings (eg. "pillow blocks"?) in the sketch. Toe and Camber now easily adjusted by moving relative position of inner and outer bearings for each half-axle.

Live Differential. This is as above, but with any sort of beam mounted differential (eg. open/LSD). Again, Toe and Camber easily adjusted.

De-Dion, with chassis mounted differential of any type (open/LSD/spool). This option may make the final drive easier, since the diff location is fixed wrt engine. This requires CV'd half-shafts and stub axles at the beam ends of similar type to independent suspensions. I suggest the stub axle housings have some means of adjustment for Toe and Camber, if only to correct for manufacturing tolerances of the beam. These can then also be used for "tuning". Again, a good opportunity for quality detail design!

Important De-Dion note. The side-view kinematics, or anti-pitch, changes when the diff is chassis mounted. A layout as in the sketch, but with De-Dion, will have lots of pro-squat under power. This can be ignored with a low power engine, or a beam-centre bump rubber (aka "third-spring", or "lateral Z-bar", as mentioned by Harry above) can be used to limit squat (axle bounce) but allow roll. Alternatively, a different kinematic location can give anti-squat (higher pitch axis) while maintaining a low roll axis. This is a quite simple structural change, but will require a sketch to explain it properly...
~~~o0o~~~

I also discussed suspension adjustments on this old thread. (http://fsae.com/eve/forums/a/tpc/f/125607348/m/33210954521?r=51010285521#51010285521)

Z

Charles Kaneb

04-14-2012, 01:15 PM

Z,

A couple things I've run into while trying to convince my team of the merits of a car with suspension other than A-arms all round:

1. With the required cockpit volume, side impact intrusion prevention, front and rear roll hoops, and supports for said roll hoops, you end up with a very torsionally stiff center section of the car. I'll mail a dollar to anyone with results showing a currently legal car with end-to-end torsional stiffness of less than 800 lbs*ft/degree. Any significant torsional deflection would have to be concentrated in a very small area near the back of the car. At this point, you'd have committed to weld in a nonadjustable twistable element with unknown damping properties that, if karting experience shows anything, will gradually change over a couple dozen hours of racing. Even if you figure out how to get good properties from this, there's nothing that says a tech inspector won't require you to weld in some supporting bars at competition.

2. I haven't had the time to draw up and do the stress analysis for a preliminary design of a beam axle rear end. I do not know whether it will save weight, or how much. The heaviest components in an FSAE suspension right now are the axle cups, the axle bearings, and the spring-damper units. If a beam axle rear end is not set up to be extremely stiff in roll, your sprocket will tip about the X-axis, and motorcycle chains or synchronous belts do not tolerate this well at all. A De Dion rear end is at least as complex as any double wishbone setup.

3. Vehicles which are soft around the Y-axis (twist mode) are used in many applications. Outside of racing and certain military off-road vehicles, there are very few vehicles where the main differences between success and failure are peak tire grip and controllability near peak tire grip.

My main experience with operation of a vehicle with a soft twist mode near its dynamic limits was on a driver-training day for garbage-truck drivers. The garbage truck consisted of a torsionally flexible twin-rail chassis with a rigidly attached cab, above which was "floated" a garbage compactor/storage box on flexible mounts. The truck entered a fairly tight, constant radius 180 degree turn, at a speed such that the tires squealed slightly. The chassis deflected about the Y-axis, storing up strain energy and keeping the inside rear tires on the ground. So far so good. Then the corner ended. The driver straightened the wheel. The chassis released its stored energy. The compactor box was tossed several inches in the air and landed in a slightly skewed orientation on the chassis. Meanwhile the rest of the truck wobbled back and forth...

4. Almost every chassis rules change since the start of FSAE has been anti-kart; in addition, up to 1/5 of the team score is in a design event with judges who are unlikely to have experience with design and optimization of karts. Just to get this out of the way, a kart with a 450cc motocross engine and a working vacuum traction system would absolutely wipe the floor with every FSAE car ever made. First, we're required to have some form of "working" suspension. Second, we're required to have a reasonably torsionally-stiff chassis. Third, we are required to have wheels that are at least 8" diameter (and no remotely competitive tire smaller than 10" exists); the resulting 18"+ tire diameter means that the suspension system must handle a large Y-bending moment during cornering and a large X-bending moment under braking. It will be lighter and cheaper to handle these moments with a small amount of material far away from the centerline of the axle than wih a large amount of material near it. Finally, the aerodynamic downforce generating components we're allowed to have are not terribly sensitive to roll or twist - more to pitch and heave.

The advantages of a fewer-moving-parts suspension have been heavily cut back by practical and rules constraints, while the risks of moving to one include possible disqualification, rules changes which would ban the car for next year and make what we learned about how to make one of these cars handle irrelevant, and a very real possibilty of a design-event score that's so bad it would wipe out any dynamic event gains this thing could make. When we build a car with four-wheel independent suspension by A-arms, with constant-rate passive springs and passive dampers, we are not simply polishing a turd - we are selecting a design that has proven to be at least OK at its job and will not be banned or drop-kicked in design.

04-15-2012, 08:36 PM

Charles,

Thanks for comments. Here are some brief responses.
~~~o0o~~~

1. The mandatory chassis safety parts (roll-hoops, side impact,...) form most of the chassis for the Twin-Beam concept. No more torsional stiffness is needed, because beams allow soft springs. I would not suggest adding any extra torsional "softness" to the chassis, again, because the soft corner springs already give enough softness. The advantages of longitudinal Z-bars is that they can give a completely soft twist-mode, even with a stiff chassis and stiff roll-mode, this latter being necessary with wishbones with small camber gain (long FVSA). Also the Z-bars make handling adjustments (ERMD) very easy.
~~~

2. I think the possibility for weight reduction by using beams over wishbones comes mainly from the much simpler chassis with its smaller number of hard points.

You say "A De Dion rear end is at least as complex as any double wishbone setup."

I have to disagree. I reckon a detailed study of a De Dion would have it roughly half as "complex" (time to make, etc.) as double wishbones. Likewise, there are many other simple suspensions that are almost never considered. The "proof" of this is that almost all FSAE teams use the completely unnecessary push/pullrods-&-rockers, so they are clearly not concerned by useless complexity, and make no attempt at "simplicity". Well, other than talking about "KISS". http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~

3. "Outside of racing and certain military off-road vehicles, there are very few vehicles where the main differences between success and failure are peak tire grip and controllability near peak tire grip."

Well, how about every farm tractor ever built.... and all the earthmoving machines....? http://fsae.com/groupee_common/emoticons/icon_smile.gif All of these rely on massive grip, so almost always have a completely soft twist mode. (BTW, to be successful in motorsport you just have to keep your sponsors happy, and back of the grid is no disadvantage.)

"The garbage truck consisted of a torsionally flexible twin-rail chassis ... The chassis released its stored energy ... the rest of the truck wobbled back and forth..."

And therein lies the problem with providing a soft twist mode with a spring capable of storing a lot of energy. Better is completely soft, like tractors, forklifts, ride-on lawnmowers, etc., etc..
~~~

4. "...while the risks of moving to [a fewer-moving parts suspension] include possible disqualification, rules changes which would ban the car..."

Any comments from someone on the Rules committee???

"When we build [the standard suspension] we are not simply polishing a turd - we are selecting a design that has proven to be at least OK at its job and will not be banned or drop-kicked in design."

The sad part is that a "NO suspension" car would also be "OK at its job" in FSAE, but a lot easier and cheaper to build, and probably faster because lighter, more testing time, etc.

The really sad part is that you really are all "Polishing A Turd". And in building the "PAT" car very few students learn how real suspensions work, because real suspensions have to cope with real roads which have real bumps on them, whereas FSAE tracks are unrealistically smooth.

Z

Will M

04-16-2012, 06:32 AM

The debate that a go-kart is better fitted for an FSAE track than an FSAE car is has been going on at least since 5 years ago when I started reading this forum and probably stated 15 years ago. So there have been about 50 to 200 competitions since the debate started. We are not politicians doomed to argue about which century old econ book is best, we can objectively prove this one way or the other. Surely at least one FSAE official owns a decent shifter car. The test is simple, before each dynamic event they take their kart out and put down a time. This would give an objective comparison and would be a good way of checking track conditions. Getting decent historical data for FSAE is a real pain (the event book has car data but no results, and the online results have no car data). This would give at least one bench mark, and could be used to compare events in different years and locations to each other.

William

mdavis

04-16-2012, 12:29 PM

Will,

We do a decent bit of our testing at a local kart track, and knowing a handful of guys that run the TAG classes (100cc 2 stroke, single gear karts), we know their laptimes around various configurations. On the big track (considerably larger and more wide open than a typical FSAE course), the fast TAG's run 38-39 second laps, and our 2006 car (4 cylinder NA, manual shifter, no aero) with our current hotshoe runs about 39-40 second laps. If we cone down the course for practice to something much closer to an FSAE course, our go kart (clone motor = 200cc $100 Harbor Freight generator motor that makes something like 10hp) is likely faster than any of our 4 cylinder cars (we haven't taken lap times, but multiple drivers have driven similar configurations).

Charles Kaneb

04-16-2012, 11:18 PM

Originally posted by Z:
Charles,

Thanks for comments. Here are some brief responses.
~~~o0o~~~

1. The mandatory chassis safety parts (roll-hoops, side impact,...) form most of the chassis for the Twin-Beam concept. No more torsional stiffness is needed, because beams allow soft springs. I would not suggest adding any extra torsional "softness" to the chassis, again, because the soft corner springs already give enough softness. The advantages of longitudinal Z-bars is that they can give a completely soft twist-mode, even with a stiff chassis and stiff roll-mode, this latter being necessary with wishbones with small camber gain (long FVSA). Also the Z-bars make handling adjustments (ERMD) very easy.
~~~

yyyy
Wouldn't a car that's soft in twist be less responsive to changes in ERMD/LLTD? I remember hearing about some older cars that couldn't have o/s or u/s tuned out of them because the chassis was too soft in twist - would you have to make changes to the twist stiffness to get some changes out of this?
yyyy

2. I think the possibility for weight reduction by using beams over wishbones comes mainly from the much simpler chassis with its smaller number of hard points.

yyyy
If your front end is legal, you are one or two tubes short of having all the hard points you need for a double-wishbone suspension. A legal rear box will have almost all of them already due to the need to triangulate the rear roll hoop support loads back to the main hoop floor in all three dimensions. You can save a couple tubes at the cost of making it harder to get in and out by making the main hoop supports come forward, which will give you almost complete freedom to get rid of the rear structure.

Thinwall steel tube is light. There will be many roughly 70-lb frames at FSAE/FSAEW. Your main hoop, front hoop, and side impact bars make up about half of that by themselves.
yyyy

You say "A De Dion rear end is at least as complex as any double wishbone setup."

I have to disagree. I reckon a detailed study of a De Dion would have it roughly half as "complex" (time to make, etc.) as double wishbones. Likewise, there are many other simple suspensions that are almost never considered. The "proof" of this is that almost all FSAE teams use the completely unnecessary push/pullrods-&-rockers, so they are clearly not concerned by useless complexity, and make no attempt at "simplicity". Well, other than talking about "KISS". http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~

yyyy
Double wishbome rear end:
2x upper a-arms
2x lower a-arms
3 spherical bearings per a-arm
2x toe control links, with 2 spherical bearings each, for a total of 16 spherijoints.

Four Link/"full-complication" De-Dion rear end:
2x lower longitudinal links
2x upper longitudinal links
2x lateral locating wishbones with toe links (you can substitute 4x lateral locating arms if you please, and I'll accept that with a laterally stiff center slider for the De Dion beam you can eliminate two of them and still get good toe control)
1x De Dion beam with rigid attachment to hub carriers and some sort of in-out sliding mechanism in the middle.
Total: 2 spherijoints per longitudinal link, for a sum of 8. 4 spherijoints per lateral wishbone, sum of 8. 16 total spherijoints plus one to-be-designed in-out slider mechanism on the De Dion beam.

"Simpler" De-Dion rear end:
2x longitudinal links leading directly forward from the hub carriers, pivoted on broad roller or needle bearings at each end.
2x lateral links leading to the center of the car, pivoted on broad roller or needle bearings at each end.
1x De Dion beam that absolutely needs an in-out slider mechanism as your axle lengths will change a lot.
I will contend that you will not achieve adequate toe and camber stiffness with this design unless your bearing assemblies can be EXCEPTIONALLY stiff in bending across the rollers/needles. The first way I can think of to do this is to build them as two-bearing assemblies with a "kingpin" between them. These will have to be pressed in and kingpin deflection, wear, and fatigue are all well-known problems in many applications where they are used. Total of 8 joints, plus the slider.

3-link beam axle with Panhard bar:
2x longitudinal links, 2x joints each
1x Panhard bar, 2x joints
Total of 6 joints. Second-simplest decent rear suspension I can think of (the Texas World Axle is my secret for now)
yyyy

3. "Outside of racing and certain military off-road vehicles, there are very few vehicles where the main differences between success and failure are peak tire grip and controllability near peak tire grip."

Well, how about every farm tractor ever built.... and all the earthmoving machines....? http://fsae.com/groupee_common/emoticons/icon_smile.gif All of these rely on massive grip, so almost always have a completely soft twist mode. (BTW, to be successful in motorsport you just have to keep your sponsors happy, and back of the grid is no disadvantage.)

yyyy
Farm tractors are limited in lateral and longitudinal force capabilities by the possibility of rollover about either the X or Y axis. They have an interesting compromise to consider - a low center of gravity will improve stability, which will broaden the range of terrain they can operate on and increase their tractive effort, but a high ground clearance is useful to clear obstacles, and more suspension travel will improve control. A lot of the time additional grip available at the tires will not provide any useful benefit! I agree with you that tractors and earthmovers are applications where traction and controllability are important near the static and dynamic limits of the vehicle.
yyyy

"The garbage truck consisted of a torsionally flexible twin-rail chassis ... The chassis released its stored energy ... the rest of the truck wobbled back and forth..."

And therein lies the problem with providing a soft twist mode with a spring capable of storing a lot of energy. Better is completely soft, like tractors, forklifts, ride-on lawnmowers, etc., etc..
~~~

4. "...while the risks of moving to [a fewer-moving parts suspension] include possible disqualification, rules changes which would ban the car..."

Any comments from someone on the Rules committee???

yyyy
As drawn, you have moving front suspension arms inside the cockpit and a heavily loaded front suspension pivot - at the back of a leading arm no less - that is right under the driver's knees. With typical FSAE design that places the driver's feet a large distance in front of the front axle, it will be in very close proximity to a rather delicate part of the driver's anatomy.

A concept of mine, with a simple axle tube with its two bearings mounted in rubber blocks, was rejected by my team's Design Review Board as very likely to be ruled illegal on not having working kinematic suspension.
yyyy

"When we build [the standard suspension] we are not simply polishing a turd - we are selecting a design that has proven to be at least OK at its job and will not be banned or drop-kicked in design."

The sad part is that a "NO suspension" car would also be "OK at its job" in FSAE, but a lot easier and cheaper to build, and probably faster because lighter, more testing time, etc.

The really sad part is that you really are all "Polishing A Turd". And in building the "PAT" car very few students learn how real suspensions work, because real suspensions have to cope with real roads which have real bumps on them, whereas FSAE tracks are unrealistically smooth.

yyyy
A passenger car's suspension doesn't actually have to work over bumps! If ride, roadholding, and handling actually mattered in a passenger car, Citroen, Mazda, and Lotus would not always be on the edge of existence. Almost every consumer willingly accepts a car that rides and handles like crap.

If I'm designing a suspension that actually matters, I'll consider more scenarios than uniform roll, one-wheel-bump, and two-wheel-bump. The point here is to design a suspension optimized for a fairly narrow scenario - a generally smooth, generally level track with a decently uniform surface. A broader range of surfaces is encountered in SAE Mini Baja, and it would be a lot of fun to try to clean up there by considering the dynamics a lot more carefully than a typical MB team does.
yyyy

Z

Charles Kaneb

04-16-2012, 11:22 PM

Originally posted by mdavis:
Will,

We do a decent bit of our testing at a local kart track, and knowing a handful of guys that run the TAG classes (100cc 2 stroke, single gear karts), we know their laptimes around various configurations. On the big track (considerably larger and more wide open than a typical FSAE course), the fast TAG's run 38-39 second laps, and our 2006 car (4 cylinder NA, manual shifter, no aero) with our current hotshoe runs about 39-40 second laps. If we cone down the course for practice to something much closer to an FSAE course, our go kart (clone motor = 200cc $100 Harbor Freight generator motor that makes something like 10hp) is likely faster than any of our 4 cylinder cars (we haven't taken lap times, but multiple drivers have driven similar configurations).

The PAX index for (125/2t/415 lb) shifter karts is .952. The PAX index for FSAE cars is .989.

On a 60 second course, the world's fastest A-Mod would theoretically run 60 seconds. Maryland's FSAE car would theoretically run 60.66, and the fastest autox kart would be at 63 seconds.

As a former karter, I can categorically state that the karts used in autocross are some distance from the state of the art in karting, and that the cream of the crop of karting drivers is not represented. I'll try to prove that I'm not bluffing when I drag a ready-to-rip built ICC to an autocross and co-drive with the fastest ace driver I can find.

mech5496

04-17-2012, 12:32 AM

As any other design, there are up and downsides on a beam axle setup. The hard task is to identify the possibilities and flaws of each design, and then choose and go with the one that suits you better ACCORDING TO YOUR TARGETS. There is no thing such as "optimum solution". I am pretty convinced that a beam axle car can have similar (if not better) dynamic performance than a "conventional" FSAE car, and there are many examples out there that favor a simple-as-hell reliable car. A recent example I can remember of...

http://fsae.com/eve/forums/a/t...20065151#11120065151 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/24620635151?r=11120065151#11120065151)

Keep in mind that we are talking about GFR's 2011 car in comparison, which is one of the fastest FSAE cars out there. Also take a look at Rob's old school (Uni at Buffalo) and teams like ADFA, CalPolySlo, Mini Baja cars etc... http://fsae.com/groupee_common/emoticons/icon_biggrin.gif At least I was surprised! We might surprise quite a few in the not-so-distant future too...

rjwoods77

04-17-2012, 06:23 AM

BTW I looked up the results in 1996 from the Akron Bajamula and they finished 11th overall even after their fuel pump quit in the enduro. They ran a pure rotation swingarm for a rear suspension and just swapped the 18hp Briggs V-Twin for the spec Briggs single. Their baja car that year if memory serves me correctly was 320lbs and there is a 30lbs difference between the motors so they were probably at 350lbs for FSAE comp.

rjwoods77

04-17-2012, 06:35 AM

Dr. Paasch's post also really got me thinking that it would make a hell of a novel idea to do a Bajamula again but with Z's interconnected suspension utilizing front leading arms and rear trailing arms (2CV style) and just replace the "black box" or trailing/leading arm linkage configuration along with engine (45 degree leaned single and 90 v twin) in between events. It would make a much cheaper vehicle that would would be very competitive and be able to run dual competitions.

04-18-2012, 01:08 AM

Charles,

"Wouldn't a car that's soft in twist be less responsive to changes in ERMD/LLTD? I remember hearing about some older cars that couldn't have o/s or u/s tuned out of them because the chassis was too soft in twist - would you have to make changes to the twist stiffness to get some changes out of this?"

Big subject here, but briefly.

The issue of "not enough chassis torsional stiffness" started, in circuit racing, when wings caused the springs to become much stiffer to take the aero loads. So, for example, the race engineer might have wanted the front tyres to carry most of LLTD so he stiffened even more the front springs/ARB. But the engine, mounted at the back, kept "leaning" on the already stiff rear springs, transfering all its load (ie. most of the car's mass) to the rear wheels. The pop-rivetted aluminium chassis didn't have the stiffness to pass any of the engine's LLT to the front tyres. So oversteer always, even with completely rigid front springs.

However (!), way back in the early 1900s the chassis was deliberately made soft. The production car would typically have its large and rigid engine mounted at four points (2F-2R) to the twin-rail chassis to torsionally stiffen it, mainly to stop the doors rattling, windows cracking, etc. For racing the engine was mounted at three points, one at the nose and two either side of the rear bellhousing. This allowed the chassis to twist, which was useful for grip on the rough roads (which was not helped by the stiff leaf spring suspension).

This arrangement was quite similar to the top-left of the Z-Bar Sketch, with the sketch's longitudinal leafsprings being the chassis rails, and the centre structure being the engine. During cornering the engine "leant" on the centre of the chassis rails, thus distributing its LLT about equally front to rear. If the engine had its mounts with 2F and 1R, then all its LLT would go to the front wheels and there would be massive understeer (all else equal).

I believe a similar thing happens with go karts when the seat mounting points are changed? The driver is the largest mass, and if during cornering his weight is transfered, via the seat mounts, closer to the front of the chassis, then US. If more to the rear, then OS.
~~~o0o~~~

Regarding complexity of De Dion versus rear wishbones.

In both cases the engine/diff/halfshafts/stub-axles are the same.

I would NOT do a "sliding-tube" DD just to avoid plunging CVs. I would do a beam as in the sketch, but without the two inner bearings.

So,
1x largish, but simple, triangular tube structure for the beam,
1x heavy duty apex BJ,
1x P&S, as in sketch,
2x (optional) bolted connections at "beam-ends/uprights", for camber/toe adjustments.

Again, the chassis now only needs two accurately placed hard points on its centreline at floor level (using stringline to align these and front points), and two less accurate points for the spring-dampers. The problem with wishbones is that more points have to be located accurately in 3-D, and their preferred locations don't always match the chassis nodes (eg. upper side-impact tube has to be at Z = 350mm (memory?), which might not be the best kinematic location for the upper wishbone mounts).

(Edit: Oops! I forgot that a DD needs different side-view kinematics. The above list should be changed slightly, but overall the "complexity" (time to build) is about the same. I might do a sketch of this option one day. It can be done with only 3 chassis hard points for the rear beam (the P&S is dropped).)
~~~o0o~~~

"Farm tractors..."

Ahhh, I love my tractors... I better not bore you. http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~o0o~~~

"As drawn, you have moving front suspension arms [the front beam] inside the cockpit and a heavily loaded front suspension pivot - at the back of a leading arm no less - that is ...
... in very close proximity to a rather delicate part of the driver's anatomy."

I would have both front and rear beams mounted UNDER the chassis's floor. The BJs would be attached to chassis with vertical bolts in single shear, to act as "fuses". In a big impact the bolt fails, chassis remains undamaged, and the beam slides under the floor (or car slides over beam). This also makes mounting of underwings easier. (I have grown fond of the "family jewels", and would not risk losing them.)
~~~o0o~~~

"A passenger car's suspension doesn't actually have to work over bumps!
Almost every consumer willingly accepts a car that rides and handles like crap."

Agreed. Sad, but true.

In the past I have suggested getting rid of the mandatory "+/-1 inch suspension" rule, and just scattering a lot of bumps around the track (say, molded rubber "cowpats", 2-3m (10ft) diameter, 0.1m (4") high in the middle, and tapering to very little at the edges).

Teams can then build a cheap no-suspension go-kart and pay the penalty of driving around the cowpats (or launching over them!), or else build a car with good suspension that allows them to take the fastest racing line, regardless of bumps.

This could be a long term benefit to consumers of production cars.

Z

Dunk Mckay

06-26-2012, 03:11 AM

Originally posted by Z:
Important De-Dion note. The side-view kinematics, or anti-pitch, changes when the diff is chassis mounted. A layout as in the sketch, but with De-Dion, will have lots of pro-squat under power. This can be ignored with a low power engine, or a beam-centre bump rubber (aka "third-spring", or "lateral Z-bar", as mentioned by Harry above) can be used to limit squat (axle bounce) but allow roll. Alternatively, a different kinematic location can give anti-squat (higher pitch axis) while maintaining a low roll axis. This is a quite simple structural change, but will require a sketch to explain it properly...

Z

Z,
I might have completely misunderstood, my kinetmatics knowledge isn't great, but the pro-squat under power you talk about, is that due to the reation moment transmitted into the diff causing a rotation about it's axis. In which case displacing the diff decreases the effect this has on the chassis? For a moment there I thought I'd got it visualised in my head, but then I lost it, I need more experience.

I would love it if you could enlighten me. (If it sounds like I'm gunning for that sketch you mentionned, that probably because I am.)

06-26-2012, 06:53 AM

Originally posted by Dunk Mckay:
... the pro-squat under power you talk about, is that due to ...
If it sounds like I'm gunning for that sketch you mentionned, that probably because I am.
Dunk,

That sketch might take some time, so here's some that might help until then.

Figure 7 below illustrates "side-view antis" (eg. anti-squat under power, or anti-lift when braking) in terms of a suspension's "n-lines". N-lines are simply the lines "normal" to the direction of travel of any point in a linkage. Alternatively, the n-lines can be thought of as the directions of "no" motion.

Importantly, a suspension's n-lines are all you need to know, in order to understand its "antis".

In the figure the point being considered is the wheelprint (simplified to a point). Since the suspensions shown have only one degree-of-freedom (this needs more explaining, but...) the wheelprint can only follow a single, roughly up-and-down path. So the wheelprint has a "planar pencil of n-lines" that is perpendicular to its path of motion. (A "PP" is a bunch of lines, lying in a flat plane, and all passing through the same point, like the spokes of a wagon-wheel). Here we are interested in the particular n-line that also lies in the side-view (vertical-longitudinal) plane.

Importantly, in any linkage, forces can ONLY travel along n-lines. So, in the figure, any component of force acting on the wheelprint that lies outside of the plane of n-lines must necessarily be reacted by some other structure, which here is the spring-damper (not shown). So if the same arbitrary force acts on the wheelprint in all of the examples in the figure, then in each case the "component of force oustide of the n-line plane" will be different, so the spring-damper will be squashed to a different length, and the "anti" behaviour will be different.

https://lh5.googleusercontent.com/-cTTmIQ9a27Q/TvHQ24CoryI/AAAAAAAAAH8/VJHR8n6dYvo/s800/MechAntiFg7.jpg

Regarding an FSAE rear beam-axle, consider Figures 7a (similar to a "live" axle), and 7b (similar to a "De Dion" axle). In both cases consider the swing-arm pivot (towards top-right of each little sketch) as being much closer to ground, so well below the axle height. This gives similar side-view kinematics to my earlier "Twin-Beam" sketch, with the "apex BJ" = "swing-arm pivot".

Figure 7a now has a side-view n-line that is close to horizontal with only a slight rise to the front (right of pic). This gives a small amount of anti-squat.

Figure 7b (= De Dion) now has its n-line sloping quite steeply down to front. This gives quite a large amount of pro-squat. The question is how to push this n-line up-at-front, for a little anti-squat, while keeping the lateral n-lines close to horizontal, for good cornering behaviour. (Answer later...)
~~~o0o~~~

Meanwhile here is another figure that might help understanding of the distribution of wheelprint forces between the control-arms (ie. along their n-lines) and the spring-damper. Shown is a car accelerating longitudinally (eg. forward to right), but same principles apply for lateral acceleration (ie. cornering). Black arrows are the forces acting on the wheelprint or car. White arrows are some of the possible components of the black arrows. Fca = Control Arm force. Fsd = Spring-Damper force. H = Horizontal. V = Vertical. G = Gravitational. I = Inertial. F1,2V = Vertical forces on wheels 1 & 2. Etc...

https://lh5.googleusercontent.com/-arTDwLtqt_A/TuasCHP62vI/AAAAAAAAAHk/TMOt63WgDmc/s800/MechAntiFg10.jpg

(BTW, I uploaded the above pics somewhere (Picassa?) sometime ago, and I can access them easily via my old posts on this forum, hence this quick reply. New pics mean that I have to go shopping for a new cable for the old (perfectly good) scanner, or buy new scanner, or???, so will take more time.)

Z

Dunk Mckay

06-28-2012, 02:33 PM

That's awesome, really helpful, I can visualize it properly now.

Ok, so I've been pondering this twin beam-wing concept of yours, Z, since a friend suggested it a while ago. Starting at the rear wheels (front can come later, much later) I've been trying to figure out the best way be able to adjust camber and toe.

The best ideas so far are these:

-big solid uprights that mount onto the beam via interchangeable plates/spacers which have the camber and toe incorporated. The issue with this is that for stiffness these will have to be quite bulky. And even though you'll generally only need one setup for running the car you'll need to fine tune it to find that first, so you'll have to machine a large variety of parts to that kind of angular tolerance, which is gonna be costly (time or money or both).

-and upright mounted with a single B.J. at it's base to the beam end, then two adjustable tie rods between the upright and either arm of the beam. These of course will impede air flow (if only a little and above the wing), and load the beams such as they will be bent in the middle unless they are made fairly bulky as well. One also ends up thinking that perhaps double wishbones might not be that much more complicated.

Much as I'd like to say "stuff it" and come up with a design with fixed camber and toe, both design judges and the academic staff at my school would rip it out of us if we made that. I also think being able to find the ideal setup is not really something worth sacrificing for the sake of oversimplifying things.

Dunk Mckay

06-29-2012, 05:30 AM

Aha! I've just had another idea, and feel really stupid for not thinking of it in the first places, my normal work is obviously draining my brain.

Essentially, similar to the from beam ends on your original sketch, the beam forks with the top fork extending upwards. An additional arm would branch off forwards or backwards, and then a very light simple upright would mount to these three point via some Shim mounted BJ's. Still fairly bulky but...less aero disturbance and less complicated (calling it more elegant would be a push, no?)

EDIT- Three roughly evenly space branches (2 mottom one top) might end up more optimal, depending on loads and packaging issues for caliper mounts, provided you are mounting brakes outboard that is.

06-29-2012, 06:55 AM

Dunk,

The De Dion is my preferred option (the sketch shows a spool because of earlier discussions on "Suspension for Spool" thread). With a De Dion I would definitely have some means of camber and toe adjustment, both to correct for manufacturing tolerances, but more importantly to tune handling.

This is a good opportunity for some original detail design (at Geoff's "Reasoning..." Level 1), mainly because there aren't many examples to copy. I can think of several ways to do it that would add less than 1kg to the total weight, and I might post some sketches later.

Meanwhile, how about asking all your team members (even the newbies) to solve this "Engineering Design 1.01" problem:

Design a joint in the middle of a length of horizontal (70mm diameter? x wall thickness?) tube, so that an accurately adjustable "bend", in both planes (ie. camber and toe), can be put in the tube, and the joint has the same strength and stiffness as the original tube (in bending, torsion, etc.). Low weight, ease of manufacture, and ease of "bend" adjustment being priorites. Camber adjustment +/- 5 degrees in 0.5 degree steps, toe +/- 1 degree in 0.1 degree steps, or better.

Who knows? Maybe a newbie will come up with a cracker!

Your last edit seems close to my preferred idea, but details are important. Otherwise, think about a wheel bearing housing that can be adjusted for camber/toe inside a larger, concentric, clamping sleeve???

Oh yes, KISS! http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

Dunk Mckay

06-29-2012, 12:07 PM

Any team members still around are busy finishing off the car at the moment. I'm actually on an work placement, although I'll be taking a long weekend in a weeks time to go help them finish build before FSUK. I'll be managing next year so I'm planning ahead, getting some ideas together for when I go back in August.

Sketches of ideas are good, sketches are always good. I can't sketch very well however although my technical drawing is excellent, seems a little contradictory I know.

However I can CAD reasonably well. I've had a crack about your problem but I think I got carried away, I have a soft spot for U-joints for some reason (worked on driveshaft and CV joint stuff last year, no actual u-joints though).

http://img827.imageshack.us/img827/2876/ujointbendforz.jpg

There's not real scale or dimensioning as such, just the concept. Additional turnbuckle could make it stronger but would also fight each other if not adjusted properly.

EDIT--my grammar is terrible.

Dunk Mckay

07-12-2012, 09:42 AM

I'm back with another challenge for your "aero-above-all" concept, Z.

You say suspension should be soft, and it must have 1inch of travel. But with this, even over small bumps, or light breaking and acceleration, you're going to have chassis ride height changes. This means changes in height of the BJs, effectively the beams and therefore wings are going to rotate about the wheels axes, meaning the aero effect is going to fluctuate. Not as much, perhaps, as a fully sprung wings, but enough so that to avoid the risk of stalling you'll have to reduce your peak available downforce somewhat.

This of course is not a problem if you go for the more complicated single "undertray" concept, but for the twin beam-wing it does reduce it's ...potency.

ZAMR

07-12-2012, 10:55 AM

Originally posted by Dunk Mckay:
I'm back with another challenge for your "aero-above-all" concept, Z.

You say suspension should be soft, and it must have 1inch of travel. But with this, even over small bumps, or light breaking and acceleration, you're going to have chassis ride height changes. This means changes in height of the BJs, effectively the beams and therefore wings are going to rotate about the wheels axes, meaning the aero effect is going to fluctuate. Not as much, perhaps, as a fully sprung wings, but enough so that to avoid the risk of stalling you'll have to reduce your peak available downforce somewhat.

This of course is not a problem if you go for the more complicated single "undertray" concept, but for the twin beam-wing it does reduce it's ...potency.

From what I can tell from his drawings, the beam-wing concept has no ability to pitch (except for flex in the beams).

I would be more concerned with the performance of the rear "wing" since the front wing will act as an obstacle directly in front of it, diverting air up and over the rear.

-Zach

Dunk Mckay

07-12-2012, 11:14 AM

Sure it does, if the whole chassis can go up and down and the front and rear beams aren't interconnected (except via the chassis) then the front can go down and the rear up, and vice versa.

mech5496

07-12-2012, 11:27 AM

If I got it right, Dunk means that moving the front axle up would decrease the angle of attack of the underwing... I might be wrong here, but I think the chassis pitching would not affect the angle of attack of any of the underwings significally; there would be so little movement on the BJ's (especially with some amount of "anti's" built in) that I could live with.

Dunk Mckay

07-12-2012, 11:55 AM

Yeah, essentially. As I see it the height of your wings is going to depend on a small number of things:

-You want them as low as possible without stalling so as to induce the maximum amount of venturi effect.
-You can't have then initially fixed at that height because of compliance in tire changing the ride height, and the change in the angle of attack with suspension travel.
-The also have to fit around your beams comfortably enough to have some amount of adjustment once built, because nothing is ever made totally accurate (especially when you have a tight schedule) and CFD is far from perfect.

With a single underbody surface you really only have to worry about tire compliance and maybe a small amount of packaging around the beams, notably at the rear actually.

I'm not saying that you can't still get plenty of DF with dual wings. But that there is even more benefit to a full body "undertray" in comparison, and I'm not so sure about how much extra work it would be over twin wings either.
While the mechanics of a full body undertray (mounting, packaging, stiffening, etc) might be a little more complicated to design, I think the aerodynamic work involved in getting the two interacting wings to work well together could end up being equal to simply working out a good F/R aero balance (and method of adjustment) with a full body design.

In the "WINGS" thread I suggested a small rear wing to adjust rear DF based on the belief that underbody DF tends to have CP relatively far forwards, but it was a long time ago t hat i read this and I need to freshen up before pushing that idea any further. Of course the additional wing will induce more drag, but can also be used to improve underbody performance so perhaps not a terrible loss. This all really needs much more investigation, investigation I intend to do as soon as I get back to uni in August.

On the full body mounting subject, do you think a simple beam (on eon each side) with a BJ at rear and sliding BJ or even just a P&S at the rear could work?

mech5496

07-12-2012, 12:20 PM

I agree with Dunk in almost everything; in fact I find a full undertray much much easier in terms of designing, building and integrating, plus it has potential for much more aero downforce. To get the CP rearwards, just use a rear wing to also "pump" the undertray exit...

ZAMR

07-12-2012, 02:33 PM

Dunk, this is from Z on the second page:

Originally posted by Z:

The bottom line is that suspension Bounce (=heave) and Pitch modes only need very short travel. This is easily done with beams by having short travel (+/- 5mm) bump rubbers fitted at the mid-beam position. With these the chassis can be run very low with no scraping, so low CG, but there can still be plenty of wheel travel in Roll and Twist modes to keep the scrutineers happy. The soft Roll mode is, of course, no problem because no camber change, and the undertray doesn't scrape because it is beam mounted.

Z

-Zach

Dunk Mckay

07-12-2012, 04:28 PM

5mm at the mid beam position is 10mm at the BJ, which over a 500mm beam is a change in angle of 1.14°, considering you initial angle of attack is probably not going to be much higher than 10° and probably more like 5°, that's a significant difference, also if you assume 5mm at the midpoint of the wing, for something that probably on starts with 20mm ground clearance that's also a fair bit of travel.

This also raises the question of how the 2 inches of travel are officially measured when put in question, I realize teams have run beams before so it shouldn't be a problem, but this is probably a slightly different setup, so I'd like to clear up exactly what the legal limitations are with someone who's done it before.

As a refresher here's the 2013 draft rule, don't think it's changed.
T6.1.1 The car must be equipped with a fully operational suspension system with shock absorbers, front and rear, with usable wheel travel of at least 50.8 mm (2 inches), 25.4 mm (1 inch) jounce and 25.4 mm (1 inch) rebound, with driver seated. The judges reserve the right to disqualify cars which do not represent a serious attempt at an operational suspension system or which demonstrate handling inappropriate for an autocross circuit.

ZAMR

07-12-2012, 05:41 PM

I think 5 to 10 degrees is a little shallow for an FSAE car, but maybe its okay for this concept. However this begs the question of how much downforce this concept can produce?

I guess it just depends on how big this concept's front "wing" is and how low to the ground you can get it. If you have no bump, then the problem is mostly solved and you can run the wing practically on the ground.

Anyways I'm still looking at the picture on page 2 and I still don't see how the beams can move in pitch. If the BJs and the "P&S" are fixed to the chassis along the x axis, or some axis nearly parallel to it, the only movement allowed is roll in the x axis.

BJ = point constraint, P&S = axis constraint?

Maybe he should comment and clarify, maybe we're looking at two different pictures...

-Zach

Dunk Mckay

07-12-2012, 05:59 PM

The BJ allows the beam to move relative to the chassis in rotation about all 3 axes (x,y,z), All the P&S does is restrain the beam laterally, preventing rotation about the z axis, it is still free to rotate about the x axis (twist) and the y axis (up and down at the peg and slot). Front and rear beams are indepenant so push the back up and the front down and the front BJ will drop lower and the rear BJ will rise higher. Having said that the proximity of the BJ's to the centre of the car mean that in theory they shouldn't move too much and that most of the travel is done in the P&S and the dampers, but they do move relative to the ground.

ZAMR

07-12-2012, 06:29 PM

OOOOOOOOOOOOOKKKKK I see now, I was looking at the preload mechanism as having a cusp, isolating the bearing in the z direction.

So what happens then if you do constrain it or use extremely short bump rubbers? Mid-beam might refer to the point directly in front of the P&S (reduce movement from 10mm to 5mm, or even less, reducing the angle of attack change to ~0.5 degrees. Should be allowed right? The wheels can still move up and down 1 in (albeit in roll or twist).

-Zach

Dunk Mckay

07-13-2012, 01:58 AM

Yeah, well that was my concern. I'm guessing it should be fine as beam axles have been used in the past under this rule with no concern. I was thinking that they were not the same as these, but from what I can tel WS10 had a front beam restrained with a BJ and P&S, albeit with a different steering mechanism, but that shouldn't change anyything.

mech5496

07-13-2012, 04:35 AM

This definitely need a clarification on HOW the suspension movement is measured, as I have mentioned before in this thread. In all competitions I have attended since 2007, one of the scrutineers just pushed down the chassis (usually by jumping on the jacking point) and measured the difference in ride height (chassis to ground). In that case, the aforementioned solution would not work as the suspension would seem to have an operating range of 5 or 10mm... Note here that in 2010 we were forced to change to much softer springs for the scrutineering in order to pass the 1" rule...

Dunk Mckay

07-13-2012, 07:17 AM

I would generally prefer to have the jacking bar attached to the beam itself, keeping as much of the chassis as forward as possible, the most rearward point being the P&S. In this case there will be as much travel as there is tyre compliance and I'm pretty sure that tyre compliance doesn't count as part of the 1".

I'm ok with changing to softer springs for scrutineering to demonstrate that the travel is there, so long as they are ok with the fact that it most likely won't be running with those springs on the car.

Dunk Mckay

07-13-2012, 06:06 PM

An additional thought that's stopping me from sleeping as I roll it around inside my head, is how, with a full undertray, you allow for twist in the suspension. Would you just let it be taken up in the flexibility of the undertray?

Separate side and middle sections? Stiffer side sections and a flexible inner section? That is assuming you're going to get less DF down the middle because of packaging for chassis, nosecone, engine, jacking bar in the diffuser section, etc. Or perhaps separate front and rear sections with a flexible membrane between the two (very tricky and probably a poor solution as it will change in shape as it is sucked down, you'd need to be very clever to make it work properly).

07-13-2012, 08:32 PM

Dunk, Zach, Harry,

A few issues to cover, so I'll do it by subject.

Peg and Slot.
==========
This acts as a lateral n-line between beam and body. As Dunk said, it is meant only to constrain y-axis movement, while allowing all other DoFs.

So similar to a Panhard bar, except that always horizontal wrt beam (because the "contact normal" is always perpendicular to the slot edges). The end of a Panhard bar moves through an arc so there is always some lateral (y-axis) movement of the beam wrt body, which then results in steer changes. Bump steer not good, but given the minimal bumps in FSAE, a Panhard bar may be tolerable.

Many other lateral control methods are possible, but the P&S is reasonably simple, compact, and symmetric (everything is on the car centreline). It is suitable for the short travel, clean conditions of FSAE, but not for off-road racing(!), or even production cars. The two ball bearings (which rotate in opposite directions during movement) and the preloaded vertical plates (one per ball bearing, and preferably with hardened rolling face) give low friction, rattle free control. A "plain" round peg in a vertical slot has higher friction, and eventually wears and rattles.
~~~o0o~~~

Heave and Pitch Control.
==================
The "mid-beam bump rubbers" I suggested would mount between the body and the "P&S-bracket" on the beam. So they would restrict travel of the peg in the slot. Details to suit... http://fsae.com/groupee_common/emoticons/icon_smile.gif ... although compliance with Scrutineers' whims is important.

One approach may be to use "preloaded coil springs" to control the vertical movement of this middle part of the beam. The beam has +/-5mm of free travel before contacting these springs (in either up or down direction). Once contacted the spring requires its preload to be overcome, say 60kg(?), then it moves at its spring rate, say 20kg/cm. So 5mm travel for any load up to 60kg, then 25mm travel for 100kg (scrutineer jumping on body). Plus the load due to the (soft) corner springs.

I do NOT think heave or pitch will be a problem aero-wise, but if it is, then simple fixes (Plan B!) are possible.
~~~o0o~~~

Aero Effects of Beam-Wing Pitch Changes.
=================================
A very important point here is that wings flying very close to ground have very different characteristics to wings up in the air. Throw away the aeroplane wing profiles!

Briefly, the trailing-edge height and slope determines (roughly) the mass flow under the wing. The minimum ground clearance (say 20-100 mm, depending on testing?) then determines the air velocity, and hence maximum suction. An aeroplane wing has max suction at its nose, but the beam-wing, as drawn, has max suction at the narrowest ground gap (ie. near mid-chord of the main element, near the axle line).

So, roughly speaking, if the TE is normally at Z = 300mm, but then drops 30mm due to downward body heave, then downforce drops by ~10%. BUT! this is compensated somewhat by the body putting extra downward load onto the tyres via the springs.

Furthermore, the flaps can be connected via a simple linkage to the body so that they change AoA according to position of the body wrt beam. So whenever the body heaves upward, suggesting lower spring loads, the flaps increase AoA. So during cornering the body roll will cause more downforce on the "inner" sides of the wings, counteracting LLT. But maybe leave this for second+ year...
~~~o0o~~~

Front Wing Obstructs Rear Wing.
==========================
Keep in mind that the front wing has double flaps (hence double-slots), and the main element is essentially horizontal. The two slots and the underwing gap will feed a lot of air to the rear wing. Just keep the front wing (mainly its flaps) well away from stall.

To repeat a point in the previous section, an aeroplane wing has a small region of maximum negative Cp (Coefficient of pressure) at its nose. At high lift this Cp approaches -10. A ground effect wing can have a similar suction (ie. low Cp) over a much larger area of its undersurface. (Hint: hence the largish, approximately horizontal main element.) Bottom line is that the front wing doesn't need to run near stall to do its job.

Note also that military fighter/bombers always carry their stores (ie. bombs. missiles, fuel tanks, etc.) on the high-pressure underwing side. This equates to the upper surface of a racecar wing, because upside-down. Putting obstructions on this high-pressure side of a wing has little effect on the wing's lifting performance (some arguments say that lift is improved, "vortex theory of lift", etc.)
~~~o0o~~~

One Piece Undertray.
================
Here is one approach.

First remove the front wing from the "Twin Beam-Wing" car (keep the front beam!). Next extend the rear wing's leading edge, at the car centreline, to the nose of the car. Keep the outer ends of these LEs at the front of the rear wheel-pods. The rear wing is now a large triangle in planform with its apex at the car's nose, like a "DeltaWing".

The front part of this DW undertray hangs from the centre of the front beam, via a single short ball-ended link, to allow for freedom of movement between front and rear beams. The rear of the DW is attached to the rear beam via two ball-joints, one next to each rear wheel, allowing the beam to pitch independently of the DW. The DW is thus suspended at only three points (2R, 1F), so can be made rigid without constraining the suspension in any way.

Next add two small "trim wings" to the front beam, similar to the sketch but smaller, and perhaps a bit higher, so just above the DW undertray. These are used to adjust aero balance by adding a bit more front downforce, because most of the plan area of the DW is towards the rear.

The under surface of the DW can be smoothly curved, or it can have "tunnels", or something completely different. All options, if done right, will work well. I might post on the "completely different" option on the "WINGS" thread, when time allows...
~~~o0o~~~

How Much Downforce?
==================
Bottom line is that I reckon it should be very easy to get Cp = ~ -4 over about 1m^2 of the under surface of the two Beam-Wings (say 0.4m^2 front, 0.6m^2 rear), with negligible drag.

At 15m/s (54kph, 33mph) this gives Force = 0.6 x 15 x 15 x 1 x -4 = -540N = ~54kg. Add to this other (lesser) negative pressures on the rest of the under surface, plus small positive pressures on the upper surface, and you are off to a good start. Because Cp = -10 is entirely feasible! http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

Gruntguru

12-14-2012, 10:38 PM

Originally posted by Z:

http://i16.photobucket.com/albums/b33/john-bucknell/ZBARFSAEsmall.jpg

Z
Z, not sure if you noticed, but the 2012 UWA car is in fact your "Z-Bar Concept" drawing shown at top left. The differences are : "Centre-pivot Leaf Springs" replaced by the aero undertray acting as twin rocker-beams and also restraining the beam axles' rotation in the Y and Z axes. An ARB acts at the "centre-pivot" locations (as you mentioned in the "Suspension Design" thread). The "Monoshocks" are replaced with an innovative "W" spring which provides lat' and long' location in addition to springing. Dampers are located at each wheel.

This is a very clever and innovative car with a very low suspension component count and one major suspension component doubling as an aero undertray. This design and future iterations are capable of great things.

12-16-2012, 06:29 PM

Originally posted by Gruntguru:
Z, not sure if you noticed, ...
...
This is a very clever and innovative car with a very low suspension component count and one major suspension component doubling as an aero undertray. This design and future iterations are capable of great things.
GG,

Indeed it is!

Yes, I recognised it straight away. I would really like to see UWA finish this car and perhaps get it over to some Northern hemisphere comps next year. Any chance? Certainly, I hope future UWA teams continue with the concept.

To restress what you said above, it is a VERY SIMPLE CONCEPT, with a minimal part count. So much so that I doubt anyone would have believed it could work if it was only suggested as an "idea" on these pages... http://fsae.com/groupee_common/emoticons/icon_smile.gif

Proof that the concept works, to some degree at least, is one of Rex's (?) photos on the Facebook page that shows the car parked with one front wheel on top of a couple of red and blue boxes, about 10-15 cm high. All other wheels are still firmly on the ground!
~~~o0o~~~

To any interested teams currently running conventional suspensions.

Some of the UWA concept and the Z-Bar sketch above might be combined to retrofit a fairly simple soft twist-mode suspension to a conventional wishbone car. This is something you might do to a previous year's car as a research project.

First, remove all normal springs (dampers can stay). Then, looking at bottom right of sketch, at front and rear of car fit lateral Z-bars to control heave and pitch only. These might be lateral steel or glass/carbonfibre leafsprings as shown, or else any conventional "third spring" arrangement. These do the job of UWA's "W" springs (silly me, thinking they looked like "E's"!), although the W's also provide axle location (clever!). Next fit an unsprung undertray, somewhat like UWA's.

The chassis is now only supported like a bicycle (with single spring at front and rear), so wants to fall over whenever going around corners. So fit a SINGLE lateral U-bar at about mid-chassis with its outer ends connected to the undertray tunnels, thus preventing body-roll (search Rex's photos). During cornering the body leans on this single ARB, which in turn pushes down on the outside tunnel, and lifts the inside tunnel.

These roll forces (up on inner, and down on outer tunnel) are passed on to their respective wheels by the tunnels acting as "balance beams". So LLTD (= ERMD in above sketch) is determined entirely by the geometry of the linkage (specifically, the ARB/tunnel attachment points), and not by any spring rates, or by any bumps or twist in the road.

Note that in the above sketch (bottom-right) there are two longitudinal torsion bars, acting as Z-bars, that control both heave and roll. This layout is well suited to production cars because of the easy packaging of the torsion bars, which are conveniently the right size to carry most of the car's weight (ie. heave loads), as well as the roll loads. The UWA single lateral U-bar is a simpler solution, although it does require the undertray, or some sort of side balance-beams to work.

Z

rwstevens59

04-06-2014, 04:03 PM

I am new to the fsae forum and have found a wealth of information here.

To clarify, I am not involved in fsae as a participant, judge or consultant.

I am a Tool and Model designer in industry by profession who spends his free time working on suspension analysis and tuning for lower level oval track race teams in the northeastern region of the United States.

I have been perplexed for quite some time on one particular point of the classical or the static analysis of a live beam axle suspension in common use in the arena I am working in and was hoping someone on this forum may enlighten me.

The problem:

A race car with beam axle suspensions both front and rear.

The main sticking point is the analysis of the live rear axle laterally restrained by a very short (approx. 18 in.) panhard bar offset to the right of the vehicle centerline as viewed from the rear. The panhard bar attaches to the axle just to the right of the axles centerline and to the sprung body just inside the right rear wheel as viewed from the rear. The overall height of the bar is adjustable relative to the axle centerline or ground as you prefer. The bars angularity is cockpit adjustable by the driver while the car is in motion. If we assume the bar to be set level at axle centerline height the range of adjustability is 10 degrees up from axle to chassis to 10 degrees down from axle centerline to chassis as viewed from the rear. The adjustment takes place at the chassis mount of the panhard bar via a vertical 'lead screw' and captive block assembly.

The remaining rear axle degrees of restraint are two parallel trailing links mounted solidly to the rear axle below axle centerline height (approx. 6 in.). The final restraint needed is for axle housing rotation about the y-axis which controlled by a torque arm from the live axle center section (gear housing) to a linear bearing 'sled' with large heim joint being used to attach the torque arm to the chassis i.e. one degree of restraint of the arm rotation about the lateral axle centerline.

The constraints in this form of racing:

There is no data acquisition.
There is no tire data.
The track surface may be pavement or dirt.
There is so little testing time it might as well be considered negligible.
There is no practice time to speak of.

You are left with driver feedback, observation, and possible video and thought to analyze possible setup changes.

My approach to date has been a simplistic 'classical' roll center based model to evaluate front and rear wheel pair loads to have a look at what limit behavior might be at assumed steady state lateral and longitudinal acceleration levels i.e. make spring changes or suspension link geometry changes (IC position changes) assume a 'g' level and calculate (spreadsheet) the front and rear tire pair loads.

The problem I have had with the 'roll center', 'shear point', control point type of analysis, name your favorite author here, IS the location of that point with the short offset panhard bar with angularity described above.

All of the classic texts I have (RCVD, Dixon, Olley etc.) say that with a basically planer linkage as I have described is that the roll center (for lack of a better term) is located where the rear axles axis of rotation as defined by the axles locational linkage pierces the lateral rear axle wheel pairs vertical plane. For the linkage I describe the rear 'control point' is always taken where the panhard bar crosses the vehicle centerline plane.

I see no kinematic nor force based reason for this to be the case and as Dixon points out the rear axles axis of rotation is a piece of engineering fiction useful in locating the notional roll center or force coupling point.

Well, the panhard bar does not cross the vehicle centerline in this case, what to do?

Consult Mark Ortiz.

In Mr. Ortiz's view the roll center can be located in this situation by one of two methods. The first he describes as the simple method of finding the intersection of the panhard bars centerline with either the vehicles centerline or longitudinal CG center plane if the car is not symmetrical and to neglect the internal jacking force and use that point as the roll center. The second he describes as the more rigorous method and uses the panhard bars mid-point to fix the roll center height but also says to include the internal jacking force caused by axle to chassis bar angularity in your calculations and to make the mid-point of the panhard bar the point for this jacking forces vertical point of application.

I have a great deal of respect for Mr. Ortiz's openness in answering any and all questions and agree with much of what he has written about asymmetric race cars but again I can find no kinematic or statics (force based) reason that makes the panhard bar mid-point any more 'special' then any other point.

When looking at this problem from a 2D statics point of view you come to realize that the panhard bar is simply a two force link attaching the beam axle to the body and if you free body diagram the body then the panhard bar force line of action 'on the body' is simply the bars angle and you could decompose that force anywhere along that line of action. (Yes, a Z n-line) So no point is 'special' from this point of view.

Two questions to the forum if I may:

1. In the situation as described where would you take the roll center height for a classical treatment and more importantly why?

2. What would be a better approach to getting a high level view of the effects of the short panhard bars position and angularity with respect to wheel pair loading with an assumed steady state lateral loading?

As one last point of observation I have worked with six different drivers two of which have been multi-time champions in this form of racing and only one of the six can describe the effects he feels when he has adjusted the bar past the point of a positive effect.

Thank you,

Ralph

nowhere fast

04-09-2014, 11:55 PM

Ralph,

This is an interesting question, as I haven’t dealt with asymmetric cars before. The following is based solely on my own reasoning, so corrections are welcome.

Normally for most suspension types the roll centre is found by making a few simplifying assumptions: the linkage is reduced to a purely planar linkage, and the tyres are pin jointed to the ground at their contact patches. The only way the chassis can move when these assumptions hold true is by rotating about the roll centre. When considered in plane; a beam axle located by a Panhard bar does not restrict the chassis to rotate about a single point (Panhard bar can rotate relative to the beam, and the chassis can rotate relative to the bar), so the concept of a geometric roll centre becomes grey.

There is also a different force based definition of the roll centre as a point where lateral forces can be applied to the chassis without causing roll. After drawing up a quick FBD I think that the point found from the intersection of a line through the Panhard bar with a vertical line dropped from the CG satisfies this definition if you assume the car is sprung such that the chassis will not roll if a vertical load is applied at the CG. Note though that this definition accounts only for a roll centre height, and does not consider a lateral position for the centre.

This would be easier to explain with a picture but bear with me. We want to apply a lateral force to the chassis, this force will be reacted by the horizontal component of the Panhard bar force. There will also be a vertical component to the bar force if the bar is not horizontal because the bar force must be aligned with the centreline of the bar.
This component will either increase or decrease the load carried by the suspension springs; the change in the spring loads can be represented as a single vertical force passing through the CG because we have assumed that the applied force does not cause roll, and that vertical loads passing through the CG do not cause roll.

Now we have 3 forces introduced by applying the lateral force. These must sum to zero and produce no roll moment for equilibrium. The bar force and the spring change force can be slid along their lines of action to the point where they intersect. We can see now that the lateral force must be applied at the height of this intersection in order for the 3 forces to cancel without introducing a roll moment. Therefore this intersection defines the roll centre height.

If for some reason the position where vertical loads could be applied without introducing roll was not aligned with the CG; then the roll centre height would be determined by the intersection of the bar axis and the line where vertical loads can be applied without causing roll.

The roll centre height depends only on the location of the chassis Panhard bar point, the angle of the bar, and the location of the line where vertical loads can be applied without introducing roll. The length of the bar will only influence how this changes with suspension movement, shorter bar = more change in bar angle for the same movement.

rwstevens59

04-10-2014, 09:38 PM

Nathan,

I would say your line of thinking very much parallels my own and is correct when using the classical roll center based model. I arrived at the same conclusions a while ago after exhausting a purely kinematic approach.

The only difference would be that I would say that with a FBD of the body the angle of the panhard bar sets the line of action of the combined vertical internal (to the system) jacking force and the horizontal force at the body mount point form a resultant force that can slide anywhere along the LOA set by the panhard bar at any instant in time. This resultant force can be again decomposed at any point along the line of action and have the same effect on the body. At any point chosen. Thank you Z.

I agree with your reasoning that for the roll center based model that this point should be at the point where the vertical component produces pure heave. For all text book models the examples all place the CoG on the vehicle centerline and assume equal left and right spring rates equidistant from the centerline. I also agree with your reasoning that if we were to add, let's say, spring split that the pure heave point decomposition point would move to the vertical line of the spring center, I think.

I just wish the most regarded texts on this subject would make it clear that this is a force based concept and not obscure this fact by mixing in the kinematic notional concept of the live axles roll axis. A useful concept I guess for picturing roll over or under steer but confuses the issue of a force coupling point for a panhard bar system in particular. Dixon comes closest to a force based description if you read his words very closely but is still making a strong reference to link geometry analysis and the notional axle roll axis.

I am now using a purely FBD and force based approach with a lot of help from correspondence with Z. I can tell opinions vary on this forum, but you must admit the man knows his classical mechanics and his insistence on rigor is correct in my view.

Thank you for your reply,

Ralph

04-19-2014, 12:40 AM

Ralph and I exchanged some PMs prior to Ralph's first post here (on previous page). Nathan seems to have grasped the gist of the problem in his answer to Ralph's question (also previous page). That is, DON'T FORGET the jacking force (Fz) component of the Panhard-Bar force!

For any students interested in these sorts of problems, here are some more general comments, from an "Old-School Mechanics" perspective.
~o0o~

First, a summary of the problem.

Originally posted by Ralph:
... The main sticking point is the analysis of the live rear axle laterally restrained by a very short (approx. 18 in.) panhard bar offset to the right of the vehicle centerline as viewed from the rear. The panhard bar attaches to the axle just to the right of the axles centerline and to the sprung body just inside the right rear wheel as viewed from the rear. The overall height of the bar is adjustable relative to the axle centerline or ground as you prefer. The bars angularity is cockpit adjustable by the driver while the car is in motion. If we assume the bar to be set level at axle centerline height the range of adjustability is 10 degrees up from axle to chassis to 10 degrees down from axle centerline to chassis as viewed from the rear. The adjustment takes place at the chassis mount of the panhard bar via a vertical 'lead screw' and captive block assembly.
...
The problem I have had with the 'roll center', 'shear point', control point type of analysis, name your favorite author here, IS THE LOCATION OF THAT POINT...
All of the classic texts I have (RCVD, Dixon, Olley etc.) say that with a basically planer linkage as I have described is that the roll center ... is located ... where the panhard bar crosses the vehicle centerline plane.
(My emphasis added.)
~o0o~

One of the keys to solving this type of problem is to appreciate that FORCES and MOTIONS are entirely separate things. A SINGLE, given problem (say, the one above) has TWO entirely separate answers, depending on whether FORCES or MOTIONS are sought.

Unfortunately, the suggestion in the "classic texts" that a single "The One-True-Roll-Centre" point can be used to solve both types of problems is shear nonsense. Even worse is to suggest that the "forces problem" can be solved by finding "The One-True-Force-Application-Point" (as always ... groooaann!!! ... education down the crapper!!! ... blah, blah, blah... :)).

However, this problem, being one of the Dynamics of a very simple mechanical linkage, is very easy to solve using the methods of Old-School Mechanics. Briefly, the problem can be divided into 3 parts, corresponding to the 3 sub-fields of Mechanics.
1. STATICS - Analysis of Forces acting on bodies.
2. DYNAMICS - Here, by using D'Alembert's Principle, showing the centrifugal Inertial-Force (say, Fi) as just-another-force that acts on the car-body in the Statics FBD.
3. KINEMATICS - Based on the changes in Spring-Forces (due to changes in Fi) in the above Statics diagram, determining the subsequent Motion of the car-body wrt live-rear-axle.

To quote Ralph (again with my emphasis):

From Ralph in a PM:
My biggest Aha moment in all of this so far has been the tearing down of the wall I had built up in my mind between my knowledge of classical Newtonian Mechanics and what I thought I was learning from the vehicle dynamics texts. For some reason I was treating VD methods as something new and different.

The following notes do not go through the full solution of the problem above, but only re-stress a few points that "all school-boys should know", but currently do not seem to be taught very well, if AT ALL... :(
~~~~~~~~~~o0o~~~~~~~~~~

FORCES.
=============
Key point here is that forces are "SLIDING" VECTORS that can be considered to ACT ANYWHERE ALONG THEIR LINES-OF-ACTION. (Because of the failed education system, this requires endless re-stressing...)

So, as pointed out by both Ralph and Nathan, the Panhard-Bar is simply a link that transmits equal-and-opposite forces between car-body and live-rear-axle. The LoA of these forces is the centreline of the PB (or more accurately, the line through the centres of the Ball-Joints at each end of the PB, neglecting friction in the BJs). So the PB force from-axle->to-car-body, say Fpb, can be considered to act ANYWHERE along this LoA.

Nathan suggested that a good point to do calculations for this force is on the LoA directly below the CG. This way the "Heave" of the car-body is easier to calculate, because the vertical component of Fpb, say Fpb.z, acts directly through the CG. Quite true.

But it is very important to realise that calculations at ANY point along the LoA ALWAYS give the same answers (when done correctly!). So the answers are the same whether the "FAP" is ten miles to the left of the car and one mile above ground, or a squillion miles underground and ten squillion miles to the right of the car.

As just one example, it is worth considering the effect of Fpb on the car body when it "acts at a point" on its LoA that is at the same height as the CG, but offset somewhat sideways. Now the horizontal component of the PB force, say Fpb.y, directly counteracts the Inertial-Force Fi, while the vertical component Fpb.z acts on its horizontal lever-arm to both Heave and Roll the car-body.

Putting all this another way, beware of anyone who suggests that their particular "Force Application Point" is better than any other (ie. don't trust them!).

All the above should be obvious from the definition of, and understanding of, a "Moment". Namely, a Moment is the vector you get when you take the Vector-(Cross)-Product of a Force-Vector and Displacement-Vector.

But nowadays students are not even taught the difference between Couples and Moments.

So ..... more ranting in next post... :)

Z

04-19-2014, 12:44 AM

COUPLES and MOMENTS.
======================
These are two very different things. Here is how I described them in a PM to Ralph (slightly editted).

"The important difference between "Couple" and "Moment" is (IMO, and also in the older teachings):
* A "Couple" is a forceful ACTION applied to a body, namely a "twisting or rotating force" (hence often with "T" (Greek Tau) for Torque).
* By contrast, a "Moment" is an EFFECT of a system of forces, capable of being calculated or measured at a particular Point, but it is NOT THE ACTION itself.

Note that it is easy to have "the Moment M, of a single Force F, at a particular Point P". However, it is impossible to generate a purely rotating force by using only a single linear force. Instead, for that "purely rotating force", you need at least a "Couple of Forces" (ie. two or more forces such that they amount to "two equal magnitude and oppositely directed forces on non-coincident LoAs")."

This is illustrated in this pic.
https://lh4.googleusercontent.com/-IEGayrpsDGE/U09M2ByMhKI/AAAAAAAAAQI/3J514PYyf-Y/s600/MAccFg6.jpg

"Also the Moment of a single linear Force is, in general, different at different Points (although with axisymetric distribution, with greater Moment the further away P is radially from the Force's LoA). By contrast, the Moment of a Couple is ALWAYS the same, no matter at which Point you measure it. So Forces are "sliding vectors" (can be drawn anywhere ALONG their LoAs, but NOT OFF the LoA), and Couples are "free vectors" (can be drawn ANYWHERE).

There are other subtle details, and it all requires a lot of practice, and more rigour than is common these days... I admit that sometimes I get sloppy in my writing and use the wrong word/phrase(s). But for better understanding I think it important in examples such as yours directly above to think more in terms of Couples, and less in terms of Moments.

So, (briefly) if you want to move all your linear Forces to the CG, then you calculate their Moments at the CG (calc'd with the Forces on their original LoAs), THEN move the Forces to CG, and THEN also ADD A COUPLE to the system that is equal to the sum of all the Moments. (Subtle point, but the Couple can be drawn acting anywhere, although drawing it at the CG is just as good a point as any other.)"

This last paragraph about moving forces AWAY FROM their LoAs is illustrated in this pic.
https://lh4.googleusercontent.com/-E3bVIjCyQyM/U09NKceHZdI/AAAAAAAAAQQ/HhqxarzcECs/s600/MAccFg3.jpg

In Figure 3a, a force F1 acts on a body. We want to know what changes to the picture must be made if a SIMILAR force to F1, say F2, acts at point P on the body (ie. F2 has the same magnitude and direction to F1, but is on a LoA passing through P).

In Figure 3b, "NOTHING" is added to the picture, in the form of two equal magnitude but oppositely directed forces F2 and -F2, with both acting along the same LoA that passes through P.

In Figure 3c, the two forces F1 and -F2 are replaced by the Couple T. The magnitude and direction of T are found as shown, and as noted above it can be drawn anywhere (ie. it is a "free vector").

Note that when doing such "geometrical calculations" the manipulations can go from a->c, or from c->a. Also, adding "nothings" to the picture, in the form of two equal and opposite forces, is very useful (eg. it can help keep all the calcs on the page). The whole process is very similar to algebraic manipulations, with, for example, "add +X and -X to LHS of equation, then ...", etc.

But the geometric approach gives a much better visual feeling for what is happening. The map is much closer to the terrain. The more abstract algebraic approach, developed by Descartes in his "Analytic Geometry", used to be called "cogitatio caeca". Literally, it is "thinking blind". It is the use of a bowl of alphabet soup to represent a spatial, physical, problem.
~~~~~o0o~~~~~

Here is another pic showing how one Couple of Forces with large magnitude but close spacing in Figure 4a, can be transformed into another EQUIVALENT Couple of Forces with smaller magnitude and wider spacing in Figure 4c.
https://lh5.googleusercontent.com/-ORos379dVP8/U1B1xDwUcqI/AAAAAAAAAQg/aTB_PjU-YTI/s600/MAccFg4.jpg

Note the arbitrariness of the positions and directions of the two Couples, and hence their "freeness". Also note the repeated sliding of forces along their LoAs, and the addition of "nothing" to move the calculation along. Lots of practice with these types of geometrical vector manipulations makes VD a very simple subject.
~~~~~o0o~~~~~

As a final note, for anyone who thinks that all this "let's draw play-school pictures" stuff is too childish for grown-up Engineers, then NOT SO. The above geometrical approach was developed hundreds of years ago (1600s+) along the same Axiomatic-Deductive lines as Euclid's Elements. And so too, originally, was Descartes' algebraic approach. So both are equally rigorous approaches to solving physical problems.

But nowadays very little of the foundational stuff of the algebraic approach is taught (except, perhaps, some "Set Theory" waffle). So the students effectively enter the movie theatre half-way through the show, and come out thinking that "Couple" and "Moment" are the same person. All the rigour has been tossed out the window, and instead it's "like, ...whatever...".

And then they look at the car in front of them, and at their bowl of alphabet soup, and they can't make sense of any of it...
~o0o~

Still a bit more ... :)

Z

04-19-2014, 12:47 AM

Last bit regarding Ralph's post on Panhard-Bars/Speedway-Cars on previous page, and solutions using Classical Mechanics.
~o0o~

DYNAMICS.
============
The main point I want to stress here is that the use of D'Alembert's Principle can turn an apparently difficult problem in Dynamics into a very simple to understand picture in Statics.

As per Newton's Axioms of Motion, the resultant of a system of forces F, acting on a massive body m, for a short period of time dt, CAUSES a change in "the quantity of motion" (<- Newton's wording, but nowadays called Momentum P) of the body dP.
So, F.dt causes dP,
or F -> dP/dt,
(or, very sloppily, F = m.dV/Dt = mA).

Since Momentum is a vector, it can be drawn in the same way as a Force. So the arrow representing the resultant F of the system of forces acting on the body (for the short period of time dt) can be over-drawn with an arrow representing the "change in Momentum" dP.

(And BTW, I suggest that this is how your VD simulation programs should be structured. Namely, a time-stepping process with forces acting on the body for time dt. Then consequent "changes in quantity of motion" at the end of each dt. Then adjust forces based on new motions, and repeat.)

Anyway, a disadvantage of the above approach is that when it is drawn as a FBD it shows a bunch of forces pushing on the body, say the road-to-tyre forces pushing leftward, and then only a dP vector at the CG that points in the SAME direction. How do these arrows, all pointing leftward, cause the suspension springs to be squashed out of their original (static) positions?

The way to get better understanding is simply to replace the dP vector with the equal sized, but OPPOSITELY directed, Inertial-Force Fi. Now the FBD shows the road-to-tyre forces pushing leftward (and upward), and the Inertial-Force at the CG pushing rightward (and gravitational force Fg acting downward). Now it is quite obvious, visually, why the springs compress or extend as they do, and the body Rolls and Heaves as it does.

Note that in this picture (ie. FBD) the spring forces are internal to the system, acting between car-body and live-rear-axle. The inclusion of Fi in the diagram provides the last bit of external information needed to solve for the internal spring forces. But if no Fi in the FBD, then no solution possible.
~~~~~~~~~~o0o~~~~~~~~~~

KINEMATICS.
================
(Again, for simplicity, consider this only a 2-D, rear-view problem of Ralph's car with Panhard-Bar.)

During cornering, where is the Kinematic "Roll Centre", or "IC", of the car-body's MOTION wrt the live-rear-axle?

Note that this problem is a lot simpler than the case with independent suspensions. As covered elsewhere (Search for "Where is the Motion Centre?" sketch) it is futile trying to find an independent suspension's "Kinematic RC/IC" of the car-body, either wrt the ground (because it depends on how much the tyres slide), or wrt the wheelprints (there are two of them!).

But here there are the two bodies (ie. car-body and live-rear-axle), so an IC can always be found. Conveniently, the two bodies are connected with the roughly horizontal, rigid but BJ-ended link, the PB, and the two lengthwise-flexible Spring-Dampers, taken to be mounted vertically between the L and R sides of the body and axle (they are not actually vertical SDs, but let's assume so...).

So the driver turns into the corner, the road pushes the tyres leftward, inertia pushes the car-body rightward, and the L and R SDs extend or compress a bit. Where is the IC for the resulting motion of the car-body wrt live-rear-axle (either taken "instantaneously", or averaged over a short time period)?

The first half of the solution is very easy. The IC must always lie somewhere along the PB's centreline, or n-line. This comes from the definition of an IC, namely, the point in either body's reference frame that has NO MOTION wrt the other body's reference frame. The PB's n-line includes all the points in BOTH bodies that have NO MOTION in the DIRECTION of the n-line, wrt the other body.

The second half of the solution is a bit trickier. Here is a hint. Consider the tops of the SDs where they attach to the car-body. Draw a line through these two points (take it as horizontal for now). Consider the extension or compression of the SDs, as calculated in your earlier Statics+d'Alembert FBD. Based on these two vertical movements of the body-mounting-points of the two SDs, find the points of the car-body that have NO VERTICAL MOVEMENT.

Problem solved!

And as should be apparent, depending on how the two SDs extend or compress, the car-body's "Roll Centre" (ie. its Kinematic IC wrt the axle) can be ANYWHERE along the PB n-line. Yep, anywhere from left infinity, to right infinity. Or, by chance, it might be under the car...
~~~~~~~~~~o0o~~~~~~~~~~

Last point.

Originally posted by Ralph in PM (with a hint of sarcasm :)):
... Now you KNOW real race cars can't have beam axles! I would love to take the purists on a 140 mph ride around a one mile dirt oval in one of our cars. Which by the way we do on a regular basis.
(My emphasis.)

Yep, 140 mph on a rather bumpy track, with BEAM-AXLES!!! :)

Z

rwstevens59

04-19-2014, 03:30 PM

z,

Thank you very much for your assistance and for re-kindling my interest in reviewing my classical mechanics. Being a grey beard I did learn all of the above many, many years ago around 1977 to 1982 but my skills had atrophied from lack of use. :(

In my view the best references I have in my library are Mechanics by Den Hartog and Statics by J.L. Meriam. I have many, many other texts concerning general physics, kinematics, machine design, descriptive and analytic geometry etc. etc. but these two works are by far the clearest. Hartog is a little unclear in describing your figure 3 above concerning the relocation of a force by the use of a force and couple but Meriam cites it almost verbatim as you have presented it. It is included in Hartog of course but presented with some subtlety that doesn't reach out and grab you.

Another good resource for a general review is MIT's Open Courseware 8.01 classical mechanics video lectures by physicist Walter Lewin. This is a video archive of his freshman fall lectures on the subject. While the students on here might view this as very trivial it is a great review of the very essence of classical mechanics and if you don't find Prof. Lewy, as he is known, as one of the most entertaining and informative lecturers you've ever seen I would be surprised. To have a single professor like him in your college careers is a very rare thing, at least in my experience.

Link: http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/index.htm

To the students who may read this thread and wonder 'why in the heck would you design a beam axle like that??' all I can say is 'I' didn't. :)

The cars as described have evolved over the course of some sixty years. They started as modified U.S. passenger cars of the 1930's and are mostly the product of 'trial and error' garage engineering. Don't laugh, it might be a slow process, but cut and try has produced many beneficial pieces of machinery.

The biggest advances in these cars over those sixty years have been in the area of construction materials available, fabrication techniques, tire size & compounding and as in all things racing aerodynamics. However, to my knowledge at least, only one car has made it to a wind tunnel test which yielded some hard data and which was published in an SAE paper by Eric Koster. The rest, cut and try.

Why did I get involved?

Well, I was actually perplexed that after all these years of evolution that all of the cars produced by basically four builders wound up in the same tiny corner of the box of design possibilities. The beam axles are a product of the rulebook so that is not a design choice. But how to suspend a beam axle car has many possibilities and many have been used over the years on these car.

So, why is a twin trailing link, torque arm, short offset cockpit adjustable panhard bar system the winner for the last ten or so years?

The ever thickening rulebooks are one possibility. Never think that what happens at the upper echelons of automobile racing doesn't eventually trickle down in some form to the grassroots level. It does, if for no other reason, than the illogical reason, of 'I want to be like the 'Big Boys' mentality of the rules makers.

The era of 'credit card' racers may also be a factor as very few participants actually build and develop their own cars anymore. Break it, buy a new shrink wrapped piece from the parts truck.

However, there are some who have asked, who think I might know at least a little bit of engineering, to have a look and explain what and more importantly why the cars are designed as they are. And what might be done to improve them. The driver behind this of course is that like in many current forms of motorsports they have achieved parity and that makes winning frequently very difficult. :)

Why would anyone pick driver adjustability of the panhard bar angle as a design criteria? I don't know but I am working to find out.

Thanks for allowing me to participate in this forum even though my questions and thoughts may not pertain directly to formula SAE.

Thank you again Z for the great illustrations and explanations. (Expect more PM's :) )

Ralph

rwstevens59

04-20-2014, 06:37 PM

Just thought I would post a picture of the type of car I have been discussing.

250

rwstevens59

04-21-2014, 06:56 PM

And then there are the extremes:

252

05-13-2014, 10:06 PM

... In my view the best references I have in my library are Mechanics by Den Hartog and Statics by J.L. Meriam...

Ralph,

Thanks for re-endorsing these "old-school" textbooks to the current generation of students. (FSAEers who have been around here for a while will know that I have recommended the old staple of Hartog several times. Even to the point that I recently splashed out ~$3.99 and ordered it off the web (+p&p)!)
~~~o0o~~~

Students,

Another book British students might try is "The Theory of Machines" by Thomas Bevan (I picked up a copy at one of my kid's school fetes for $0.50?). The preface to the first edition (1939) states that the book is "...based on lectures given at the Manchester College of Technology ... [and] ... I have chiefly had in mind the needs of the student who is preparing for a University degree in engineering ... but I hope that many of the sections will appeal to the draughtsman and designer."

So, although this is a textbook suitable for "trade school" students, IMO it explains Mechanics better than most modern University level books.

(FWIW, Bevan's ToM gives an account of a reciprocating engine's "inertia torque" that is infinitely better (yes!) than all my other modern textbooks on "Advanced Engine Technology..." (<- a hint here on a really bad book!). However, a downside of ToM is that it uses imperial units (albeit in a well explained way), and some of the examples may seem a little odd. For example, the "inertia torque" example has a horizontal single-cylinder engine of Bore = 9", Stroke = 24", Conrod-length-c/c = 5 ft, Piston-weight = 580 lbs, Conrod-weight = 500 lbs, RPM = 120, ... etc. But the torque calculations even include the effect of gravity acting on the Conrod... :))

The IMPORTANT POINT I want to make is that, IMO, the above old-school Mechanics books can give you a much better understanding of the essentials of "Vehicle Dynamics" than all the currently fashionable, subject specific textbooks on VD, as well as the various Computer-Sims and seminars that are frequently advertised on these pages.

The big difference is this:

* The old-school textbooks teach Mechanics as a very general subject that has been proven to work over many hundreds of years, beyond any measurable accuracy, and in a huge range of different fields. It is based on very clearly explained foundations (the Definitions and Axioms), with everything else then deduced from these in a very rigorous way. Man went to the bottom of the oceans, and then to the top of the atmosphere, and then on to the Moon, and did a whole lot of other things, all using this stuff.

* Production car, or worse yet, racecar specific VD, is usually taught as if it is some sort of very specialised field that is unique to itself. It is full of its own specialist jargon, most of which is NEVER clearly defined! There is rarely any mention of foundational concepts, and instead there is much use of arbitrary simplifications, most of which, again, are NEVER explicitly stated. These thus leave error margins that are completely UNKNOWN. And with all its talk of "magic numbers" (go to the seminars) it is closer to voodoo and witchcraft, than to real engineering.
~~~o0o~~~

I'll have another, maybe longer, rant in the next post. :)

But in the meanwhile here is one of Ralph's pictures again.

252

Keep this image in mind whenever people tell you that "BEAM-AXLE CARS WILL NOT WORK" on the bumpy FSAE tracks - "Hey, sometimes there are cracks in the pavement about..., like ..., you know..., a whole 1/2" high!!!"

Oh, and remember that the above cars lap at 140 mph (~220 kph = ~2 x fastest FSAE).

Z

05-13-2014, 10:13 PM

... Another good resource for a general review is MIT's Open Courseware 8.01 Classical Mechanics video lectures by physicist Walter Lewin...
Link: http://ocw.mit.edu/courses/physics/8...1999/index.htm

I have much to say about these lectures (mainly, they are undeniable proof that the education system is truly spiralling down the S-bend), but will try to keep it brief.

First, THE GOOD NEWS.
====================
* Lewin proves that a generous dose of showmanship can make apparently boring subjects (ie. maths, science, tech-stuff, etc.) quite entertaining. Lots of simple experiments, preferably all with the expectation of catastrophic results, certainly works well for the "Mythbusters", and IMO it works well in the classroom too. More please!

* Along with simple, but REAL experiments, the blackboard is a good means of communicating difficult concepts. The act of drawing (mainly spatial) problems allows each part to be explained as it is introduced. Then erasing a small part and redrawing it allows changes-over-time to be depicted. I reckon Lewin proves that modern, gee-whiz, Computer-Aided-Presentations are a backward step. Ie. they are a boring slide-show, with very little "theatre" (... and none of those dotted lines!).

* SHOUTING IS GOOD, to get IMPORTANT points across!!! :)

* VERY IMPORTANT - Lewin stresses in the early lectures that,
"... any measurement is MEANINGLESS, without an estimate of its uncertainty".
This is something that students here should note well, because it is perhaps even more important in Engineering than in Science. As noted elsewhere, bad error estimates in Science = dud experiment, but in Engineering they can = jumbo jet falls out of sky and kills many people. So, please, no more wishbone-pickup-points, etc., given to 5 decimal places (in millimetres!!!).
~~~o0o~~~

Now, THE BAD NEWS!
===================
(Here I should note that Lewin is teaching the "Establishment View of Science", so below is not exclusively his fault.)

* The whole subject is presented as a hotch-potch of seemingly unrelated factoids. IMO it should be taught, as it used to be, as a rigorous Axiomatic-Deductive system of enquiry. Namely, (and see Newton's "Principia", or better yet Euclid's "Elements", for good examples):
1. Start with clear DEFINITIONS of the important concepts.
2. Make very clear statements of what is NOT KNOWN, but must be ASSUMED so that progress can be made (eg. Euclid's "Postulates", or Newton's three "Axioms", or "Laws of Motion", all of which are UNPROVABLE). Fewer of these Unprovables is better (see N's "Rules for Reasoning...").
3. Deduce other useful stuff (ie. the "Propositions") in a rigorous way that can always take you back to the above foundations alone.

* FAR TOO MANY EQUATIONS. Certainly, too much time spent cranking the handles of these equations. The lectures are presented in a way that suggests that "equations" are the foundational constructs of the whole subject, when they most certainly are NOT! The true foundations are the above Axioms->Deductions approach, while equations are merely chimney pots on the roof. They are just one of the types of tools that can be used to calculate some of the answers. Frankly, all the time spent on the equations is boring, and detracts from the learning.

* An example of the above two points is the section on friction. The "Friction-Force = Mu x Normal-Force" equation is, more or less, presented as if it is on an equal level to Newton's Laws of Motion. It is nothing like them! The "friction equation" is nothing more than an empirical "best-fit" approximation. It is based on the observation that in a lot of experiments (but NOT ALL) the area of the contacting surfaces does not make much difference. Based on this very limited approximation, FSAE cars should corner just as fast when they are on skinny little pram tyres. In fact, many Physicists today still insist that wide tyres are of no help in motorsports!

* Another example of the sloppy, ad-hoc approach is the introduction of "Statics" near the end of the series, when it should be much closer to the beginning. This is made even worse by the very sloppy usage of the concept of "Torque". There are occasional vague mentions of Torque being DEFINED as the Vector-Cross-Product of one (!) Radius and one (!) Force vector. This is very wrong, and very misleading, because this same "Torque" is then used (correctly) as the net "Couple" acting on the body, after ALL the forces have been moved to the CG. (For a brief explanation of this, see Figure 3 a few posts up, and extrapolate to all forces acting on the body.)

* Another example of sloppiness is Lecture 11 where Lewin claims Newton "postulated" the Universal Law of Gravitation. Rubbish! Near the front of "Principia" Newton POSTULATES his three (unprovable) Axioms, and towards the end he DEDUCES that an "inverse-square..." relationship best fits the available empirical data. Regarding any deep and meaningful explanation of gravity, he famously says "hypotheses non fingo" (= "I frame no hypotheses").

* And now for the most DISGRACEFUL, SLANDEROUS, REVISIONIST NONSENSE of the lot! In Lecture 6 Lewin (as with too many other Scientists today) claims that Newton's Second Law is "F = mA". He then claims that as the speed of the body approaches the speed of light "... Newtonian Mechanics no longer works, and we must use Einstein's Special Relativity...". Utter codswallop!!! So wrong, on so many levels... The least bit of research shows that NII is, essentially, "Force is proportional to rate of change of Momentum" (ie. F = P-dot, as appears buried in the middle of a list of equations late in the series, as if it is "just another equation"). Bottom line, all evidence available today suggests Newton's version of NII is correct all the way up to the speed of light!
~~~o0o~~~

I am not sure which of the above points is most troubling.

Regarding the last point, I have heard or read this clearly explained several times over the years. (In fact, adding one more Postulate to Newton's three allows E = mc^2 to be deduced.) And I am NOT in the business of teaching this stuff. Professor Lewin should know better! I can only assume this is Modern Science's attempt to feel better about itself, by claiming (falsely!) that "We are a lot smarter now, and our modern theories are so much better than that olden-day stuff...".

But I think that the whole modern approach to teaching this subject is the bigger problem. It should not be treated as if it is a glossy, coffee-table-book, that can be randomly dipped into at any page, while still claiming to give a deep understanding of Nature. Without a deep appreciation of the foundations of the subject, and how the rest is then rigorously built on top of those foundations, there is really NO UNDERSTANDING AT ALL.

As always, comments and criticisms most welcome. :)

Z

Jay Lawrence

05-14-2014, 02:15 AM

rrobb

05-14-2014, 12:53 PM

The examples mentioned aren't attempts to approach the limit dictated by the underlying principles like motorsports and engineering competitions.

rwstevens59

05-14-2014, 05:13 PM

Z,

1. Old texts:

Yes, I too seem to find many of the older texts more 'readable' and understandable. Newer texts (physics, mechanics, machine design etc.) are very flashy, lots of useless graphics, colors, etc. but totally disjointed and frustrating, to me anyway.

2. Professor Walter Lewin:

I will not defend him or his teaching methods. I will just say I personally learned something from his video lectures and that his showmanship helps make the basic points stick in some way for me.

His is the perspective of a physicist not an engineer. And as you say there is a pretty big difference.

Lastly from the course outline:

"8.01 is a first-semester freshman physics class in Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory. In addition to the basic concepts of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory, a variety of interesting topics are covered in this course: Binary Stars, Neutron Stars, Black Holes, Resonance Phenomena, Musical Instruments, Stellar Collapse, Supernovae, Astronomical observations from very high flying balloons (lecture 35), and you will be allowed a peek into the intriguing Quantum World."

Quite a bit of ground to cover for a fall semester freshman course on classical mechanics. And also quite an advertising pitch for a basic freshman physics course.

Hmm...I guess I did wind up defending him in a way despite what I said above. :)

Oh, and for those interested and who did not come up with an answer for the ball and track demonstration problem, the answer can be found in lecture 29.

3. Too many equations:

Try a few of these videos on for size from one of MIT's basic dynamics courses:

http://ocw.mit.edu/courses/mechanical-engineering/2-003sc-engineering-dynamics-fall-2011/index.htm

Now there is an alphabet soup course designed to be 'specific' after a freshman gets past Lewin. Makes Lewin's course seem absolutely devoid of the maths. :)

I fundamentally agree with your insistence for a grounding in the very bedrock of the logic and deductive reasoning used by the creators of this subject. However, I also know that we have created an engineering profession so heavily reliant on technology, computing power in particular, that there just isn't time in four or five years to even scratch the surface for a student.

That is what makes FSAE important in my opinion. If for no other reason than there will at least be a very few engineering students who have truly attempted to build something, anything, and found out for themselves how difficult the process can be. What they build is immaterial to me, personally. Think of all the rest...:(

As far as the false profits of engineering science are concerned, they have always been there and will continue to be, most likely even in vastly greater numbers with the availability of the internet to pedal their wares.

And... Back to Beam Axles! :)

Ralph

rwstevens59

05-14-2014, 07:20 PM

Z,

One last point on all the confusion concerning the terms moment, couple and torque. Look for torque in the Hartog index, none. In index of Statics by J.L. Meriam 'Torque, see Moment of Force'. In any physics text I have torque is defined as r X F.

Couples in Hartog are designated as C in Meriam as M (same as moment).

Point, physicists use torque, no moment or couple and engineers use moment, couple and torque with only one source of clear distinction I could find on Wikipedia under Torque of all places. Did you write that entry?:)

No wonder students get all turned around and confused.

Ralph

Jonny Rochester

05-15-2014, 07:08 AM

rrobb

05-15-2014, 11:43 AM

Z,

I was thinking about this 'everything from 1st principles' point of view and wonder if we as humans skip steps so that we may progress? I don't need to know how an engine works to put one on a cart and therefore make it 'better'. I don't need to know how radio waves work in order to control an R/C car. I don't need to know a great deal about aerodynamics to play golf. I learn about things such as these because they are of interest. If everyone had to learn all there is to know from the very basic principles upwards, we'd run out of life before we made any progress! Something about giants and their shoulders...

Just a thought.

My post in response to this was not clear.

If I may, I'd like to restate my point;

I don't believe that Z is advocating reducing every task to first principles. As you state, that would be inefficient.

However, there is a fundamental difference between pursuits like motorsports and the examples given in the above quote.

Take the case of controlling an RC car. The underlying physics of signal transfer through electromagnetism are not an area where you can get much of a performance boost. Radio waves are, in this case, a commodity. If one were to devote years of study to devising a more efficient manner of sending control inputs to the car, the improvement over standard off the shelf items would be minimal.

A similar situation applies to the golf example. No amount of study into aerodynamics will net you the same performance improvement that learning how to swing a club consistently will.

Contrast those with the design of vehicles whose primary purpose is to operate at the very edge of their performance envelope. Motor racing vehicles spend almost there entire life at or near design limits. With the exception of maybe single use space launch vehicles, nothing else even comes close.

This performance envelope is defined by the laws of physics. Understanding these laws has a massive impact on our ability to develop a vehicle able to test these limits.

Cory

Jay Lawrence

05-15-2014, 11:15 PM

Yes, but like learning how to swing a golf club consistently, I can learn how to apply magic numbers and simple 'roll centre' approximations without having to go down into first principles of mechanics (or aerodynamics/projectile motion in the golf example). Maybe I will lose a tiny amount of initial performance (i.e. my more learned competitor might get to the track with perfect spring rates and no need for dampers and have a car that is immediately at its design limit) but it is likely that I would have a vehicle ready quite earlier than he/she because I have stood on some shoulders, applied a top down approach, and not spent the time to get to the very basic fundamentals. The extra time is what I use to tune the car in the real world and bridge my theory gap.

Perhaps my examples were a bit off, and I'm not necessarily advocating to forget the classical side of things, it was just a thought.

Tim.Wright

05-16-2014, 05:14 PM

I agree more or elss to the last few posts. The problem with many óf these short cuts (e.g. roll centres...), is that it is often taught as though they ARE the first principles.

I'm pretty resentful of the fact that the first few years of my professional life as an automotive engineer were spent unlearning stuff that I was "taught" in various books and seminars

05-17-2014, 07:32 AM

Firstly, thanks to everyone above for giving some thought to these educationally fundamental, but not-directly-FSAE-related, issues. Here is some more general ranting. More specific responses next post... :)
~~~~~o0o~~~~~

I do not blame Prof. Lewin for any of the teaching errors above. As noted, he does a great job of explaining the subject in an interesting way. The problem is with the modern education system in general, which nowadays seems to be,
"Well, it's all about this humungous jumble of equations, all of which you will have to learn. You have to learn all of them individually, because they are all a bit different. But they are also all kind of the same. Err..., in the same way that these days 'all answers are equally correct', and 'everyone's opinions must be equally respected'. Yep..., that way we can always give all the kiddies a gold-star...".

IMO the best way to teach Mechanics would be more of the Lewin/Mythbusters style of simple, real, and interesting experiments, but with much more honesty, clarity, and rigour in the explanations. This takes no more time than the current method. In fact, probably less, because most of the unnecessary equation-crunching can be dropped. So;

HONESTY - Don't tell lies about what people did or said hundreds of years ago! How is that educational?! An honest historical account is more ethical, and also often more interesting. For instance, in Newton's Definition 1 he defines the "quantity of matter" (= "mass" nowadays) as "... its density and bulk conjointly". Note how we do it the other way around these days (ie. density = mass/volume) .

Also, the notion that "We are cleverer than Newton because we know that General Relativity gives more accurate answers than Newton's ULG..." is nonsense, as noted before. High school teachers might mistakenly suggest this, but University Professors should not teach this sort of slanderous rubbish. Unfortunately, when they all do it, they can all get away with it. And all you students are the losers.
~o0o~

CLARITY - "F = P-dot" is really much easier to understand than "F = mA". I only started to think that way well after I finished my schooling, and I highly recommend it. Lewin often mentions that rotating dynamics are very "non-intuitive". This is, IMO, due to too much "F = mA". And you can forget about ever understanding gyroscopes (the most "non-intuitive" of the lot, according to Lewin) until you move to "F=P-dot". Then it all suddenly falls into place! :)

BTW, "Angular Momentum" (Lewin calls it L) was in the olden days called the "Moment of Momentum". It is simply the sum of all the "Moments" (= Cross-Products) of the Linear-Momentum-Vectors of the various particles and their Radius-Vectors, taken at a particular point. There is still a bit more explaining required here (maybe with some simple experiments), but seen geometrically it is all quite simple, and it gives "T = L-dot".

In the preface to Bevan's ToM book (ref'd earlier) he says "As so many of the problems which arise may be solved more quickly and easily by graphical methods, particular care has been taken to draw the diagrams correctly...". I note that in Lewin's lectures the "man climbing a ladder" problem is "solved more quickly and easily" in the simple act of drawing the FBD! (Lewin has to work through quite a lot of algebra for the same end result).

Similarly, the "time period of the hula-hoop pendulum" is solved in one, simple, do-it-in-your-head step, based on "equivalent mass systems". (Hint - What length dumb-bell has the same (2-D, planar!) mass-distribution as the hula-hoop?) And the "sliding vs rolling-ball pendulums" (ie. problem asked on other thread) is solved by simply noting the paths of motion, in side-view, of different points on the two bodies. (Hint- Which body has greater changes in its "quantity of motion"?)

Bottom line here, geometrical (or "graphical", as Bevan calls them) methods can give greatly improved insight into problems, and much quicker solutions. Your schools NOT teaching them is your loss.
~o0o~

RIGOUR - It should be constantly restressed that Newton's 3 LoMs are unprovable "Axioms", while most of the other "Laws" are deductions from these. It is a heirarchical system, starting with foundations at the bottom, and then other stuff built on top. The closer to the foundations, then the more widely applicable are the concepts. The further away from the foundations, then, typically, the more simplifying assumptions that have been used, and the LESS USEFUL is that "Law" (see eg.s below).

For a general feeling for how this works, ask the good citizens of Pisa how things go when you get the foundations wrong. Ok, so they do make some tourist-lira out of it now, but that is mainly because people enjoy looking at huge cock-ups. And the good citizens are having to pay quite a lot to prop-up their cock-up, lest it disappear into a pile of its own rubble... :)

As an example of the heirarchical approach, Kinetic Gas Theory is deduced from Newton's Axioms, typically with a few other assumptions thrown in (eg. the molecules are assumed to bounce off each other like elastic billiard balls). Likewise Bernoulli's Law is deduced from N's Axioms, again with a bunch of simplifying assumptions thrown in. Now, if you happen to forget any of these more superficial Laws, then, with practice, you can always re-deduce them from the very small set you started with (ie. N's I, II, & III). Fortunately, doing this reminds you of ALL those simplifying assumptions. Namely the times when said "Laws" DO NOT APPLY! (<- A hint here to FSAE-aero-guys that Bernoulli does NOT ALWAYS apply!).

An even more superficial example is the "Law of Friction", which barely qualifies for that title. Worth noting that back in the 1960s, when racing tyres started to get ridiculously wide (from 4" to 6"!, then 8"!!, then !!!) there where many experts, those that, ahem, understood the "Laws of Nature", that claimed that "wider tyres won't make any difference!". The "Friction Law" is a reasonably good approximation for hardish and smoothish materials sliding on each other, over a smallish range of pressures. But not much good for soft, sticky stuff sliding on a rough surface. And certainly no good at balancing your car's handling via LLTD and TLS.
~o0o~

Bottom line, it does not take a lot of time to constantly restress this idea that there are different "levels" of Laws (and some SHOUTING might help get the message across in less time :)). The fundamentals are by far the most important, and should be understood the best. The more superficial stuff is less important, and if you happen to forget some of it, then no problem, because it is not that accurate anyway...

MOST IMPORTANTLY, never forget that the superficial stuff is usually built on a whole lot of simplifying assumptions, many of which might not apply to your particular problem!

Z

05-17-2014, 07:36 AM

I was thinking about this 'everything from 1st principles' point of view and wonder if we as humans skip steps so that we may progress?
...
If everyone had to learn all there is to know from the very basic principles upwards, we'd run out of life before we made any progress!

Jay (and others with similar comments),

I hope I have addressed this sufficiently above. But in case not, just be aware that only a very small part of what you learn in Science/Engineering is solid bedrock. The greater part is [...thinking of metaphor...] like quicksand with a very thin, but hardish looking, crust on it. You can pitch a tent on the latter, but don't go building an office block there (or a Pisa-esque tower :)).

And racecar VD is even worse. For example, there is the "Law of Never Letting Your RCs Migrate Sideways". This is pure poppycock that has never been "deduced" from the more fundamental stuff, but has somehow entered the field as an old-wives-tale. It is relatively harmless (it just stops you having "ground level RCs", or horizontal n-lines), but it can waste you a lot of time.

Knowing how to distinguish the important stuff from the trivial nonsense, is, well..., IMPORTANT! :)
~~~o0o~~~

Originally posted by Ralph:
One last point on all the confusion concerning the terms moment, couple and torque...
Couples in Hartog are designated as C in Meriam as M (same as moment)...
... only one source of clear distinction I could find on Wikipedia under Torque of all places. Did you write that entry?

Ralph,

I don't do any Wikipedia editing. It is too much "design by committee" for me. In fact, I reckon it is accelerating the descent down the S-bend by introducing more and more poorly phrased definitions, and thus legitimising this sort of sloppiness in the eyes of the younger generation. For example (from Wiki- "Torque");
"In US mechanical engineering, the term torque means "the resultant moment of a Couple,"[5] and (unlike in US physics), the terms torque and moment are not interchangeable. Torque is defined mathematically as the rate of change of angular momentum of an object..."
So two different definitions right next to each other!

The second one comes from "T = L-dot", and, strictly speaking, should read as "a Torque CAUSES, and is proportional to, a rate of change of angular momentum". But the double translation, first into algebra, and then back into English, gives the impression that the torque is an end result, or effect, with the L-dot being the cause. Anyway, the whole quote above is very misleading, because it loses the direction of the causality.

Personally, for "a purely rotating, forceful, action" I prefer "Couple". This makes it very clear that for such a rotating action you need at least TWO matched forces (ie. "a couple of..."!). "Torque" would be ok, except that it doesn't stress this "two-ness". "Moment" is far too vague, because it is used in too many different ways (eg. 1st/2nd/3rd - Moment of - Area/Mass/Force/whatever...).

With regard to symbols, I think "T" (often Greek Tau) first started to be used for Couple (which later became Torque) because in Descartes' "Analytic Geometry" (c. ~1600) he used A, B, C for general purpose constants, and X, Y, Z for the unknown variables. This has since become universal, so "C" doesn't really suit a variable vector. Descartes' abstraction into alphabet soup means that even with two whole alphabets (Greek and Roman), and quite a lot of different fonts these days, we still don't have enough symbols to uniquely label all the different concepts (T is also time, L is also length, etc...)

Doing it graphically is much easier because we just draw a different sort of arrow for each concept. So, as in the earlier figures, a ring-like arrow around a normal arrow indicates rotational stuff. Add different sorts of feathers, and you can represent Force, Motion, or whatever you want...

Z

(PS. Don't bother googling images of "Couple Moment". You just get pictures of couples canoodleing...)

rwstevens59

05-18-2014, 09:33 PM

Tim.Wright,

I would have to agree with you 100%.

What frustrates me the most is I feel that I should have known better but I took the ride anyway.

Starting to learn VD much later in the game then most students and having a fairly good but ancient (i.e. pretty rusty) understanding of classical mechanics I always had the feeling I came in at the middle of the story while studying the excepted seminal works.

I would be skeptical many times and fall back to drawing very basic FBD's then convince myself that my gut instinct was wrong, because after all the author(s) are the practiced experts, right? I just need to read and study more, I thought.

So, after many fits and starts, a lot of dead end alleys explored I am finally to a point of a somewhat better understanding.

Am l resentful, no. But I am quite disappointed and concerned with many of the sources proclaiming educational content in vehicle dynamics.

BillCobb

05-19-2014, 08:52 AM

rwstevens59

05-19-2014, 05:19 PM

If you want to be on top of the Vehicle Dynamics game, learn something about nonlinear partial differential equations, the methods to solve them, the ways to characterize their response traits and the means to synthesize a system from known foundation properties that achieves targeted goals.

Otherwise, this subject matter Forum is probably just Vehicle Statics. (Just doesn't sound as cool though, does it ?)

BillCobb,

Vehicle Statics it is. Guess I should use V.S. from now on. :) Being that my mental toolbox is a few wrenches short for an all out assault on better modeling it will be a slow climb up hill. And since my work in this area is strictly for the fun of it, the climb will be even slower. But you are correct of course.

Ralph

slicktop

05-19-2014, 09:00 PM

If you want to be on top of the Vehicle Dynamics game, learn something about nonlinear partial differential equations, the methods to solve them, the ways to characterize their response traits and the means to synthesize a system from known foundation properties that achieves targeted goals.

Otherwise, this subject matter Forum is probably just Vehicle Statics. (Just doesn't sound as cool though, does it ?)

I recently finished a 5 dof multibody tire/suspension/chassis model that i used lagrange's equation to solve and simulink to model. Only 2D though... It was a great learning experience. The equations are very tedious to write, easy to make mistakes, and time consuming to track down mistakes. But, in the end, not all that difficult to do. Although, during the process i found myself wondering if it was even worth it - maybe I would be better off spending my time learning Adams instead.

rwstevens59

05-19-2014, 10:53 PM

I recently finished a 5 dof multibody tire/suspension/chassis model that i used lagrange's equation to solve and simulink to model. Only 2D though... It was a great learning experience. The equations are very tedious to write, easy to make mistakes, and time consuming to track down mistakes. But, in the end, not all that difficult to do. Although, during the process i found myself wondering if it was even worth it - maybe I would be better off spending my time learning Adams instead.

I guess my only question would be when this model was or will be validated by experimental observation i.e. track testing how much closer to reality was it than the simplified statics type of analysis that has been discussed above? I am not trying to disparage your work in any way nor questioning your approach. I am truly interested in knowing how much smaller your model to observation error was.

Thanks,
Ralph

slicktop

05-20-2014, 12:24 AM

No offense taken. I disparage my work all the time. :) When I get the time, I am planning to post some results in order to get some feedback from the members here. I have not done a comparison of the model to logged data of our car yet or compared it to a statics approach, but it is definitely on the to do list. I have moved on to trying to learn cfd/openfoam so it will probably be a while before I return to the VD model.

The best answer i can give at this time is this: The full vehicle model uses the multibody model to provide the normal loads of the tires, which then uses Pacejka tire model to calculate tire forces, which give the vehicles yaw and sideslip responses in the road plane. Initially though i used a statics approach in place of the multibody model to approximate tire normal loads, and can say that there were differences in the result. Enough to warrant the time spent on developing the multibody model? Can't really say as of yet. I think I might have developed a tool that is too complex to use effectively with my limited manpower. Getting lost in the data can be a problem, i'm quite certain this trap has been discussed here before. I think that may be the lesson here... So I guess I am no help. :(

rwstevens59

07-18-2014, 04:54 PM

I would like to ask the forum members for input and constructive criticism on the attached 2D CAD drawing of the planer view of a twin trailing link torque arm rear suspension linkage layout.

This is a plot of axle movement with respect to body quickly done in response to a question I received regarding the effect of varying effective torsion bar arm length with axle travel. The torsion bar arms are shown as the rectangles. The large circle is the solid live axle tube, the next smaller circle in the triplet is a roller which actuates the torsion arm through line contact with the torsion bar arm and the small circle at the bottom of the triplet is the trailing link radius rod mount to the axle. On the actual car the torsion bar arm roller and rear trailing link heim end are all fixed to the axle via a twin plate bracket.

The question which arises is that this arrangement (twin trailing link, torque arm, panhard bar for lateral location) with the trailing links at static ride height, as shown in black, having an upward angle toward the front should produce roll understeer. It should be mentioned that the torque arm is mounted on a slider and has only one contraint on the axle, that of torque reaction therefore in the sketch its chassis mount point is allowed to travel along the horizontal line shown.

The driveline is considered to be locked and therefore the tire and axle assembly must rotate about the trailing link axle housing mounting points.

The fixed construction points chosen are the trailing arm chassis mount point shown to the right in space and a horizontal line or the torsion arm chassis mount point and the sliders line of action.

So is the roll steer indicated by the movement of the contact patches relative to ground or by the axle housing tube?

284

I would appreciate any input anyone might be willing to give.

I am at a location where I am limited to 2D CAD or a drawing board at the moment and don't have access to my usual array of solid model tools. So a bunch of geometric construction and 2D projection are what I have in the toolbox.

Thanks,

Ralph

Loz

07-20-2014, 09:04 PM

So is the roll steer indicated by the movement of the contact patches relative to ground or by the axle housing tube?

That question is a little confusing..

Steering, steered angle, under/oversteer etc. are all relative terms used to describe a change in orientation of the wheel. Through connection to the wheel, the tyre also follows the change in orientation in the general sense. If we consider the wheel and tyre as a rigid assembly, then relative change in orientation of a [u]static[\u] contact patch could be used to assess steered angle, in which case it would be the same as the fore/aft relative movement of each end of axle with respect to some pivot point some where near the middle (dictated by the panhard rod attachments and the ratio of fore/aft movement of the axle on each side due to the trailing arm constraints. Given the tyre and the axles tube are concentric, they should have the same relative change at the tube as the rigid wheel at the ground.

It would be very difficult to estimate the actual change in direction at the contact patch as a result of a steer input without extensive information about the tyre itself, but it would equate to something like the difference between the difference in wheel steered angle and the difference in slip angle (i.e. a difference of 2 differences: e.g. angular change=delta [ delta(SlipAngle1-SlipAngle2) - delta(SteerAngle1-SteerAngle2) ]. It would also be troublesome selecting a definition for the contact patch change that is a true representation of any changes in steered angle (unless of course the tyre is rigid and moves in unison with the wheel in which case we only need be concerned with the change in orientation of each wheel and we are back to using the axle housing).

rwstevens59

07-21-2014, 09:19 AM

Loz,

Confusing! Upon a re-read it is simply awful and I am surprised you took the time to answer.:p

I think we'll just chalk this one up to a 'brain fart' and leave it at that. I was investigating one thing and starting to ask questions about a completely different topic. Too quick to the keyboard I guess.

Thanks for the attempt at a response and I will pose a well formed question when I have a little more time.

Ralph

07-21-2014, 10:35 PM

...
The question which arises is that this arrangement (twin trailing link, torque arm, panhard bar for lateral location) with the trailing links at static ride height, as shown in black, having an upward angle toward the front should produce roll understeer.
...
So is the roll steer indicated by the movement of the contact patches relative to ground or by the axle housing tube?

Originally posted by Loz:
... (unless of course the tyre is rigid and moves in unison with the wheel in which case we only need be concerned with the change in orientation of each wheel and we are back to using the axle housing).

Ralph,

As Loz suggested, "roll steer" is determined by the direction of the wheel-planes, namely the direction perpendicular to the Axle-Housing (AH). So for a Roll motion of the AH, wrt the car-body, you want to determine the relative movements of the wheel-centres, NOT the wheelprints (= contact patches).

BUT (!), unfortunately, you can NOT determine these Roll steer effects purely from a 2-D side-view of the linkage.

Your side-view diagram does let you determine the "Pitch-plane" (or "side-view") "anti-squat/lift" properties of the suspension. Assuming that yours is a live-axle (diff fixed to AH, so not a De-Dion which works differently), and the brakes are also fixed to the AH (not on "birdcages", etc.), then the analysis is as follows.

The two Trailing-Links are n-lines for the motion of AH wrt body. However, in side-view these two n-lines are on top of each other, so appear as one. The Slider on the torque-arm has a "contact normal" which is a vertical line passing through the S contact zone (assuming the sliding surface is horizontal). This vertical line is a third n-line for AH motion wrt body.

Draw the vertical S n-line on your drawing. The point where this S n-line passes through your TL n-lines is the Instant Centre for the 2-D side-view motion of AH wrt body. A line through the IC and wheelprint determines the wheelprint n-line. This in turn determines your anti-squat and anti-lift properties (ie. horizontal = 0%, steeper = more).

BUT (!), your roll-steer is NOT determined by the apparent movement of the wheel-centres in this side-view!!! This is because the Roll motion takes place in the [drum roll...] THIRD-dimension. So you must also do the analysis there. I will definitely get around to doing some sketches of this one day (yes, promises, promises...) but briefly for now.

Your Panhard-Bar is the fourth n-line that constrains AH motion wrt body. Four constraints = two degrees of freedom, which means the left and right wheelprints can move independently up-or-down. Or you can think of the AH moving independently in a Roll motion or a Pitch motion (with this Pitch motion covered above).

Strictly speaking, the "Pitch" motion (of AH wrt body) is about an APPROXIMATELY horizontal-lateral line that intersects the two TLs and the vertical S n-lines, and also intersects the Panhard-Bar-n-line. Only when this "Pitch-axis" intersects ALL four of the AH-to-body n-lines (ie. 2 x TLs, S, and PB) is this line an Instantaneous Screw Axis (ISA) of zero thread pitch (ie. it is a "revolute" joint, like a simple hinge).

The second ISA of zero pitch (there are always two of them) might be called the Roll-ISA, and is roughly longitudinal and (going from the rear of the car forwards) intersects the PB-n-line, then the vertical S-n-line, then the two TL-n-lines. If the two TLs converge towards the front of the car, then the Roll-ISA intersects both of them at their mutual intersection point. If the two TLs are parallel, then this Roll-ISA is also parallel with them, intersecting them "at infinity".

BTW, the generalisation of all this is that ANY four straight lines in 3-D space (eg. 4 x n-lines) can ALWAYS be intersected by 2 other straight lines (eg. 2 x ISAs of zero pitch). The two ISAs of zero pitch then determine the position of the "cylindroid", which in turn determines all possible ISAs for this 2 DoF linkage. Maybe more later...

Lastly, the slope of your Roll-ISA (two paragraphs up) determines your Roll-Steer. If Roll-ISA slopes up-to-front, then Roll-OVERSTEER. If Roll-ISA slopes down-to-front, then Roll-UNDERSTEER. Assuming your TLs are close to parallel, then it is most likely (for typical PB position) that the Roll-ISA will have a similar slope to the TLs, so your sketched car should have Roll-OVERSTEER.

Enough for now...

Z

(PS. The torsion-bars will give variable rate springing from their changing geometry, but that should not directly affect the Roll-Steer kinematics.)

rwstevens59

07-22-2014, 01:15 PM

Z,

Thanks for the very clear response to a very poorly worded question. Have both of Jack Phillips books now but I'm still wrestling with those as I guess I've spent too many years in front of a 2D drawing board or CAD station. :)

The original question as posed to me that I was working on when I created this side view was, 'what would be the difference between the torsion bar springing as shown and replacing the torsion bar arrangement with linear coil springs?'. My answer to that was do not try and emulate the varying rate of the torsion bar system but simply calculate the static deflection for the travel needed, pick a pair of coils that will give close to that deflection and start testing/tuning with the coils.

The side view diagram then caused a bit of a ruckus with the local racers who saw it and questioned the axle housing motion as drawn. Hey wait a minute with a trailing link, torque arm, panhard bar suspension we should have roll oversteer meaning in this right side view the housing should be moving back not forward. I tried to explain the if you were to support the car on jackstands and then used a pair of jacks to return the axle housing to a level condition at a measured static ride height WRT chassiss (torsion bar stop removed, i.e. no windup, and shocks removed) and then were to jack the rear axle housing in pure level bump and then let the jacks down in pure level droop that the axle motion as drawn should be what you see/measure.

I then wrote my very hastily and poorly worded question here on the forum.

Two questions I really have are:

1. For a symmetrical left/right car with live solid axle,with spool (no differential) and outboard brakes using parallel trailing links, torque arm and panhard bar would this 2D drawing be reasonable?

2. If we were to plot the contact patch arc produced when the driveline is in a locked condition would a line drawn perpendicular to this arc also be the n-line for the contact patch?

I am working on a true representation of axle housing roll to satisfy the doubters that they do indeed have roll oversteer. :rolleyes:

Thanks again,

Ralph

P.S. Jack Phillips definitely has a unique 'style' in his writing. :)

Loz

07-22-2014, 08:37 PM

Thanks for the very clear response to a very poorly worded question. Have both of Jack Phillips books now but I'm still wrestling with those as I guess I've spent too many years in front of a 2D drawing board or CAD station. :)

This can still be done on a drawing board and in 2D views. BUT, it is necessary to also include a top view and rear view with many projection lines, kinematic paths and Euclidian geometrical construction techniques. It would still be palatable for a mechanism such as this, but unnecessarily time consuming compared to other techniques available (especially a simple 3D CAD based linkage model with 1D elements).

The original question as posed to me that I was working on when I created this side view was, 'what would be the difference between the torsion bar springing as shown and replacing the torsion bar arrangement with linear coil springs?'. My answer to that was do not try and emulate the varying rate of the torsion bar system but simply calculate the static deflection for the travel needed, pick a pair of coils that will give close to that deflection and start testing/tuning with the coils.

Your answer would be the more sensible approach and certainly quicker and ultimately more likely to result in spring selection that works rather than pursuing a lot of needless calculations only to arrive at the same starting point. Either way you still have to test and tune the spring selection to take into account all of the real world variables on that day for those track conditions.

It wouldn't be difficult to determine the torsion bar non-linearity and upper and lower bounds of stiffness. However, there would not be a singular value of non-linear stiffness but multiple values given there are different kinematic positions the suspension could assume during operation - i.e. different combinations of positions the torsion arm rollers could be acting on the arms due to combined modes of pitch, roll, etc...).

1. For a symmetrical left/right car with live solid axle,with spool (no differential) and outboard brakes using parallel trailing links, torque arm and panhard bar would this 2D drawing be reasonable?

The use of a panhard bar for lateral constraint automatically dictates that it is not a symmetrical setup. If the panhard bar is close to horizontal and only moves vertically up and down a small amount (i.e. small n-line slope changes away from horizontal), then it may be approximately symmetrical enough to be considered as symmetrical (this symmetrical condition is the same as required for having a revolute-joint pitch axis.
e.g.

Only when this "Pitch-axis" intersects ALL four of the AH-to-body n-lines (ie. 2 x TLs, S, and PB) is this line an Instantaneous Screw Axis (ISA) of zero thread pitch (ie. it is a "revolute" joint, like a simple hinge).

2. If we were to plot the contact patch arc produced when the driveline is in a locked condition would a line drawn perpendicular to this arc also be the n-line for the contact patch?

What do you mean by contact patch arc? And when you say "locked condition" do you mean a spool/locked axle or that some kinematic movement in constrained?

I am working on a true representation of axle housing roll to satisfy the doubters that they do indeed have roll oversteer. :rolleyes:

It would probably be quicker and more convincing to the skeptics to take the wheels off and springs out, attach a couple of plumb-bobs to the wheel centres, jack the car and wheels up and down in the motions you require and draw some points and lines on the ground in chalk (plus you inadvertently take out any error you introduce into a 2D/3D model from measurement errors of the mechanisms). Despite not using "high-tech" whiz bang technology such as a computer, methods like this can still be extremely precise for the accuracy and resolution required for assessing and developing vehicle dynamics. A prime example is using a string line to do a wheel alignment.

rwstevens59

07-22-2014, 10:46 PM

Loz,
My question two is referring to the following example, one of several given to me by Z to locate the longitudinal n-line slope. In the case of my diagram I did not plot the path of the contact patch in the three positions shown, but if I had the locked driveline would cause a point marked on wheel centerline at the ground tire interface to rotate forward and back as the axle was moved from full droop through static to full bump which would, based on only the three points shown, produce an arc.

The question: Would the example stated below be applicable?

Z:
"1. You have a car in front of you, and your job (as Junior Test Engineer) is to determine its "% Anti-Squat" or some similar number. Ie. you want to find the side-view, longitudinal-n-line slopes of the rear wheels. Unfortunately, the car is covered in so much mud that you can barely recognise any suspension links...So, you might lock the transmission somehow (put in gear, or vicegrips, etc.), paint a mark at the 6-o'clock point of the wheel (= wheelprint), somehow move the wheel up-and-down through its full suspension stroke (wrt car-body), and mark on a piece of plywood (again fixed wrt body) the not-quite-vertical Path-of-Motion of the wheelprint. The longitudinal-n-lines are the lines that are perpendicular to this PoM, at different points along the path (ie. PoM is probably curved, so n-lines have different slopes at different points).The road-to-wheelprint force is doing a similar thing to JuniorTE here, in that it has no hope of knowing where the "IC" is. It simply pushes on the wheelprint, and if it can compress/extend the suspension a bit, because it has a component along the PoM, then that is what happens."

Thanks,

Ralph

Loz

07-22-2014, 11:42 PM

Loz,
My question two is referring to the following example, one of several given to me by Z to locate the longitudinal n-line slope. In the case of my diagram I did not plot the path of the contact patch in the three positions shown, but if I had the locked driveline would cause a point marked on wheel centerline at the ground tire interface to rotate forward and back as the axle was moved from full droop through static to full bump which would, based on only the three points shown, produce an arc.

Semantically, but pertinent to your description, in a geometric description, a point is a zero-dimensional vector and cannot rotate.
So the contact patch point originally at the ground cannot rotate, but the position vector (i.e. a line joining two points), can rotate. In this case perhaps the points used could be the original point at the contact patch and some point infinitesimally close (but not coincident with the original point) which are both on the path you describe (i.e. the "arc"). They are by nature tangent to the path. The lines perpendicular to any two adjacent infinitesimally close points on the arc are the n-line vectors in the example.

This is for the static case only. Add some vehicle dynamics and variations of tyre loads and tyre-loaded-radius and path of motion of the contact patch "point" will follow a different path with an infinite number of variations possible.

rwstevens59

07-24-2014, 03:50 PM

Z and Loz,

Attached a very, very rough lunch time ball point pen rough sketch of what I imagine to be the relevant n-lines as described by Z.

This is the part with which I am struggling:

Quote Z:

"Strictly speaking, the "Pitch" motion (of AH wrt body) is about an APPROXIMATELY horizontal-lateral line that intersects the two TLs and the vertical S n-lines, and also intersects the Panhard-Bar-n-line. Only when this "Pitch-axis" intersects ALL four of the AH-to-body n-lines (ie. 2 x TLs, S, and PB) is this line an Instantaneous Screw Axis (ISA) of zero thread pitch (ie. it is a "revolute" joint, like a simple hinge)."

"APPROXIMATELY horizontal-lateral line that intersects the two TLs and the vertical S n-lines"; I can visualize that.

"and also intersects the Panhard-Bar-n-line."; This I can not visualize. In my mind the line crossing the TLs n-lines and the S n-line would be in a different plane, at least as I picture it for this particular linkage and would never intersect. Unless of course I am not visualizing the correct n-lines particularly for the panhard bar.

Again pardon the very poor blob used while I was thinking and not going to post but...what the heck it would not come out any better if we were all sitting around the table at lunch at the first go.

Any help and clarifications would be welcome.

285

Thanks,

Ralph

07-25-2014, 12:02 AM

Ralph,

Your sketch is good. I will try to do a similar one, with a bit more added, in the next week or so. Have to get a few other things out of the way first.

"APPROXIMATELY horizontal-lateral line that intersects the two TLs and the vertical S n-lines"; I can visualize that.

"and also intersects the Panhard-Bar-n-line."; This I can not visualize. In my mind the line crossing the TLs n-lines and the S n-line would be in a different plane, at least as I picture it for this particular linkage and would never intersect. Unless of course I am not visualizing the correct n-lines particularly for the panhard bar.

Firstly, it is a truism of Euclidean geometry that ANY four straight lines in 3-D space can ALWAYS be all intersected by another two straight lines. So, it is just a matter of going a-hunting for those other two lines.

If, in your sketch, the PB was exactly horizontal-lateral, then the "Pitch-revolute-ISA" (ie. a "simple hinge" for "pitching" motion of AH wrt body) would also be an exactly horizontal-lateral line, parallel to the PB (so intersecting it "at infinity"), and intersecting the 2 x TL and 1 x S n-lines. So roughly along the line you have drawn through the two TL mounting points to body.

However, if the PB slopes down-to-left, as you have drawn, then the Pitch-revolute must be rotated anti-clockwise about the S n-line in plan-view. Since this Pitch-revolute must still intersect the 2 x TL n-lines, its right-end moves up-and-forward, while its left-end moves down-and-backward, as it slides along the two TLs. Eventually it intersects the PB n-line somewhere to the left of the car.

Regarding the "Roll-revolute", you have drawn the two TLs converging slightly to the rear of the car. If the TLs intersect somewhere behind the car, then the Roll-revolute is roughly horizontal-longitudinal and passes through this TL intersection point, then through the PB n-line, then through the S n-line. If the two TLs DO NOT intersect at all (ie. if they are slightly "skew"), then there will still be a roughly horizontal-longitudinal Roll-revolute that intersects all 4 x n-lines. However, this Roll-revolute might not be as close to longitudinal as before.

Jack Phillips used to make lots of 3-D models of these things. Typically, they would be a largish lightweight steel frame, then lots of different coloured strings stretched within the frame, to represent all the different straight lines.

Z

(PS. If the Slider mechanism is to ONLY constrain vertical movement of the end of the torque-arm (via a single vertical "n-line"), then, yes, it must necessarily be a "5 DoF" joint. Ie. 6 DoF of a free body, minus 1 constraint = 5 DoF.)

Loz

07-25-2014, 01:17 AM

Ralph

I have seen far worse, less "rough" sketches than that. I would say it is quite reasonable actually.

Quote Z:

"Strictly speaking, the "Pitch" motion (of AH wrt body) is about an APPROXIMATELY horizontal-lateral line that intersects the two TLs and the vertical S n-lines, and also intersects the Panhard-Bar-n-line....

Only when this "Pitch-axis" intersects ALL four of the AH-to-body n-lines (ie. 2 x TLs, S, and PB) is this line an Instantaneous Screw Axis (ISA) of zero thread pitch (ie. it is a "revolute" joint, like a simple hinge)."

"and also intersects the Panhard-Bar-n-line."; This I can not visualize. In my mind the line crossing the TLs n-lines and the S n-line would be in a different plane, at least as I picture it for this particular linkage and would never intersect. Unless of course I am not visualizing the correct n-lines particularly for the panhard bar.

They key here is the approximately horizontal-lateral line which isn't actually horizontal and is in fact most likely ever so slightly angled in some direction such that it intersects the panhard bar n-line. Where is intersects though is likely to be way off in the distance unless the panhard bar is angled away from the horizontal by large angle.
Where your visualisation probably goes wrong is from assuming the panhard bar n-line and the pitch axis are exactly parallel (not approximately). In which case they don't explicitly intersect, rather they implicitly intersect at infinity.

Realistically, only when the panhard bar is exactly horizontal and the approximately horizontal ISA is parallel to this line, is there likely to be a true revolute ISA (pitch axis). In all other cases, even for small angular angular changes in panhard bar or TLs in roll, there is an ever changing set of instant pitch and roll axes.

Loz

rwstevens59

08-29-2014, 02:52 PM

Well the stubborn old man is back with some preliminary drawings for plotting body roll and heave WRT an assumed fixed solid rear axle. i.e The use of descriptive geometry from the 'old days'.

What follows are pictures that I hope are mostly self explanatory.

Assumptions:

The axle is fixed in space and acts as the 'frame' while the body points are moved about it.

In the initial layout all links are co-planer with the knowledge that as soon as movement takes place they will not be.

Right from the start the very first problem I encountered was how to rotate the body about the axle, i.e. what frame of reference should I use?

Right or wrong I have chosen, for pure roll, to rotate the body around a horizontal line connecting the body spring/damper mounting locations. Due to the lateral restraint of the panhard link this will require a rotation and an associated translation of the body WRT the solid axle. Again your input on how correct or incorrect this might be would be appreciated.

Some pictures to go by:

309310311312313

Looks like I will need to add a second reply????

rwstevens59

08-29-2014, 03:05 PM

To continue...

Body Rotation followed by body translation along a horizontal line to realign the body panhard link body attachment point with its fixed arc of motion.

314315

The body is now rolled one degree to the right and has also translated.

I would appreciate your thoughts, experience in doing a 2D layout and constructive criticisms.

Several caveats:

Yes, I use SolidWorks daily in my real world job but will not have a seat of Solidworks anytime soon to carry on what is essentially a hobby.

For the same reason I do not, for solid axle suspensions, plan on investing in any of the 3D kinematics programs that actually work.

Performing the same task analytically in three dimensions leaves me with no pictures and I unfortunately need pictures to get my head around what is happening.

Thanks,

Ralph

rwstevens59

08-29-2014, 04:28 PM

Or...

Would it be more correct or conventional to roll the solid axle WRT the body??

316

rwstevens59

08-29-2014, 04:41 PM

Better picture
317

rwstevens59

08-29-2014, 05:23 PM

A comparison showing the discrepancies of the two methods used so far.

318319

So what I am clearly struggling with here is a clear definition of beam axle suspension roll. Dixon's definition of body roll is suspension roll plus axle roll on tires equals total body roll. Where he appears to measure the respective angles at the kinematic roll center.

I am clearly and purposefully neglecting axle/tire roll here because my only interest is in the motion path(s) of the axle WRT the body. I am just trying to form a clearer picture of axle motions, scrub and relative magnitudes of axle steers and link positions when moved from measured static positions.

08-29-2014, 09:38 PM

Ralph,

Well, it was only a little over a month ago that I said I would post a sketch and some more words on this "in the next week or so...". And I actually have most of the words written, and the sketch is half finished on the drawing board (honest!).

Unfortunately, there was that whole thing with the changed Rules that came up. And a few other questions via PMs. And Geoff has started an interesting thread that I have already started a looong reply to.. And I've got some boring but urgent business that must be finished by end of next week (deadlines!). And an old-boys' reunion tonight. Ahhh..., this "retirement" stuff is hard work! :)

Anyway, I'll do my best to get that sketch finished by end of next week. I think that once you get the gist of Ball's "Cylindroid" (aka Plucker's "Conoid"), then the 3-D Kinematics of 2 DoF joints (ie. Beam-Axle to Car-Body) becomes a lot easier to understand.

Z

rwstevens59

08-29-2014, 09:39 PM

One last iteration. I have also attempted stepping around the conventional kinematic roll center while making the appropriate rotation point change between each step as the roll center has moved.

As you can see by the panhard bar link length change this method is very close but certainly not perfect.

320

rwstevens59

09-03-2014, 08:56 AM

09-14-2014, 05:08 AM

FOUR N-LINE CONSTRAINTS = TWO REVOLUTE DoFs = ONE CYLINDROID.
================================================== ============

I have been wanting to give some more information about the 3-D kinematics of beam-axles for some time. Unfortunately, to do this properly requires quite a bit of preliminary theory, because most students will have never learnt any of it (ie. because of "failure of the education system", the 2-D-only approach used by the automotive-cottage-industry, etc., etc.). So a lot of work required before we can get to any practical applications, and many other things to do...

However, prompted by Ralph's specific questions above, I will just dive into the 3-D explanation of that particular example here, to give anyone interested in this subject a "taste" of it. I might come back to some of the more rigorous foundations later.
~o0o~

THE FOUR N-LINE CONSTRAINTS - The mechanical linkage of Ralph's rear suspension is shown at the top-left of the sketch below. I have distorted the geometry a bit to make it more general. The two main "links" are the Car-Body and the Axle-Housing. These are interconnected by four smaller links, namely the 2 x Trailing-Links, 1 x Slider, and 1 x Panhard-Bar. These four minor links determine the four n-line constraints between the Body and Axle, shown as n-TL1, n-TL2, n-SL, and n-PB. As explained many times before, an "n-line" is simply a straight-line along which there can be NO relative movement between the two bodies.

As noted in an earlier post these four n-lines can ALWAYS be ALL intersected by two other straight-lines. (Note that there can be "degenerate" cases where the intersections are "at infinity", and sometimes there can be infinitely many straight lines intersecting all four n-lines.) Here the two straight lines doing the intersecting are labelled ISA-'R' and ISA-'P'. The four n-line intersection points on each of these ISAs are shown as little white "balls". Note how the two Trailing-Link n-lines are deliberately drawn so that they do NOT intersect each other behind the car (ie. they are mutually "skew"). Nevertheless, it is still quite easy to find the line ISA-'R'.

The two ISAs are, of course, "Instantaneous Screw Axes" (see much Z-ranting elsewhere). In this particular case their screws have a "thread-pitch" = zero (ie. shown as "p = 0"), so they are "Revolute" joints (ie. like simple hinges). ISA-'R' might be called the "Roll Revolute", but it is only APPROXIMATELY so, because it is not necessarily exactly parallel with the centre-line of the car (hence the quote marks around the 'R'). Similarly, ISA-'P' might be called the "Pitch Revolute", but even more roughly so, because it is not very lateral to the car. More on this below...
~o0o~

THE TWO REVOLUTE DEGREES of FREEDOM - Any body that is completely free to move in 3-D space has 6 DoFs. Therefore, putting 4 x constraints on the body leaves it with (6 - 4) = 2 DoFs. Importantly, there are "two infinities" of different ways of specifying these 2 DoFs. At the right of the sketch is shown JUST ONE WAY of doing this, albeit a neat and easy to find way.

Here the Axle can move wrt the Body, and AT THE INSTANT, either as a pure rotation about the Roll-Revolute ISA-'R', or as a pure rotation about the Pitch-Revolute ISA-'P', or as two small pure rotations about BOTH these revolutes AT THE SAME TIME. In this last case, the Axle's motion wrt the Body is a SCREWING motion (ie. both rotating and translating) about another ISA that lies on the unique Cylindroid that is determined by the two revolutes. More details below...

Note that this "conceptual mechanical linkage" of two revolutes could equally have the central T-shaped-link, which interconnects Body and Axle, reconfigured so that ISA-'R' is between the central-link and Body, and ISA-'P' is between the central-link and Axle. For motions of Axle wrt Body, these two different mechanical configurations (ie. Body-P-R-Axle, or Body-R-P-Axle) are identical AT THE INSTANT. However, they will behave differently after significant finite displacements. This is worth keeping in mind when designing actual linkages like this.

Also note that, in general, any 2-DoF joint can be physically implemented as FOUR x 1-Degree-of-Constraint n-lines IN PARALLEL (eg. 4 x ball-ended-links, as at top-left of sketch), OR as TWO x 1-Degree-of-Freedom joints IN SERIES (eg. 2 x revolutes, as at right of sketch). Similarly, a 3-DoF joint can be done as 3 x (1-DoC) n-lines in parallel, or 3 x (1-DoF) revolutes in series. Or a 1-DoF joint, such as an "independent suspension" can be done as a "Five-(1-DoC n-line)-Links-in-Parallel", or as a "Single-(1-DoF revolute)-Swing-Arm".

Interestingly, less ingenious engineers prefer the "multi-link in parallel" approach (see most suspensions), whereas Nature prefers the serial approach (see most skeletons). Roboticists have tried both, but wisely follow Nature when persuing maximum versatility.
~o0o~

https://lh4.googleusercontent.com/-b-Uodba0jlc/VBVQgd1JBmI/AAAAAAAAARI/prK6q3OkgHw/s800/TheCylindroid.jpg

THE ONE CYLINDROID - A glimpse of this creature of 3-D Kinematics is shown in the middle of the linkage at the right of the sketch, with its "spine" lying on the common perpendicular of the above two revolute axes. A more detailed, close-up view of the Cylindroid is shown at the bottom-left of the sketch.

Actually, only a "core" taken from the Cylindroid is sketched, and you should imagine it extending outwards to infinity in all directions perpendicular to its spine. It is a "ruled-surface" formed by a straight-line generator that is always perpendicular to the spine, and moves sinusoidally up-and-down the spine as it rotates about it. This straight-line generator is shown more explicitly at each end of the spine, with these two positions being mutually perpendicular when viewed along the spine. So, after rotating 180 degrees, the generator is back to where it started.

Thus, the entire ruled-surface of the Cylindroid exists between two parallel planes that are at each end of the spine, and that are perpendicaular to it. So, when viewed from a large distance, the Cylindroid looks like an almost flat surface, but with a little wrinkle in the middle that is its spine.

In 3-D Kinematics the Cylindroid is probably second only in importance to the ISA/Motion-Screw. Hopefully by now most of you students will be aware that ANY 3-D MOTION of any one body, with respect to any other body, is best described by the ISA that exists between them. This ISA is also an extremely simple concept to understand, being nothing more than "a nut moving on a bolt". All of the straight-lines lying on the Cylindroid, and intersecting its spine, are ISAs. So the Cylindroid is formed from "a single infinity of ISAs".

The "thread-pitches" of these ISAs vary sinusoidally according to the ISA's rotational position around the spine. It is possible for all ISAs on a particular Cylindroid to be Left-Handed, or all to be Right-Handed, or, as in this example, some to be LH and others to be RH. The dividing lines between LH and RH ISAs are, quite obviously, ISAs of zero-pitch, namely revolutes. The magnitudes of the "thread-pitches", measured as distance-translated per radian-of-rotation, of all the ISAs on the Cylindroid are easily and uniquely determined, but I will leave that for another time...

But for now, a quick quiz:
Q1. Which of the ISAs on the above Cylindroid are RH, and which are LH?
Q2. Over what range do their pitch magnitudes vary?

Answers are quite easy...
~o0o~

While the Cylindroid is almost as ubiquitous a creature as the ISA, it is, like the teenage werewolves and vampires of modern movies, rather shy. So only keen-eyed, or well trained, geometric hunters can spot it. One of its first recorded sightings, in the early 1800s, was by William Rowan Hamilton, the Irish mathematician who also discovered Quaternions. Later, in the middle 1800s, the German mathematician Julius Plucker (pronounced Ploo-ker) tracked some down, and called them his Conoids. Shortly after, still in the middle 1800s, another Irish mathematician, Robert Ball, snared a few of them, and called them Cylindroids.

Because it is such a common creature it is always being rediscovered. So in the 1960s the Australians Jack Phillips and Ken Hunt stumbled across some of them in a small field of Kinematics. (They then did their homework and found that these creatures had been sighted many times before, as above.) In this case they found that whenever ANY three bodies are in relative motion, then the three ISAs that exist for the relative motion of each pair of those bodies ALWAYS lie on the same Cylindroid (eg. picture three asteroids floating about in deep space, and their mutual ISAs, 1-2, 2-3, and 3-1).

But the Cylindroid is also found in 3-D Statics, an entirely different field to Kinematics. Here, any three WRENCHES (ie. Force-Screws, and I hope all you students also understand this concept by now) that are in mutual equilibrium also ALWAYS lie on the same Cylindroid.

And it is also found in many, many other places...
~o0o~

More coming next post (10K char limit!!!).

Z

09-14-2014, 05:11 AM

FOUR N-LINE CONSTRAINTS = TWO REVOLUTE DoFs = ONE CYLINDROID. (Last bit...)
================================================== =======

Getting back to Ralph's suspension, since this is a 2-DoF joint between the Axle and Body, then there is ALWAYS a unique Cylindroid associated with that joint. Thus ANY instantaneous relative motion of Axle wrt Body must ALWAYS be about ONE of the ISAs lying on the Cylindroid. So as noted earlier, the motion can be about ISA-'R', or about ISA-'P', or about any ONE of the other ISAs that lie on the Cylindroid.

Repeating this last point for emphasis, a very small rotation about ISA-'R', TOGETHER with a very small rotation about ISA-'P', is EQUAL to a small SCREWING motion (ie. = rotation + translation) about ONE of the other ISAs that lie on the Cylindroid. The particular ISA that results from the two small rotations about ISA-'R' and ISA-'P' depends on the relative sizes of said rotations. (In a more rigorous explanation we would have to speak of relative "rotational velocities", namely dTheta/dts, because "rotational position vectors" DO NOT COMMUTE!)

Back to this specific example, a pure "Roll" rotation of Axle wrt Body, about the particular ISA that is purely LONGITUDINAL to the car in plan-view, will have a small amount of "screwing" (ie. as the Axle "rotates" about the ISA, it also "translates" along it, like a nut on a bolt). Similarly, a pure "Pitch" rotation about the ISA that is purely LATERAL in plan-view, will also have some "screwing".

More importantly, because the spine of this particular Cylindroid is not vertical (ie. the "plane" of the Cylindroid is tilted away from horizontal), ANY rotation about any of the ISAs that are not exactly horizontal (ie. all but one of them) will have some vertical component of rotation. Therefore, just from a glance at the Cylindroid, we see that almost all motions of the Axle wrt Body have some degree of axle-steer.

In general, for this sort of beam-axle 2-DoF joint, it is a good idea to try to keep the plane of the Cylindroid close to horizontal. That way any motion of Axle wrt Body has no, or negligible, axle-steer. However, as long as the Cylindroid's spine is not tilted TOO far away from vertical, or if it is tilted in the "right direction", then the amount of axle-steer might be acceptable. In practice it is a matter of knowing the numbers.
~o0o~

Bottom line, the "usefulness" of the Cylindroid is that just by taking a quick glance at it, we can get a good feel for different suspension behaviours.

EG1. "Whoa..., that rear-beam-axle's Cylindroid is leaning backwards far too much! The car is going to have terrible roll-oversteer."

EG2. The two axles on skateboards have Cylindroids designed to give very large roll-understeer. In fact, the skateboard rider rolls the Body (ie. tilts the "deck" in to the turn) to make the skateboard steer.

EG3. A double-wishbone (or "5-link") suspension WITHOUT the toe-link is a 2-DoF joint (ie. with Body fixed, the Upright can rotate about the ~vertical "steer-axis", OR it can rotate about the ~horizontal "instant-axis", OR it can move about both together). So there is a Cylindroid in there! Adding the toe-link determines which of the single-infinity of ISAs on the Cylindroid becomes the unique ISA for motion of Upright wrt Body.
~o0o~

Enough for now...

Questions welcome, and maybe some sketches of different beam-axle-linkages and their Cylindroids later...

Z

rwstevens59

09-14-2014, 03:34 PM

Z,

Whew, thank you for putting in the effort to keep me on the path to learning more and more about 3D kinematics. There was no way I was pulling the above out of Jack Phillips book on my own.

Many more questions and comments to follow.

For now I just wanted to express my gratitude for the work you have done to produce the above.

Ralph

Jay Lawrence

09-16-2014, 12:06 AM

Loz

09-16-2014, 01:34 AM

Jay

A few things to note.

... I have distorted the geometry a bit to make it more general.
I would guess that to enable general discussion, the sketch is an adapted version of Ralph's system which includes ISA's drawn at more convenient locations (i.e. easier to interpret).

The effects of the panhard bar link are taken into account in the series swing-arm/revolute joint mechanism.
Which is what the following statement pertains to:

Here the Axle can move wrt the Body, and AT THE INSTANT, ...or as two small pure rotations about BOTH these revolutes AT THE SAME TIME.

But importantly, we are effectively talking about infinitesimally small time steps and analysis at a singular instant (implicit in the term "Instant screw axis"). At another instant the ISA's have shifted to take new directions. Which is where the cylindroid comes into play. At each instant the two revolute ISA's can shift up or down the cylindroid spine with the sinusoidal variation defining the cylindroid.

This is a main reason that it is necessary to consider the suspension mechanism in 3D and not 2D because things like the ISAs aren't necessarily fixed in space, especially in the case of these multi-link mechanisms with more than 1 DOF.

Loz

Kevin Hayward

09-16-2014, 02:32 AM

Z,

Thanks again for your drawings and descriptions. I find it much easier to work through numerical methods through simulation, a side effect of studies in computer science. I never liked looking at 3d problems using 2d sketches. Although with improved 3D CAD packages the geometric methods are very easy to setup. Creating the cylindroid in a 3d sketch in Solidworks was a trivial exercise and it reveals quite a lot very quickly. Not prepared to give up on the numerical methods in design purely for the fact that iteration and analysis of results can be very easily automated and reviewed in bulk. Please note I am not talking about plugging away at OptimumK (or similar kinematics programs). They are fantastic to use, and I am pretty happy with what we achieved at OptimumG. However, not being able to program sweeps and solution search routines limits the effectiveness of these tools for fast design. It was the reason we included a excel spreadsheet input. This allowed the use of a spreadsheet to aid in the creation of suspension points in the first place. Much better to make your own geometry code and explore the solution space.

...

It should be noticed that for a simple four bar / symmetrical rear end the two ISA lines have been stated as the pitch and roll axes of the suspension system. In which case the tilting of the cylindroid can be controlled by altering the slope of the roll axis (which for this case will lie on the centre-plane of the car). I am reluctant to mention this simplification. I only do so to show how you can see existing (incomplete) knowledge of kinematics as drawn in a few texts applies in special cases. It does become a useful simplification in a few design cases.

I find design of these mechanisms to be purely a case of working through the unknowns. Keep adding your constraints until only one variable is changing the desired output. In the case of a beam axle with 4 links (8 points, 24 variables) you can make choose the following contstraints to simplify the problem (excluding spring/dampers):

- Assume symmetry (24 to 12 variables)
- Try and get as much lateral direction on the links as possible to provide inherrent lateral stiffness (12 to 10 variables)
- Given packaging use the lower mounts on the beam to be inboard, the upper to be outboard.
- Move lower mounts on the beam inboard as much as possible
- Move upper mounts on the beam outboard as far as possible
- Keep your beam mounts as close to the same plane as possible to improve inherrent beam stiffness (10 to 6 variables)
- Design to your anti-squat requirments / desires (6 variables to 5 variables)

Once this is done you are only playing with your 4 chassis mounts. Add a few more constraints based on the chassis:
- Width from template and structural design (5 to 3 variables)
- Decide height of "roll axis" (3 to 2 variables)
- Fix either lower or upper chassis mount based on packaging, ability to put a decent hardpoint, alternatively make one link as long as possible befor erunning into strength concerns (2 to 1 variable)

The only thing you are left to alter is the ratio of length of the top arms vs. the lower. This one variable will have direct control over the rollsteer of your beam. Sweep a value using geometry software, choose the result you want. Alternatively (or addittionally) use a geometric approach to view the cylindroid.

The problem with stating a solution method you use is that others will read it as the only way to solve a problem. However change the constraints just a little and you need to apply a new method. Hence the disconnect with how-to design texts and dynamics literature. In order to design you will need to introduce constraints, the trick is making sure you don't over-constrain the problem, and force yourself into a sub-optimal solution (i.e. we must have double a-arms with push-rods).

Make sure you have all your KPI's decided before you even start:
- Target component stiffness (really important for a beam, toe stiffness is likely more important than camber stiffness and could swamp the effects of mild rollsteer quite easily)
- Target component strength (make all the links close to planar with the car's centre planes and watch the axial loads climb through the roof. Good luck keeping it stiff and together.)
- Target pitch jacking (anti-squat)
- Target roll jacking (roll axis height)
- Target roll steer

I'm not sure if this adds anything to this discussion, but design of a good beam system is a lot easier than a double a-arm. You start out with a lot less variables in the first place. Assuming symmetry and non steering we have 18 for the double a-arm vs 12 for the beam. Of those variables for the beam it is quite easy to eliminate (or severly restrict) a number of them simply through structural concerns. One thing that is not often mentioned is that on a beam you can add some extra mounting points to decouple your heave and roll rates. i.e. Springs closer in will have the same heave rate, but softer roll. So if we compare the following symmetrical suspensions (double for asymmetric):

- Double a-arm with push/pull rods, coilovers, and an anti-roll bar (~43 variables)
- Beam with direct acting coilovers and an added variable for altering distance between spring mounting for tuning roll/heave characteristics (19 variables)

Structurally a beam is no harder to design than an upright, and the links can just be big tie-rods. Welding can be easier than an upright or a-arms as you have a bit of space to get to everything, and you wont want super thin sections. Weight differences of the components are negligable. The beam requires a lot less support structure (i.e. 6 chassis mounting points vs. 14 for the double a-arm), so a beam system will be lighter overall (quite significantly lighter). Add in the fact that the chassis mounting points will be closer to the COG of the car and your chassis structure can be a lot shorter as well.

Every team should consider the option and do some preliminary designs. It takes very little time to do the early studies. If you then decide to go double a-arm at least you ahve a good idea of the trade-offs you have made in cost, weight, ease of manufacturing, component count in order to get whatever you wanted from the double a-arm.

Kev

Mitchell

09-16-2014, 03:34 AM

Structurally a beam is no harder to design than an upright, and the links can just be big tie-rods. Welding can be easier than an upright or a-arms as you have a bit of space to get to everything, and you wont want super thin sections. Weight differences of the components are negligable. The beam requires a lot less support structure (i.e. 6 chassis mounting points vs. 14 for the double a-arm), so a beam system will be lighter overall (quite significantly lighter). Add in the fact that the chassis mounting points will be closer to the COG of the car and your chassis structure can be a lot shorter as well.

Every team should consider the option and do some preliminary designs. It takes very little time to do the early studies. If you then decide to go double a-arm at least you ahve a good idea of the trade-offs you have made in cost, weight, ease of manufacturing, component count in order to get whatever you wanted from the double a-arm.

Kev

UQ Racing has shifted to a beam axle this year for the reasons in bold. The rear of the chassis is now just the regulated roll hoop support bars.

We are using a peg and slot (hidden behind the bottom of the shock) and 4 link.

332

The biggest saving is in chassis structure, with the change in unsprung being (at least for us) negligible.

It has also improved access to the engine and general working on the rear of the car, which can be removed with only 5 bolts.

Mitchell

rwstevens59

09-16-2014, 04:53 PM

Z,

To repeat Ralph's sentiment: thanks for that! This is all (unfortunately) quite brain frying in a way, and I don't claim to properly understand it yet, so this question may sound quite silly:

I'm confused by the way you have modelled Ralph's ISA-'R' wrt the Panhard bar. On the ISA-'R' portion of your 2 revolutes (RHS of sketch) there doesn't appear to be any effect from the location of the Panhard bar. I would have thought that the Panhard bar link would allow roll but at the expense of providing some level of lateral axle movement (unless we assume that the Panhard bar is located on some frictionless joint at the centre of the 'diff'). i.e. I would think that the ISA-'R' line/revolute would be angled in plan view

Jay Lawrence,

Maybe it would help if I explain my thought process while studying my own 2D drawings and why the need for 3D thinking becomes obvious albeit not necessarily intuitive for one not trained to 'spot cylindroids'.

Some conditions first as per my 2D drawings:

The trailing links are parallel longitudinally in plan view at static setup.
The trailing links slope down from the body mounts to axle mounts at 5 deg. Both links are parallel in side view i.e. not skewed.
The panhard bar is located in front of the axle and about 3.5 in. below axle centerline and is level (i.e. in the center of its arc of travel) at static setup.
The live axle pinion nose angle is at zero degrees i.e. level with the ground as set by the torque arm slider at static setup.

Now lets attempt to roll the axle with respect to the body about some point, axle centerline or axle roll axis and roll center as described in Milliken, Olley and a host of other chassis reference texts.

You are correct as the axle rolls WRT body the axle will move laterally due to the panhard bar arc radius.

Simultaneously the side view trailing links are moving in opposite directions along their side view arc paths causing the axle to steer in plan view.

But wait...if the axle is moving laterally in rear elevation view are not the trailing links also moving in arcs in plan view WRT their respective body mounts.

And if that is true than the side view arc paths of the trailing links are being skewed by the action of the panhard lateral movement so we can not say that the trailing links follow their side view arc paths the moment any roll takes place.

To make matters worse if all of what has been said up to this point is true than the steer of the axle has moved the axle out of parallel with the panhard bar causing an additional albeit small further lateral movement of the axle due to the now angled panhard bar in plan view.

OK. Now that your head hurts as much as mine you can see why two wheels on a pipe connected to a body with four links is anything but simple as it would appear.

We now have two choices (maybe more, but the only ones I can think of) set up our coordinate system(s) and use analytic geometry coupled with an iteration routine to plot our points through some arbitrary magnitude of axle roll with respect to body or start to learn more about 3D kinematics as shown by Z to give us a picture of what is happening at any instant in time.

Being a 'picture guy' first before heading for the computer I much prefer the latter to develop my 'gut feel' for the motions first.

Lastly, I am not trying to design this suspension. It already exists in hundreds of cars that race here in the U.S. and I am simply doing an exercise in reverse engineering to better understand the layout as well as dispel some of the setup voodoo I hear all the time.

So that, to date, is my thinking on the interactions and complications of thinking about a beam axle in 2D vs. 3D.

Corrections, observations and criticisms welcome as always.

Ralph

Jay Lawrence

09-16-2014, 11:50 PM

Thanks Ralph. In reality, for me it is easy to crack open Solidworks, model it up and see how it all works, but I guess like you I'm trying to use some crayons (which gets tricky for all the inter-related constraints you've mentioned).

Mitchell, thanks for the image. I'm interested to see how your car works out. Is there a better picture that shows things a bit clearer? Bit hard to see how it all works with all those black links. Love the majestic magenta highlights by the way :)

09-17-2014, 12:15 AM

Jay,

"... all ... quite brain frying in a way, and I don't claim to properly understand it yet,..."

Like most other things, the first step to understanding these things is to learn how to "talk the talk".

So now you know that there is a thing called "the cylindroid"...
and it is intimately related to 2 DoF Kinematic joints...
and you can also find it in double-wishbone suspensions...
but it also is common in 3-D Statics, with Wrenches and stuff...
and it sort of looks like a long threaded rod (of variable thread-pitch, apparently?) that spins around a short axle called the "spine"...
and ...,

Well, that is a pretty good start. :)

Hopefully by now the concept of Motion and Force Screws is also starting to become more of an everyday thing. I reckon all this would be a lot easier if all the "Whizo Suspension Programs (now in all-new, full-colour, 3-D!!!)" would show these Motion and Force Screws as standard. The "understanding" would then sink in without you even realising it. The cylindroid, of course, is simply made up of a lot of these "screws" spun around the spine. So any genuinely 3-D program that claims to model beam-axle linkages should also show where the cylindroid is (perhaps just in an abreviated way as in my sketch).

But ..... I am not aware of any suspension program that shows the ISAs yet... Come on guys...
~o0o~

"I'm confused by the way you have modelled Ralph's ISA-'R' wrt the Panhard bar...
... I would think that the ISA-'R' line/revolute would be angled in plan view."

I hope Loz answered that. The Panhard-Bar n-line ("n-PB" at top-left of sketch) intersects ISA-'R' just to the right of the differential. So, yes, ISA-'R' is at a slight angle, being on the car centreline near the Slider, but angling outwards-going-backwards, to pass to the right of the diff.

(I should note that I started the sketch about a month ago, then got interupted with a bunch of other stuff. When I got back to finishing the sketch I decided to change a few things, kind of forgot a few bits (at top-left, the "Body" should have an "arm" reaching back to the PB...), drew a few bits in slightly the wrong places, etc., etc...)

To help with the general understanding I will try to do some more sketches of more conventional (ie. symmetric) beam-axle linkages, suitable for FSAE cars, ... err... soon.

In these cases the quite conventional description, which shows a side-view of the various link-axes (ie. n-lines) intersecting at a "Pitch-centre", and maybe also shows the "Roll-axis" of the beam, is pretty much all you need. In such cases the cylindroid's spine is the short line, perpendicular to the Roll-axis, that joins the Roll-axis (ie. the revolute = ISA-R) to the Pitch-centre (ie. the revolute = ISA-P, but seen only as a point in side-view).
~~~~~o0o~~~~~

Kev,

"It should be noticed that for a simple four bar / symmetrical rear end the two ISA lines [of zero thread-pitch] have been stated as the pitch and roll axes of the suspension system. In which case the tilting of the cylindroid can be controlled by altering the slope of the roll axis (which for this case will lie on the centre-plane of the car). I am reluctant to mention this simplification. I only do so to show how you can see existing (incomplete) knowledge of kinematics as drawn in a few texts applies in special cases. It does become a useful simplification in a few design cases."

Yes, as I wrote in the last paragraph above. I do agree that this simplified approach (ie. side-view only) is almost all you need to get a good design. The extra 3-D information is only necessary to check what happens towards the ends of the wheel travel, when everything goes skew, and only for cars with long wheel travel (ie. off-road), or maybe when using very short links.

I want to do a few sketches of variations of your (ECU's) four-link rear end. I reckon it is a good layout for FSAE, for a whole lot of reasons. But there are also lots of little variations that can be made that may make it easier to do in a different car (ie. with different engines, whatever). The thought processes involved in making the variations, while constantly going back to the 3-D Kinematics, then becomes useful for solving a whole range of other problems.

Err..., soon ... hopefully. :)
~~~~~o0o~~~~~

Mitchell,

Now you have to start driving it like you stole it! :)

And then keep ironing out those little bugs...
~~~~~o0o~~~~~

Ralph,

"We now have two choices ... use analytic geometry ... or start to learn more about 3D kinematics."

I remember a class with Jack Phillips (late-1970s?) where we were discussing something very 3-D-ish (I think about the ISAs spread around a "regulus" = hyperboloid of revolution?). The next class was the following morning. He walked in with a model he had made up overnight, consisting of a ~half-dozen, metre long dowels of wood (maybe 10 mm diameter), some bits of fret-sawed plywood to hold the dowels together, and, no doubt, quite a few lengths of different coloured string.

The "answers" became very clear, very quickly.

For a four-bar beam-axle linkage, I might start with a box of toothpicks (the ones that are sharp at both ends) and two matchbox-sized blocks of polystyrene foam to represent Body and Axle. All at about 1/50 or 1/32 scale (metric or imperial). Plasticine could be used instead of the PS-foam. Then I might upgrade to shish-kebab skewers about 20 cm long x 3 mm diameter. Pretty soon I would be wanting to use Jack's 1 metre long dowels, and a scale of about 1/4, or even 1/2...

Two advantages of this approach for FSAEers.
1. The 3-D problems become very easy to see, and hence easier to understand.
2. Good hands-on practice for building the real car!
~o0o~

Another thing I have been wanting to mention for some time is your particularly short Panhard-Bar. Since your cars spend most of their time cornering to the left, this PB will mostly be in tension, being pulled by the Body's centrifugal force horizontally to the right. So, like a pendulum turned sideways, the PB, with the Body on the end of it, will always be trying to "hang" horizontally (ie. when cornering).

The shortness of the PB means that any relatively small up-or-down movements of the Body's PB-attachment-point (wrt Axle), changes the angle of the PB quite a lot, and so results in quite a large restoring force from the PB that tries to get the Body-PB-attachment-point back to its "comfortable" position where the PB is horizontal. This restoring force that tries to pull the Body down-or-up, naturally has an equal and opposite reaction-force pulling the Axle, near the right-wheel, up-or-down.

I would have to watch the cars' racing before conjecturing what sort of effects the above has on handling. But my guess now is that if the PB was on the other side of the car, where it would be in compression, then the cars would be UNDRIVEABLE! The unstable "inverted pendulum" action of the PB would, during high lateral-G cornering, either pull the left-side of the Body hard down on its bump-stops, or it would flip the left-side of the car upwards, with the PB possibly rotating a full 180 degrees (unless stopped by the dampers or whatever).

So the PB location and size makes sense. Unless the cars start cornering to the right!

Z

rwstevens59

09-17-2014, 06:10 PM

Z

And here is a quick example of a class of car run here in the states with a short panhard bar mounted on the left of axle centerline, totally decoupled four trailing links and a highly compliant torque arm mount.

While it flies in the face of convention, some seem to make it work!

A lot more differences than the suspension I am interested in, but too long to go into now.

334

09-17-2014, 09:36 PM

Ralph,

Interesting! It looks like the left-side PB was trying to flip the left-side of Body upwards (as I suggested above), but was stopped by the left-side suspension droop-stop.

Also, the action of the PB pushing the left-side of car upwards seems to have had the reaction of planting the LR wheel (pushing it down onto the road) as seen by the wrinkling of the LR tyre wall, which, presumably, it is still giving forward thrust.

(Edit: So effect of the PB+droop-stop is LR hard on ground, but LFront lifted OFF ground?)

I guess if the driver doesn't mind the Body moving around like that, then the car IS driveable.

Lots of ways of skinning a cat... :)

Z

Jay Lawrence

09-17-2014, 11:38 PM

Thanks Z.
I understand the concept of the cylindroid and ISA's, but the practical implementation and relation to a given system is still taking its time getting into my head, but I will get there.

Can't remember if I've asked this before, but why do you talk about centrifugal force?

09-20-2014, 12:16 AM

Can't remember if I've asked this before, but why do you talk about centrifugal force?

Jay,

Just calling a spade a spade. :)

A "centrifugal force" is the VERY REAL inertial force that pushes/pulls the driver, or the car, or anything else, outwards (ie. = "centre-fleeing") when going around a corner.

An interesting example of how far the Education system has spiralled down the S-bend is the fact that nowadays most Schools teach their students that such "inertial forces" are NOT REAL, or are FICTITIOUS, or have some other lame name to suggest that they are somehow lesser than the other "real" forces.

Is that what you are suggesting?

The really funny part is when you ask the, ahem, "Teachers" to explain their reasoning behind that ideology. Wow, such poor clarity of thought!!! (Followed by much :) on my part.)

If anyone cares to give their arguments for why "inertial forces" are NOT real, then please do!

Z

Markus

09-20-2014, 07:40 AM

I'm not a teacher and honestly don't even care about todays education, but I'm bored enough to bite the bullet (this is not an answer to why inertial forces aren't real though, 'cause I consider them real, and there's nothing here you wouldn't know from before anyway). :)

Intertial forces are called fictitiuos (stupid choice of name IMO) because they are a "byproduct" of accelerating an object with mass into any direction, caused by the objects resistance to be accelerated. For example nothing "pushes" the car outwards when cornering, instead the car is resisting the acceleration caused by being pushed inwards by the tires, and trying to return to zero acceleration state i.e. landing in the woods. :)

If you draw a FBD of a car negotiating a corner, either centrifugal force "doesn't exist", Fy generated by the tires "doesn't exist" or your data acquisition is lying about the lateral acceleration of the car, because you can't have acceleration if the sum of forces is zero. In essence the whole subject is just a "flaw" of the system we use to simulate reality.

But I didn't pay that much attention in school, so I don't know the extent to which inertial forces were bullied... :D

Jay Lawrence

09-22-2014, 12:02 AM

Fair enough. I just struggle to define a centrifugal acceleration, which means I struggle to understand how there can be a centrifugal force (separated from centripetal force obviously).

09-24-2014, 01:06 AM

INERTIAL FORCES.
===================

Jay,

If your car's velocity vector is to turn around a corner, then the car needs a centripetal ("centre-seeking") acceleration. Inertial forces are always in the OPPOSITE direction to the acceleration of a massive body, hence you car feels a centrifugal ("centre-fleeing") force.
~~~~~o0o~~~~~~

Intertial forces are called fictitious ... because they are a "byproduct" of accelerating an object with mass into any direction, caused by the object's resistance to be accelerated. For example nothing "pushes" the car outwards when cornering, instead the car is resisting the acceleration caused by being pushed inwards by the tires, and trying to return to zero acceleration state... (My emphasis.)

Markus,

Thank you. Your explanation is similar to those typically given by today's Education system. Sometimes the emboldened words are replaced with "the body wants to...", or "has a tendency to...", etc., but otherwise with the same gist as yours.

I will now show just how ABSURD that kind of thinking is.

(Markus, please note that this is not directed at you, since you are simply repeating what you have been taught. This is directed at the failed Education system generally.)

Also, what follows is quite long, and has little to do with Beam-axles. It is mainly big-picture stuff, aimed at giving anyone interested a better appreciation of the quality of your current education.

And maybe it's a fun distraction from the ongoing Rules debates... :)
~o0o~

To aid my argument, first imagine this scene. You are lying on the soft, green, grass of a meadow. The Sun's rays, which are a form of Electro-Magnetic radiation, a system of "very real forces", gently warm you. The Earth's Gravity, another "very real force", gently pulls every particle of your body downwards. The contact forces between the ground and your lower body, which are again "very real EM-forces", counteract the Gravity forces. Aahhh, so relaxing...

Except that a short while ago you were enjoying a scenic balloon flight. Unfortunately, being a high-spirited student, you were goofing-off and accidentally fell out of the basket. For a short time you experienced a very pleasant period of "free-fall", where you felt almost no forces acting on your body at all. Just a gentle wind...

But then ... a very sudden upwards force from the ground subtracted speed from your, by then, quite large downward velocity. The end result of that short period of upward acceleration is that your body now looks like a super-sized pepperoni pizza!

BUT (!!!!!!) you know that things can only get squashed-flat like you now are, when there are TWO opposed forces squashing the things together. For instance, you can remember playing with that large hydraulic press in the FSAE workshop, and you know that stuff only gets squashed when BOTH the top AND the bottom plates of the press are pushing hard on the body, in OPPOSITE directions, and at the SAME TIME.

BUT (???) you also remember being taught that the ONLY "real force" acting on you a moment ago was the upward one from the ground. Err..., because that's the "very real EM-force". Apparently, there was NO DOWNWARDS INERTIAL FORCE whatsoever acting on your body, because those forces are NOT REAL!

So why is your body squashed so bloody flat!! And why does it hurt so bleeding much!!!
~o0o~

Let's use reductio ad absurdum to show how silly your teachers are. We start by assuming that the standard argument above (ie. in Markus's quote) is a VALID one. We now apply that reasoning to different situations.

1. When an apple is ripe enough, it releases its EM bonds with its tree, and accelerates downward toward the Earth.

But, according to M-reasoning, this common natural phenomenon has nothing to do with a "real force of Gravity". This is because we choose to call the concept of Gravity a "fictious force", which is to say, it is UNREAL!

Rather than being the work of a "real force", we say that this phenomenon is simply a "tendency" that apples have, whereby they "want to", or are always "trying to" (to use the correct M-terminology) get closer to the Earth. Similar "tendencies" afflict all massive objects, even big ones like the Moon that is always "trying to" get closer to the Earth.

We say that all these phenomena are just "by-products" of the relative positions of different bodies that have the property of mass.

Therefore, we have "proved" that Gravity is NOT a real force.

2. When a compass needle is turned to face East, and then released, it swings around to again face roughly North.

Again, this has nothing to do with a "real Magnetic force", because Magnetism is a "fiction", and is NOT a real force at all. Instead, those sorts of phenomena are simply something that compass needles "try to" do. They are a "by-product" of electrically charged particles moving in circles, or something like that.

Likewise, all those electric motors that misguided FSAE students use DO NOT generate any "real forces" at all. All those observable phenomena of E-cars scooting around racetracks are just "tendencies", and "by-products", of stuff "trying to" behave in certain ways.

Therefore, we have also "proved" that Electro-Magnetism is NOT a real force.

3. Similarly, we can "prove" that the Strong and Weak-Nuclear forces, or any other phenomena that anyone cares to describe as "a real physical force", is NOT REAL. We simply call them "tendencies", or "by-products", or some such...

So, are we making progress?

Summing up here, the standard arguments for why "Inertial forces" are NOT real, can be equally used to "prove" that none of the other forces are "real" either. Or, looking at it from the other direction, exactly the SAME arguments that are used to prove that Inertial forces are "UNreal", are also used to show that other forces ARE "real"! This is an ABSURD approach to reasoning, and we should try something more sensible.

If it walks like a duck, and it quacks like a duck, then call it a duck.
~o0o~

What can we classify as "real physical forces"?

Example 1. When the prices of things go up and down, the phenomena is said to be the result of "market forces". Unfortunately, the whole process is rather complicated, and it is very difficult to accurately, and consistently, predict future results from some reasonably simple theory. So maybe better to call these phenomena the process of "supply and demand pressures" (ie. because the word "pressure" is so frequently abused in its meaning).

Example 2. In Springtime, when boys show a "tendency" to bump into girls, the phenomena is referred to as "the force of love". Unfortunately, this whole process is very complicated, and it is all but impossible to accurately, and consistently, predict future results from some reasonably simple theory. So maybe better to call this phenomena "hormonal urges", or some such...

Example 3. When particles of stuff that have something called "electric charge", which can be either "positive" or "negative", are placed in a certain POSITION relative to each other, then they "try to" either move closer together, or move further apart. These phenomena are said to be the result of "Electro-Static forces". They can be very accurately, and very consistently, predicted with a very simple theory. So, yep, this is a good contender for a "very real physical force".

Example 4. When the above charged particles are moved at certain VELOCITIES relative to each other, then they "try to" change their relative velocities in certain ways. These phenomena are said to be the result of "Electro-Dynamic forces" (or sometimes "Magnetic forces"). They can be very accurately, and very consistently, predicted with a slightly more complicated theory. So, yep, another good contender for a "very real physical force".

Example 5. When particles of stuff that have something called "mass" are placed in a certain POSITION relative to each other, then they always "try to" move closer together. These phenomena are said to be the result of "Gravitational forces". They can be very accurately, and very consistently, predicted with a very simple theory (ie. in fact, very similar to Example 3 above). So, yep, another good contender for a "very real physical force".

Example 6. When any single particle of the above sort of stuff with "mass" is ACCELERATED relative to all the other such massive stuff in the Universe, then it always "resists" this change in its motion (to use M-terminology). These phenomena are said to be the result of "Inertial forces". They can be very accurately, and very consistently, predicted with an exceedingly simple theory (ie. the simplest so far, just "F => P-dot"). So, yep, another good contender for a "very real physical force".

And so on with the "Nuclear forces", where the theory gets a bit more complicated, but the predictability remains good.
~o0o~

Bit more coming (10k char limit!)...

Z

09-24-2014, 01:08 AM

INERTIAL FORCES (last bit...).
======================

So, what went wrong with Example 6 in above post? Why were Inertial forces given the cold-shoulder?

It seems to me that the problems started a bit over a hundred years ago. The following is a very abbreviated account.

In the 1800s there was much progress in understanding EM forces. Maxwell and others eventually developed the "field equations" of EM-theory. These led to a realisation that "light" was a wavelike EM phenomena. But waves like sound need a "medium" to travel through, and light was known to travel through a vacuum.

No problem, because "The Luminiferous Aether" was simply conjectured to be this medium. The concept of an ever-present Aether was around for much longer, even before Newton's Absolute Space. But then various experimentalists, such as Michelson and Morley, found that there was no measurable Aether-drift, namely no measurable shift in the speed of light due to Earth's movement through the Aether. Bummer!

In the first years of the 1900s, Einstein, ahem, borrowed Mach's ideas regarding relativity. These ideas were an attempt to abolish concepts like Newton's Absolute Space and the Aether. Einstein then stole Lorentz's, Poincare's, and others', work and presented it as his Special Relativity. Ten years later he stole Hilbert's maths and presented it as his General Relativity.

These two Relativity theories are fundamentally opposed to any ideas of an Absolute Space, or anything like an Aether. (Bizarrely, GR has at its very core a version of Galileo's Law of Inertia (= Newton's First), although in an unstated way.) But Einstein was a great self-promoter, SR and GR had a great marketing campaign behind them, and eventually they became The Absolute Truth.

So, even though SR and GR have some huge holes in them (eg. google "Twin's Paradox"), they are nowadays the only way that Modern Science is allowed to describe things at these macroscopic scales (QM is just for small stuff). And since SR and GR have no mechanism for explaining Inertial forces, it is the Inertial forces that had to be kicked out...
~o0o~

The twist in the tale.

The latest bit of populist science you students might have heard about is the "discovery" of the Higgs-Boson. Interestingly, while this discovery amounted to a few blips on a computer screen somewhere in Switzerland, many Scientists consider it rock-solid, 100%, iron-clad, proof of existence. Some are a bit more cautious. But its moniker as "The God Particle" certainly has a lot of people talking about it.

Anyway, the key point here is that the Higgs-Field is conjectured to give all other particles their property of Inertial Mass. That is, it gives everything a "resistance to acceleration". So the HF is very much a modern version of the Aether, or Newton's Absolute Space, or so on. Try googling Higgs + Inertia + Aether/Ether, etc.

Lots of other interesting stuff here, but I have waffled on too long. The key points you students might want to think about are:

Why is your Science Education so IDEOLOGICAL? That is, why is it a belief system remarkably similar to many religions, where you must believe what is written in some Gospels, even if those ideas are utterly ABSURD?

Will your Teachers ever admit that they were rather stupid to claim that "Inertial Forces are NOT REAL"? That is, will they ever admit that a hypothesis different to the one that they have hung their hat on, might now have more evidence favouring it (ie. the HF+)? Do experts ever admit that they got it wrong?

Will there ever be a return to WELL-REASONED discussions in Natural Philosophy? Or will the decline in standards continue?

Finally, are Double-Wishbone+Push/Pull-Rod&Rocker suspensions really The One and Only Absolute Truth? Are Beam-Axles really the work of the devil?

Z

Markus

09-24-2014, 03:13 AM

Firstly, I want to apologize for not using "Z-approved" terminology. I'm not native in down-under, and I'm lazy enough to prefer using describing words to finding the correct words.

Secondly, this post merely continues the discussion about inertial forces or todays education system but criticizes the downward spiral of our forum discussion culture...

INERTIAL FORCES.Markus,

Thank you. Your explanation is similar to those typically given by today's Education system. Sometimes the emboldened words are replaced with "the body [B]wants to...", or "has a tendency to...", etc., but otherwise with the same gist as yours.

I will now show just how ABSURD that kind of thinking is.

(Markus, please note that this is not directed at you, since you are simply repeating what you have been taught. This is directed at the failed Education system generally.)

Also, what follows is quite long, and has little to do with Beam-axles. It is mainly big-picture stuff, aimed at giving anyone interested a better appreciation of the quality of your current education.

And maybe it's a fun distraction from the ongoing Rules debates... :)
~o0o~

[so long, read from post above]

Gravity causes acceleration in the body, inertial forces are caused by accelerating the body. Apples vs oranges, would have been more aid to leave your nice short novel to the table.

BUT (!!!!!!) you know that things can only get squashed-flat like you now are, when there are TWO opposed forces squashing the things together. For instance, you can remember playing with that large hydraulic press in the FSAE workshop, and you know that stuff only gets squashed when BOTH the top AND the bottom plates of the press are pushing hard on the body, in OPPOSITE directions, and at the SAME TIME.
It would be possible to "squash" the stuff with a hammer and without an opposing plate by hanging the object on a string and hitting it with a hammer. Thus the opposing force would be the inertial force and there would be acceleration to the body in each hit. :)

But the squashing is a bit different between the two: imagine hitting an apple with a baseball bat (inertial opposing force) and hydraulic press (direct opposing force). Or a superball. ;)

Let's use reductio ad absurdum to show how silly your teachers are. We start by assuming that the standard argument above (ie. in Markus's quote) is a VALID one. We now apply that reasoning to different situations.

[list of three examples, see post above]

So, are we making progress?

Summing up here, the standard arguments for why "Inertial forces" are NOT real, can be equally used to "prove" that none of the other forces are "real" either. Or, looking at it from the other direction, exactly the SAME arguments that are used to prove that Inertial forces are "UNreal", are also used to show that other forces ARE "real"! This is an ABSURD approach to reasoning, and we should try something more sensible.

If it walks like a duck, and it quacks like a duck, then call it a duck.
I appreciate your use of latin, but the term you are looking for is straw man, not reductio ad absurdum.
Reductio ad absurdum would require an initially correct analoque and reducing it into absurdity.

What can we classify as "real physical forces"?

[Example 1-6 check post above]

Examples 1&2 are called fallacy of equivocation.
In examples 3-5 the contenders for force cause acceleration.
In example 6 the contender for force is caused by acceleration.

This still doesn't mean that inertial forces aren't real, but how they differ from the rest in this flawed system we're using.
Maybe an example of an inertial force causing acceleration would really stir this conversation up?

Will there ever be a return to WELL-REASONED discussions in Natural Philosophy? Or will the decline in standards continue?
I agree with this completely. To begin with please practice what you preach and please stop with the red herring and gish gallop (almost 2000 words, really?), it would result in a lot more (fruitful) discussions.

On a final side note, I'm not a huge fan of todays educational system either (even though it seems to be a bit better in Finland than Australia if Eric's blood pressure is an indicator of some sort) and would hope for more criticism towards it, however in a better constructed way compared to above...

Disclaimer: I did not consider the "vulnerability" of not using full quotes, so the original posts might or might not be like they were when I wrote this. Likely there's edits, so take this with a grain of salt.

rwstevens59

09-24-2014, 11:59 AM

Gosh!!

And I thought I was just an old 'backward' mechanic who thinks about certain dynamic problems as frames from a film strip. Taking each frame, setting up an FBD of known conditions and then applying D'Alembert's principle to solve as a statics problem. Who knew! :)

All in jest, everyone!

Ralph

09-24-2014, 10:48 PM

Marcus,

Firstly, I want to apologize for not using "Z-approved" terminology....

My use of the phrases "M-reasoning" and "M-terminology" was a reference to your (Marcus's) quoted version of the standard Modern Education argument for "why Inertial forces are NOT real". As I noted, you have learnt this absurdity well.
~o0o~

Gravity causes acceleration in the body, inertial forces are caused by accelerating the body. Apples vs oranges...

Gravity does NOT always "cause" acceleration. You only have to stand on some bathroom scales to see that.

But, yes, Gravity and Inertial forces are different types of "real physical forces", so somewhat like apples and oranges are different types of "real fruit".

Also, in more formal discussions it is wise to say "... are conjectured to cause...".
~o0o~

It would be possible to "squash" the stuff with a hammer and without an opposing plate by hanging the object on a string and hitting it with a hammer. Thus the opposing force would be the inertial force and there would be acceleration to the body in each hit.(My emphasis.)

Yes. That is exactly my point. And that is why Inertial forces hurt so much.
~o0o~

... the term you are looking for is straw man, not reductio ad absurdum.

No.

From my Dictionary, "reductio ad absurdum Latin. n. 1. a method of disproving a proposition by showing that its inevitable consequences would be absurd."

Which is exactly what I did. I assumed M-reasoning to be correct, then showed that its inevitable consequences are that NO FORCES ARE REAL, which is absurd (or, at least, pointless).
~o0o~

Examples 1&2 are called fallacy of equivocation.

No.

The word "force" can be used in many ways, such as "the force of law", "force of personality", etc. I was NOT misusing this ambiguity to try to prove a point. Rather, I was trying to find which if those many types of "forces" could be classified as "real physical forces". The first two examples are NOT suitable, the rest are.

I think the main problem here is that Modern Education doesn't do DEFINITIONS anymore. By contrast, open Book 1, Page 1, of Euclid's Elements and the first word is...
~o0o~

In examples 3-5 the contenders for force cause acceleration.
In example 6 the contender for force is caused by acceleration.

This still doesn't mean that inertial forces aren't real, but how they differ from the rest in this flawed system we're using.
Maybe an example of an inertial force causing acceleration would really stir this conversation up?(My emphasis.)

The double-negative in there suggests that you think Inertial forces might be real, even though in your ME-indoctrinated M-reasoning you said that they are "fictitious". I sense a confused young man.

The small boy in you knows that the fall is NOT the problem, rather it is the sudden stop at the bottom that hurts. This is a matter of common sense, which all small boys understand.

But the educated young man has been so thoroughly indoctrinated in the belief-system that whenever there is any mention of acceleration, then all common sense must be abandoned, and you must believe that any pain at the end of the fall is pure FICTION!

And why the obsession with acceleration, and not position, velocity, electric-charge, etc.? (Rhetorical question, so think about it.)

(Or perhaps the confusion might be from Autumn-time hormonal urges... :))
~o0o~

On a final side note, I'm not a huge fan of todays educational system either ...
... and would hope for more criticism towards it, however in a better constructed way compared to above...

When you eventually decide what seems more reasonable to you (eg. Inertial forces are real, or NOT real, or on any other ME-related subject...), then please post your thoughts here on the Forum. I think we all enjoy well-reasoned discussions. But try to avoid the mistakes above... :)
~~~~~o0o~~~~~

Ralph,

... dynamic problems as frames from a film strip. Taking each frame, setting up an FBD of known conditions and then applying D'Alembert's principle to solve as a statics problem.

Gee, wish I said it so sweetly! :)

Z

rwstevens59

09-24-2014, 11:04 PM

I believe I warned you at some point Z, that I can't resist heavy sarcasm! It is part of my DNA. :)

Still working with, sketching and thinking about 2 DOF linkages. I'm getting there, just more practice needed.

Ralph

Markus

09-25-2014, 03:32 AM

My use of the phrases "M-reasoning" and "M-terminology" was a reference to your (Marcus's) quoted version of the standard Modern Education argument for "why Inertial forces are NOT real". As I noted, you have learnt this absurdity well.
Which I find funny, as I have never even learnt these terms in english. Also it seems you didn't read my post at all but just used it as an excuse to your (beforehand composed?) post to question the educational system (well you did literally ask for it, which implies planning, "I bit the bullet" to see what you come up with).

In any case, using such references is pointless and even disobliging, especially when you're jumping into conclusions and implying I stated something I didn't actually state (feel free to read my post now). Oh, and by the way it's written with "k" (see note about glasses further down).

Gravity does NOT always "cause" acceleration. You only have to stand on some bathroom scales to see that.

But, yes, Gravity and Inertial forces are different types of "real physical forces", so somewhat like apples and oranges are different types of "real fruit".

Also, in more formal discussions it is wise to say "... are conjectured to cause...".
Yes, it doesn't cause acceleration when there's a normal force present. Do we also have to start playing stupid?

I'll keep that term "conjecture" in mind if I ever end throwing up hypothesis' in any formal discussions.

Yes. That is exactly my point. And that is why Inertial forces hurt so much.
So you agree to my argument that the inertial opposing force is the "by-product" of the acceleration caused by hitting with a hammer?

If I just leave the thing hanging from the string will the inertial force squash it on it's own?
If I park my car in the corner should I be worried that the inertial forces will push it in the woods?

When I ride my bike and twist the throttle the inertial forces push it into a wheelie (almost analogue to cornering with car).
Should I be scared the inertial forces might push it into a wheelie when I'm just trying to cruise around town?

No.

From my Dictionary, "reductio ad absurdum Latin. n. 1. a method of disproving a proposition by showing that its inevitable consequences would be absurd."

Which is exactly what I did. I assumed M-reasoning to be correct, then showed that its inevitable consequences are that NO FORCES ARE REAL, which is absurd (or, at least, pointless).
Does your dictionary also teach you how to use reductio ad absurdum correctly? :)

No.

The word "force" can be used in many ways, such as "the force of law", "force of personality", etc. I was NOT misusing this ambiguity to try to prove a point. Rather, I was trying to find which if those many types of "forces" could be classified as "real physical forces". The first two examples are NOT suitable, the rest are.
Well, let's call it spamming then. If you were not trying to prove a point, what where you trying to achieve? Gibberish?

I think the main problem here is that Modern Education doesn't do DEFINITIONS anymore. By contrast, open Book 1, Page 1, of Euclid's Elements and the first word is...
I agree it's a problem.

The double-negative in there suggests that you think Inertial forces might be real, even though in your ME-indoctrinated M-reasoning you said that they are "fictitious". I sense a confused young man.
Also if you read the first sentence of my post, it "suggests" (actually says) that I indeed consider inertial forces real. I sense an old man with an acute need of replacing his reading glasses.

I used the term "fictitious force" as it's the generally used term for inertial forces, not as any sort of reasoning. By the way, the only finnish translation equals "inertial force", so nothing to do with being real or not. Does this mean our education system is now better than yours? :)

The small boy in you knows that the fall is NOT the problem, rather it is the sudden stop at the bottom that hurts. This is a matter of common sense, which all small boys understand.

But the educated young man has been so thoroughly indoctrinated in the belief-system that whenever there is any mention of acceleration, then all common sense must be abandoned, and you must believe that any pain at the end of the fall is pure FICTION!
Again gish gallop, but for the sake of answering I think it's the force caused by hitting the ground (declerating me into a stop) that causes the pain.

And why the obsession with acceleration, and not position, velocity, electric-charge, etc.? (Rhetorical question, so think about it.)

(Or perhaps the confusion might be from Autumn-time hormonal urges... :))
I think it's up to everyone to decide what approach they choose to work with. I usually use D'Alembert's principle as it works for me, and it's often approached with acceleration.

(Are you implying that you are too old for the hormons to effect or maybe stuff downstairs is not working anymore, so you have to relieve yourself to the FSAE forums?
I won't travel deeper into the path also known as ad hominem, you can keep it in your list of special latin-named repertoire.)

When you eventually decide what seems more reasonable to you (eg. Inertial forces are real, or NOT real, or on any other ME-related subject...), then please post your thoughts here on the Forum. I think we all enjoy well-reasoned discussions. But try to avoid the mistakes above... :)
For the time being I think I will continue the same way (inertial forces are real, and they're caused by accelerating an object). And I will also continue being openminded if I find something better or more suitable for me in the future.

I think the most important thing is to understand the flaws of the system you are using to simulate reality. The worriying thing for me is that there's a lot of people that don't understand this.

So for the University of 2015, we now want:
1. Change the name of fictititous forces to stop the discrimination of inertial forces
2. Better education about reasoning, argumenting and logical fallacies
3. ???

Markus

09-25-2014, 05:29 AM

Actually, nevermind.

09-25-2014, 10:43 PM

Markus,

No problem, I don't mind. So just some final clarifications for anyone else still interested in this subject.
~o0o~

Tiny little detail first.

Oh, and by the way it's written with "k"...

I know! (Marcus, it was NOT a mistake. Think about it... :))
~o0o~

Does your dictionary also teach you how to use reductio ad absurdum correctly?

Does anyone else think that my use of reductio ad absurdum (a few posts ago) was incorrect?

If so, then please post how it should be done. These Forums are supposed to be about sharing knowledge, and I would love to learn more...
~~~~~o0o~~~~~

Back to INERTIAL FORCES.
======================
The following are quotes taken from Markus's posts above. Importantly, note that the following sort of thinking is typical of most (99.9...%?) of students of the technical arts today (ie. Engineering, Science, etc.), so not directed at Markus.

I indeed consider inertial forces real.
...
...
...
Intertial forces are called fictitiuos because they are a "byproduct" of accelerating an object with mass...
...
If you draw a FBD ... you can't have acceleration if the sum of forces is zero.
...
So you agree to my argument that the inertial opposing force is the [B]"by-product" of the acceleration caused by hitting with a hammer?
...
I used the term "fictitious force" as it's the generally used term for inertial forces,
...
[After I (Z) suggest that Inertial forces cause the pain at the end of a fall]
Again gish gallop, but for the sake of answering I think it's the force caused by hitting the ground (declerating me into a stop) that causes the pain.

To me, there is undoubtedly great confusion above. Inertial forces are described as both "real" and "fictitious"! In fact, they are so "fictitious" that apparently they cannot hurt you!

Anyway, the crux of the Modern Science way of thinking, as given above, is that because...

... Inertial Forces are a BY-PRODUCT of ACCELERATION...,

... they MUST have a split personality, where they are both "real" and "fictitious".

(Although, the more "educated" is the Scientist, then the more "fictitious" is the force.)

BUT WHAT IS SO SPECIAL ABOUT "ACCELERATION"!!!???
~o0o~

As I noted earlier, all the other "Four Fundamental Forces of Nature" are "by-products" of quantities like mass, or electric-charge (or other sub-atomic stuff), and the kinematic POSITION or VELOCITY of these things relative to each other.

Inertial forces are the "by-product" of the mass of a body, and its kinematic ACCELERATION relative to [insert dramatic drum-roll...] ...
the rest of the Universe (ie. ALL the other masses, or Absolute Space, or the Aether, or the Higgs Field, or...).

It is the last line above that has lead to the IDEOLOGICAL banishment of Inertial forces from the "real world". Pure ideology, and quite pointless when solving Engineering problems.

Oh, and DO NOT believe the ideology that tells you that Inertial forces cannot hurt you. All small boys know better...

Z

09-25-2014, 10:53 PM

So for the University of 2015, we now want:
1. Change the name of fictititous forces to stop the discrimination of inertial forces
2. Better education about reasoning, argumenting and logical fallacies
3. ???

Markus,

YES! This I agree with 100%. :)

Z

Markus

09-26-2014, 02:55 AM

To me, there is undoubtedly great confusion above. Inertial forces are described as both "real" and "fictitious"! In fact, they are so "fictitious" that apparently they cannot hurt you!
Siding this... If you are hit with a baseball bat, what causes the pain? ;)

mecwill

09-26-2014, 07:03 AM

Does anyone else think that my use of reductio ad absurdum (a few posts ago) was incorrect?
Z

Sorry for me to bugger in, but I wanted to 'hear' that, the incorrectness; i've seen some other posts with several lines with incorrect logic/ values etc.. Maybe you just want to test us. Thats what a teacher should be, if he meets the right students.
I've understood a lot of what I know now from you ambitious posts; I have read and still read you posts.
If there's use of offtopic, I,ve said to write stuff :)

Thanks

Radu
TUIasi Racing

09-27-2014, 12:13 AM

If you are hit with a baseball bat, what causes the pain?

Markus,

The indoctrination is strong in you. :)

As all small boys know, if the the bat is moving very slowly, but unstoppably (ie. like a hydraulic press), then it slowly and gently pushes you out of the way. So, NO PAIN.

However, if the bat is moving very quickly, then Inertial forces hold your body in place, and the bat's (EM) contact forces squash the impact zone against the opposing Inertial forces. So, MUCH PAIN!
~o0o~

A good example of the absurdity of the Modern Education system is seen in the teaching of Special and General Relativity (SR and GR).

About 1915, Einstein based GR on the Equivalence Principle. Briefly, the EP says that Gravitational and Inertial forces are indistinguishable. The usual thought experiment used to describe this is as follows:

You are standing in a small room with no windows. You feel yourself being pulled downwards against the floor. The EP says there is no way that you can tell if there is a very large mass, say, the Earth, just below the floor pulling you down with Gravitational forces, or if the room is out in deep space and there is only a small rocket engine under the floor that is accelerating the room upwards at 1 G, and you are feeling the resultant Inertial forces acting downward.

So, by this very Principle, if Gravitational forces are "real", then the INDISTINGUISHABLE Inertial forces should be just as "real"! If it walks like a duck...

Furthermore, if the very large mass just below the floor happens to be a Neutron star, then your body feels exactly the same "forces" on it as if the upward acceleration of the room is extremely large, perhaps caused by a mega-Mythbusters'-style explosion. Namely, your body is squashed extremely flat! And the last thing that goes through your mind, is ...
... your feet.
~o0o~

Here is an example like the Hi-G one above. ("G" = Gravity, or acceleration, or same-same!?).

The Mythbusters' Rocket-Propelled-Truck-Hits-Stationary-Car. (http://www.discovery.com/tv-shows/mythbusters/videos/rocket-sled-meets-binary.htm) (Ignore that the boot of the car is filled with explosives, because they don't go off.) In particular, watch the slow-motion at about 45 seconds, and even better at times 1:20 and 2:20.

Even with no narration, you know when the film is slo-mo just from the behaviour of the truck and car. IMPORTANTLY, if those slo-mo bits were "real-time" speed, with the truck travelling at only a few mph, then the truck would simply push the car forwards and there would be very little damage. Maybe only a cracked tail-light.

BUT (!!!) it is very obvious that those sections are happening very quickly, with very high accelerations. And hence also very high "Inertial forces". It is also very obvious that something, let's call it "The Force of Inertia", is holding the front of the car almost stationary, while the truck progressively crumples the rear of the car.

If there are NO Inertial forces pushing leftward on the front-half of the car, in opposition to the truck pushing rightward, then NO squashing of the rear-half of the car.
~o0o~

The absurdity of the Modern Education system is that for most of the time between 1915 and now, the ideological dislike of an Inertial reference frame like an "Absolute Space" was put before good reason (see my previous posts). So nowadays GR is taught with little reference to the above Equivalence Principle (ie. the EP is very quickly skipped over, or even ignored) and Inertial forces are called "fictitious".

The real problem, IMO, is that the expert Teachers cannot say "We DO NOT KNOW how all this stuff really works. Nevertheless, here are some different, and inconsistent, hypotheses...". Being "experts", they want you to believe that they know everything, and have all the answers.

The big question is that now that the Higgs Field/Mechanism/Ether provides a slightly more justifiable way of explaining Inertial forces as being "real", will the Teachers start teaching so? Here I should note that these Higgs ideas only started to be developed in the 1960s, and although they fit in reasonably well with the "Standard Model" (ie. the one with Quarks, Gluons, etc.), they were considered speculative until those few blips on the computer screens in 2012.

My guess is that you will continue to be taught the absurdities until the current generation of Teachers get old and retire, or die. Perhaps when the students who are now growing up with the Higgs ideas become Teachers, then maybe things might change. But given the scarcity of well-reasoned thinking nowadays, I doubt it.

Idiocracy, here we come...

Z

11-20-2014, 05:58 AM

BEAM-AXLE KINEMATIC DESIGN.
=======================

A few months/pages ago I posted on "The Cylindroid" (http://www.fsae.com/forums/showthread.php?1324-Beam-Axles-Front-Rear-or-both.&p=121114&viewfull=1#post121114) and its connection with Beam-Axle kinematics. That post started with a given particular suspension linkage (ie. Ralph's Beam-Axle example), and that SPECIFIC LINKAGE was then ANALYSED to get some idea of how it behaves.

That is, we first identified the four "idealised" n-lines of the given physical linkage. Those four n-lines then determined a unique Cylindroid. That Cylindroid told us ALL the possible ways the Axle could move with respect to the Body, namely all the ISAs, and thus ALL the possible n-lines for the axle. Finally, this knowledge of the Cylindroid allowed us to predict how that particular suspension would behave when travelling over bumpy roads, namely its bump-steer, etc., or how it would respond to horizontal forces at the wheelprints.

(Note that the Axle's behaviour when subject to horizontal wheelprint forces (ie. due to acceleration, braking, or cornering) was NOT explicitly covered in that earlier post. Very briefly, the "anti-" effects of these forces are roughly as described in the "Jacking Forces" thread. However, note that Beam-Axles "jack" DIFFERENTLY to Independent-Suspensions, albeit according to exactly the same principles of Mechanics! I have covered this in a recent PM and might include it in a further post...)

BUT (!!! :)) the above process does not work when designing a NEW suspension, because there is NO GIVEN "specific linkage" to start from.

So, how do we go about SYNTHESIZING a new Beam-Axle suspension to suit a given problem, such as, say, FS/FSAE?

Well, I would suggest simply running the above "analysis" process backwards.
~~~o0o~~~

Namely,

STEP 1. - First, decide what sort of behaviour is wanted. This includes the amount of bump-steer wanted (if any!), the amounts of "anti-" squat, dive, or roll wanted, and consideration of any other desirable or undesirable Kinematic behaviour (...more details below).

STEP 2. - Next, determine a range of Cylindroids that characterise the above desirable motions of Axle wrt Body.

STEP 3. - Finally, from an appropriately chosen Cylindroid, choose four suitable n-lines that can be approximated by real, physical, links between Axle and Body. Choose these n-lines and their links so that they fit in well with the rest of the car's "big-picture" design, and also so that they work well structurally.
~~~o0o~~~

This is all easier understood by working through some examples. So below are five posts and sketches that go through this SYNTHESIS process. That is, from a high-level list of "wants" -> to detailed practical implementation.

Please note that all this was a bit rushed (ie. Silly-Season fast approaching, and exploding laptop power supply not helping...). So the "practical examples" should be taken only as a rough indication of what might work, but are not necessarily completely accurate in detail.

Also I haven't explicitly justified every decision made in the words written below. This is due to lack of space and time, but not due to lack of reasons. Any questions regarding the "reasoning" will be happily answered...

Z

11-20-2014, 06:01 AM

BEAM-AXLE (1) . REAR - CONCEPTUAL.
==================================
We wish to SYNTHESIZE a Rear Beam-Axle design. Following the above advice, we start by considering the Kinematic behaviour we want.

STEP 1. DESIRABLE KINEMATIC BEHAVIOUR.
======================================
1. AXLE ROTATIONS.
=================
1.1 STEER (ie. Axle rotation about vertical Z-axis) - This is a very important behaviour to consider. Imagine trying to drive fast around a bumpy corner while a "gremlin" is randomly steering your rear wheels. NOT desirable!

So, as a first approximation, we want NO steering of the Axle under any of its possible Kinematic motions (ie. NO "Yaw" rotation of Axle, wrt Body).

From a simple consideration of rotation vectors (strictly speaking, rotational "velocity" vectors) we see that the Axle can only steer wrt Body if it rotates about an ISA that has some vertical component. This means that we want ALL possible ISAs for the motion of the Axle to be horizontal wrt Body. It follows that the spine of the Cylindroid should be vertical, or at least close to vertical.

Importantly, note that because of manufacturing tolerances, etc., no Kinematics can work EXACTLY as expected. Nevertheless, the GOAL here is for horizontal ISAs. Any deviations from this goal can be considered later. Also note that we are NOT considering "compliance steer" here. In practice, this might be the biggest problem, but also to be considered later...

1.2 CAMBER (ie. about longitudinal X-axis) - The nature of a Beam-Axle fixes this behaviour. The Camber-Change of the whole Axle, and also of each individual wheel, is simply, and always, the change in the two wheelprint heights divided by Track-Width. Fortunately, this is the best possible Camber-Change that can be expected when driving on a smoothish road (ie. one that is essentially a straight-line between the two wheelprints).

(As noted elsewhere, on very bumpy roads (ie. with short wavelength bumps), the Camber-Angle between road-surface and wheel, at any instant, is set by the L-R position of the bump under the wheel. There is nothing a passive suspension can do to control this angle. Also, any quick changes in Camber can give very large gyroscopic forces. So, on very bumpy roads, best is end-view wheelprint movement that is vertical, and NO Camber-Change at all.)

1.3 CASTOR (ie. about lateral Y-axis) - This has some importance for a front-axle, because of its influence on the Steer-Axis, but less importance for a rear-axle. It is connected to longitudinal "antis-", as covered below. It can have a BIG influence on "wheel-hop" during braking. This is a big subject, I think already discussed elsewhere, but NOT hugely important in FS/FSAE.

Without going into too much detail, we can say that we do not want very large Castor-Changes, but "moderate" amounts of it are acceptable. It is MUCH LESS important to control than Steer.
~o0o~

2. WHEELPRINT TRANSLATIONS.
============================
We skip the consideration of translations of the whole Axle here. These have some influence on behaviour of the whole car, but not enough to warrant a detailed discussion. Instead, we consider only the movements at the two wheelprints, because that is where the biggest forces are acting.

2.1 VERTICAL (ie. bump/droop of wheelprints in Z-direction) - Controlled by Spring-Dampers, so consider elsewhere...

2.2 LONGITUDINAL (X-direction) - This has a BIG influence on the "Anti-Pitch" behaviour, either during acceleration (ie. "anti-squat"), or during braking (ie. "anti-lift" for rear-axle). For FS/FSAE an "anti-squat" value between 0 and 100% is suitable for AutoX and Enduro. For the Acceleration event anti-squat of 100+% can be beneficial.

Note that there is a BIG, BIG, difference between having Inboard or Outboard Drive/Braking (more details below). Also, longitudinal jacking behaviour of Beam-Axles is essentially the same as with Independent Suspensions, and as covered in the "Jacking" thread (... unless front and rear Beams are somehow connected, eg. UWA!, in which case LESS of a problem).

2.3 LATERAL (Y-direction) - This determines "anti-Roll". Put simply, lateral n-lines that are horizontal give 0% anti-Roll, and loosely translate as "Roll-Centre on ground". Lateral n-lines that slope steeply up-to-car-centre give positive anti-Roll. If, in end-view, the n-lines intersect the Body's CG, then 100% anti-Roll, and NO ROLL through corners. This is acceptable for Beam-Axles, because they DO NOT JACK in the same way as Independent Suspensions (maybe more explanation later...).

BUT (!!!) steeply sloping lateral n-lines (ie. = high RC) implies a lot of lateral wheel scrub when driving over bumpy roads. This lateral wheelprint movement then either shakes the Body sideways, or shakes the wheelprints sideways, possibly pushing them over their "Fy limit", or a bit of both. As a sweeping generalisation, it is best to have anti-Roll = 0 - 100% (ie. "RC" between ground and CG height), but closer to 0% if expecting bumpy ground, especially in corners.
~~~~~o0o~~~~~

STEP 2. FIND THE CYLINDROID.
============================
From the above desirable Kinematics we determine a suitable Cylindroid.

For minimal adverse steer effects, the Cylindroid should have a vertical spine, wrt Body.

Because of the general L-R symmetry of FS/FSAE Dynamic events, the Cylindroid's spine should be on the L-R symmetry plane of the car. Also for symmetry reasons, the two ISAs at the ends of the Cylindroid's spine, which are always mutually perpendicular, should be oriented laterally and longitudinally to the car, and they should be of zero thread-pitch (ie. "revolutes").

We call the lateral ISA the "Pitch-ISA" for motion of the Axle wrt Body, and designate it "P" in all these sketches. Similarly, we call the longitudinal ISA the "Roll-ISA" and designate it "R". So, in plan-view we have R running down the centreline of the car, P is perpendicular to the centreline, and the spine appears as a dot. But we do not yet know P's longitudinal position, nor do we know the heights of R or P above ground.

To determine R's height above ground we consider an end-view, as at the bottom-left of the sketch below. As per the "Desirable Kinematics" above, we choose lateral wheelprint n-line slopes such that R is slightly above ground, say about 100 mm. For typical FS/FSAE CG-heights (~300 mm) this gives an anti-Roll effect that reduces the cornering Roll couple carried by the springs by about 1/3 from the case with horizontal n-lines (= ground level "RC"). So softer springs can be used. But these n-line slopes do not introduce too much lateral scrub, so are acceptable on moderately bumpy tracks.

To determine P's longitudinal position and height above ground we consider a side-view, as at bottom-right of sketch. For appropriate longitudinal "anti-" behaviour we want the longitudinal wheelprint n-lines to slope slightly up-to-front of the car.

IMPORTANTLY, note that for Outboard-Drive/Braking, this n-line is n2, but for Inboard-Drive/Braking it is n1. This is because in the Inboard case the DRIVESHAFT AND CV-JOINTS ARE PART OF THE "SUSPENSION" LINKAGE that transmits forces from the wheelprints to the Body, so they MUST be considered when determining the correct n-lines. For the Inboard case the correct wheelprint n-line (ie. n1) is always parallel to the n-line through the wheel's axle, namely n0, because the driveshafts and CVs always keep the "wheel-leg" (ie. from axle to wheelprint) in a vertical position.

In short, the side-view n-lines shown in the sketch give quite large anti-squat/lift (~150+%) for Outboard-D/B (= n2), but only moderate anti-squat/lift (~50%) for Inboard-D/B. The sketched Kinematics are more suited to Inboard-D/B, namely a "De-Dion Axle" with Inboard brakes. For many reasons, but no space to cover here, it would also work acceptably with Outboard brakes.

So, finally, based on the above reasoning, we have placed P, and thus also the Cylindroid's spine, at about the half-wheelbase position. Note, however, that the Cylindroid could also be placed a LONG way in front of the car, albeit with P much higher above ground. Or the Cylindroid could be BEHIND the car, with P possibly underground. The position shown here was mainly chosen to make the sketches easier, although it is also well suited to some of the practical linkages below. But it is worth thinking about the alternative longitudinal positions.

https://lh4.googleusercontent.com/-aucdo6rqzTE/VG2_QdiFa0I/AAAAAAAAARg/fBM_AI_zx0o/s800/Beam-Axle-1.jpg

In summary, a Cylindroid has been chosen that has its top-most ISA P lateral to the car, and its bottom-most ISA R longitudinal. In most suspension design literature, these P&R axes ALONE are used for Beam-Axle design discussions. For symmetric designs, such as here, this P&R-only approach is good enough. The additional knowledge of the Cylindroid given here "merely" gives a deeper understanding of the Kinematics, and helps explain what happens when everything goes cockeyed, as in Ralph's earlier examples.
~~~~~o0o~~~~~

(More coming, 10k limit!!!)

Z

11-20-2014, 06:03 AM

BEAM-AXLE (1). REAR - CONCEPTUAL. (Last bit...)
=====================================

STEP 3. FIND A SUITABLE PHYSICAL LINKAGE.
=====================================
As noted earlier, because this is a 2 DoF joint, we have to find four n-lines to act as the 4 Degrees-of-Constraint of the Axle wrt Body.

The Cylindroid offers us many, many, potential n-lines to choose from. Our choice is guided as follows.
1. The n-lines, and their subsequent real links, should connect to convenient positions on the Axle and Body.
2. The n-lines should NOT pass through regions that are occupied by other important stuff, such as the engine or driver, nor should they be in inaccessible regions, such as a long way from the car, or underground.
3. The four n-lines should be configured in space to provide good rigidity to the Axle's "constraint". This is a similar problem to designing a stiff spaceframe structure. It can be summed up by saying that the n-lines should be widely spaced and as orthogonal to each other as possible. Having two n-lines that are close together and almost parallel makes one of those n-lines almost redundant. (Similarly, long narrow triangles in spaceframes are BAD design!)

A methodical process for selecting the n-lines is as follows.

From symmetry arguments again, it makes sense to have n-lines/real-links that are mirrored on left and right sides of the car. This reduces the problem to finding only two n-lines on one side of the car. Each of these n-lines MUST pass through both of the P and R axes. So, pick any one point somewhere on P on one side of the car, and another point somewhere on R, and then draw a line through these two points for one n-line. Do similar for the other n-line.

Thus, only FOUR INFINITIES of choices. And MOST of them are easily eliminated! Sift through these choices to see which best meet the criteria listed above. Done! :)
~o0o~

The next three sketches all have identical Cylindroids to the one in this concept sketch. They differ only in the choice of n-lines and their real, physical implementation. Obviously, many other variations are possible. Just follow the above process...

Z

(Edit: See also Kevin's post (http://www.fsae.com/forums/showthread.php?1324-Beam-Axles-Front-Rear-or-both.&p=121127&viewfull=1#post121127) from a few pages back for a different, but also quite similar, approach to reasoning your way from a big-picture list of "wants", down to nitty-gritty mechanical hardware.)

11-20-2014, 06:04 AM

BEAM-AXLE (2) . REAR - PRACTICAL.
================================
This layout starts with a triangular Axle structure similar to the first "Twin Beam-Wing" (http://www.fsae.com/forums/showthread.php?1324-Beam-Axles-Front-Rear-or-both./page3) sketch I did on this thread (page 3 current Forum).

As explained in that post, that rear linkage only gives ~0% anti-squat, and it only manages that because of the slope of the final-drive chain run. Using that sort of linkage for an Inboard-Drive, De-Dion Axle would give quite large PRO-SQUAT during acceleration. However, the linkage in the sketch below could be quite easily retro-fitted to the "Twin Beam-Wing" car with minimal changes to its Axle and Body structures. This linkage would give positive anti-squat and the other desirable behaviours described above when run as a De-Dion (ie. with Inboard-Drive).

The approach here to finding suitable n-lines for the links is as follows. Two points are chosen on P, which are symmetrically disposed left and right of the car centreline. Two points are also chosen on R, one in front of, and the other behind, the rear-axle-line. These four points are then connected by four n-lines, such that each point on P and R is intersected by two n-lines.

The result is effectively a single "tetrahedral link" that connects Axle to Body, as seen at bottom-left of sketch. The wide base of this tetrahedral link on both the Axle and Body gives a stiff and strong connection.

https://lh6.googleusercontent.com/-7t3zF3hyHNk/VG2_RU8LuUI/AAAAAAAAARo/GUNLqFXsy2w/s800/Beam-Axle-2.jpg

In the more practical example shown at the top-left of sketch there are two "ball-ended-links" following the two rearward n-lines, and a single, smaller, "3 BJ wishbone" that acts as the two forward n-lines. As a general rule, the real links only have to follow their n-lines for a short distance. But the longer the real link, then the less the n-line changes its orientation as the suspension moves through its full range.

An advantage of this layout is that all connections to the Body are at a single bulkhead near the car's CG, which in FS/FSAE might be the Main Roll Hoop. Hence, a structurally simple and efficient chassis is possible.

The apparent disadvantage of the large triangular Axle structure is not so bad, because it stiffens the Axle from bending "in steer", and it carries some of the ground-to-Body forces closer to the MRH. Also, a low mounted engine can be positioned "inside" the triangle, the forward-most part of the Axle doesn't move around much (ie. much less than the wheelprints) so doesn't interfere much with other parts located there, and an "underwing" surface can be conveniently fixed directly to the bottom of the "triangle".

Z

11-20-2014, 06:05 AM

BEAM-AXLE (3) . REAR - VARIATION ON B-A(2).
========================================
This layout is very close to B-A(2) above. This Axle has the same three attachment points as before, but its structural shape is changed from a triangle to a "Y". Either Axle shape would work equally well in either of these two sketches. The choice of Axle shape depends on other packaging requirements.

The two major differences with this layout relate to the way the same four n-lines have been realised with different links.

In B-A(2) the two rearmost n-lines, which intersect R behind the car, have links that go from their Axle connections FORWARD to the Body. Here the links for these two n-lines go from the Axle REARWARD to a single connection on the centreline of the Body, and behind the axle-line.

This, of course, is only desirable if there is some suitable Body structure in this aft position. I would suggest this layout for a car that has a "backbone" chassis, and is perhaps a front-engine-rear-drive, with a diff or transaxle mounted between the rear-wheels. This way the rearmost suspension point on the Body can share the strong chassis structure already needed for the final drive.

(Edit: This De-Dion B-A would well suit a Lotus-7/Clubman type car, especially if built with a backbone chassis (as per the 1960s Lotus Elan).)

https://lh3.googleusercontent.com/-b8_9NsAe1MY/VG2_SKo17ZI/AAAAAAAAARw/f52fhW1jdtA/s800/Beam-Axle-3.jpg

The second difference is that the two front n-lines are now realised by a "Ball-in-Tube" joint, rather than the earlier wishbone. See detail at bottom-left of sketch. The 4-DoF, or 2-DoC, "B-T" joint is Kinematically very similar to the wishbone. Both produce a "planar-pencil" of n-lines that amounts to all the straight-lines that pass through a single point, and lie in a flat plane, and look somewhat like the spokes of a wagon-wheel.

In both cases P always lies somewhere in this plane. So P always lies in the plane of the wishbone, or it lies in the plane that passes through the centre of the B-T Ball and is perpendicular to the centre-axis of the Tube. The main Kinematic difference is that the n-lines of the B-T joint maintain the same angle (wrt Body here) throughout its range of movement, whereas a wishbone's n-lines change their angle as the wishbone pivots on the Body.

Practically, the B-T joint is very compact, but not suited to large travel. In the layout shown the B-T joint would only require a short travel, much less than the vertical wheel travel. In the production car world such a joint would be made as a one-piece rubber bush, which combines the rotation of the Ball plus the short axial plunge of the Tube.

Also worth noting here, is that this layout works as if the Body is connected via the R-revolute to a middle-link, and the middle-link is then connected via the P-revolute to the Axle. This is the OPPOSITE way around to all the previous sketches, which are closer to Body-P-R-Axle. The advantage of this layout is that R is thus very stable wrt Body, throughout the suspension's range of motion. This means less chance of adverse Axle-steer effects in the middle of bumpy corners.

Also note that the big separation between the two Body attachment points (ie. at front and rear of R, and along the Body's strong "backbone") implies good potential stiffness of the linkage against Axle-steer effects. But, as always, the "stiffness" of any chain is governed by the stiffness of its weakest link.

Z

11-20-2014, 06:06 AM

BEAM-AXLE (4) . REAR - WITH SIMPLER BEAM.
========================================
This layout keeps the the same two rearward n-lines/links as B-A(2) (ie. those that intersect R behind the rear-axle-line), but it uses a simpler Axle structure. Now the Axle is just a straightish tube connecting the two wheels via "uprights" at each end. (And these uprights can be conveniently used to directly mount a rear wing.)

With the forward end of the triangular Axle structure gone, there must now be two new n-lines to get full control of the Axle. These new n-lines/links attach to the Axle at the tops of the uprights at each wheel, and then go forward to attach to the Body, probably near the MRH for FS/FSAE cars. The n-lines then continue forward to eventually intersect R a long way in front of the car. I believe, from photos, that ECU's current car uses something like this.

https://lh4.googleusercontent.com/-g7iiqQIp6oQ/VG2_SrBMpJI/AAAAAAAAAR4/Lu8GXkwSqOg/s800/Beam-Axle-4.jpg

The plan-view, at top-right of sketch, shows how the four n-lines/links form a "W" shape to control both longitudinal and lateral forces between Axle and Body. The wider the connection points on both Axle and Body (ie. in the lateral direction), then the stiffer will be the Axle's "steer" control, wrt Body.

A big advantage of this layout is that, like B-A(2), the only connections to the Body are near the MRH. Thus no chassis structure is necessary behind the MRH, other than mandated by the Rules. Also like B-A(2), having multiple attachment points for the links on the Body allows the height and position of P to be adjusted quite easily. This allows easy variation of anti-squat between different events.

If a P-revolute and Cylindroid closer to the rear-axle is considered acceptable, then only two BJs on the Body are needed. These BJs will be on P as it passes through the Body (see bottom-left of sketch). Note that in side-view this gives much steeper n-lines for Outboard-Brakes (ie. n2 in B-A(1)), and a quite short "Side-View-Virtual-Swing-Arm". The steeper n-lines will give high levels of anti-lift during braking, which, in itself, can be advantageous.

BUT (!!!) the short SVVSA can possibly result in severe "wheel-hop" during braking. This depends on many factors, too many to cover here, but CAUTION is advised. At worst, the problem is solved by fitting Inboard-Brakes.

Z

11-20-2014, 06:07 AM

BEAM-AXLE (5) . FRONT - WITH SIMPLE BEAM.
=========================================
Lastly, for now, here is similar thinking to above applied to a front Beam-Axle.

This layout shares the same Kinematics as the "Twin Beam-Wing's" Model-T-Ford layout way back on page 3 (see link in B-A(2) post above). Namely, the Cylindroid is squashed flat like a disc, and sits a short distance behind the front-axle-line. Whenever a Cylindroid is squashed flat like this, all its ISAs form a planar-pencil of revolutes. So any motion of the Axle, wrt Body, is a pure rotation about a horizontal axis that passes through the centre of the Cylindroid (ie. intersection of P and R).

(BTW, in the original TBW sketch, the main BJ connecting Axle and Body has 3-DoF, or 3-DoC, so can be represented by any three orthogonal n-lines passing through the centre of the ball. The Peg-in-Slot joint provides only one lateral contraint (ie. it is 5-DoF), so is represented by a lateral n-line through its contact point. Any straight-line intersecting all four of these n-lines is a revolute joint for the relative motion of Axle and Body (ie. = ISA of zero thread-pitch). Thus all such revolutes pass through the BJ-centre, and lie in the plane defined by the BJ-centre and the P-S n-line.)

In practice, and especially if the chassis's Front-Bulkhead is behind the front-axle-line, I prefer the Model-T style layout of the TBW sketch. It is simply more simple, and rugged. However, if the car has a FB forward of the front-axle-line, then the layout in this sketch can work well. This layout also allows the Cylindroid and P to be moved much further rearward for less anti-dive, or for P to be moved up or down for further anti-dive tweaking.

But note that the Cylindroid of the TBW is very stable throughout the range of suspension movement. The Cylindroid below will move around a bit as the suspension moves.

https://lh6.googleusercontent.com/-smRoViUfOQY/VG2_TYH_lKI/AAAAAAAAASA/otRZi2dRMLU/s800/Beam-Axle-5.jpg

Perhaps the main advantage of this layout is the very simple Axle structure. The Axle is simply a straight-tube connecting the two wheels' King-Pins. Having the Axle pass through the Body allows the Body to have a flat-floor for easy build. For low ride height FS/FSAE cars the Axle might have a slight bend in the middle, to form a very wide "V". This lowers its centre section and gives more room for the foot-box template to pass over it.

The plan-view of this layout illustrates how well chosen n-lines give strong and stiff Kinematic constraint to the Axle, especially in steer as seen here. The four n-lines, and their real links, are spaced as widely and orthogonally as possible, while still attaching to convenient positions on the Axle and Body. The side-view shows that under hard braking all the links are in tension, which avoids the buckling problems that can occur when links are in compression.

Also in side-view, the links form a "Watt's linkage" to give good control of Axle Castor. The instantaneous Castor-change is a rotation about P, which is acceptable as shown. Moving P rearwards gives less Castor-change. In general, moderate levels of Castor-change are acceptable, but DO NOT LET TRAIL GO NEGATIVE! Very large motions of this linkage towards both full bump and droop will INCREASE Castor, and so also increase Trail, so it is quite safe (ie. it just gives more "self-centring" at full travel).
~~~o0o~~~

STEERING - Also shown at bottom-left of the sketch is a suitable steering-linkage for this front Beam-Axle.

I strongly suggest considering the inverted "Tractor King-Pins" for steering. Or the Citroen-2CV style king-pins that have been used recently by UWA. The fact that a Beam-Axle can use "revolute" steer-axes gives it several advantages over the more common double-wishbone layouts, namely the possibility of using stiffer and lower friction roller bearings. See this SLT-Swing-Arms post and sketch (http://www.fsae.com/forums/showthread.php?8950-Suspension-Design&p=45363&viewfull=1#post45363) for more details. Bottom line here is that just because everyone else uses tall and bulky "uprights", with teeny-weeny little BJs at their ends, does NOT mean they are the best solution.

A key feature here is that the vertical shaft of the Bevel-Gear-Box should be allowed to slide axially up-down. This shaft is then spring-preloaded downwards to always keep the larger crown-gear in tight mesh with the horizontal-shaft pinion-gear. This eliminates all backlash between the teeth, which is the bane of all FSAE Rack-and-Pinions I have ever seen. Bizarrely, the prior-art of every production car R&P ever made shows just how easy it is to solve this problem (ie. spring-preload)!!!

Below the BGB is a "flex-disc" type UJ that accomodates any horizontal motions of the Axle, wrt Body/BGB. These motion are small, so large angle UJs are NOT needed, and the flex-disc type has less potential backlash. Below this is a splined-shaft to allow for the significant vertical motions of the Axle. Again, backlash should be kept to a minimum here, perhaps by using off-the-shelf "ball-splines". The "UJ+spline" can be replaced by a single "plunging-CV-joint", but again, aim to minimise stiction and slop!

Finally, the Pitman-Arm and linkage out to the wheels gives potentially very good Ackermann control. I suggest using quite long Steer-Arms and Pitman-Arms (ie. at least 100+ mm) for stiff and precise steer-angle control. However, making the PAs a bit shorter than the SAs will make it easier to get the right Ackermann. Also, with the same BGB layout, the PAs can point rearward, and the SAs can point forward, as in the TBW sketch. This has further potential advantages for Ackermann...

Enough for now...

Z

rwstevens59

11-20-2014, 08:52 AM

Z,

I've been quiet lately on the forum but reading intently. Thanks for all of the work to produce the above. Lots to study!

Ralph

Jay Lawrence

11-20-2014, 11:40 PM

Thanks Z, lots of very cool information that I sure didn't learn at uni :)

I realise you didn't intend to delve into details with these systems but I do have a couple of queries:
In order to get the desired n-line slopes (for the rear) you have depicted some quite far forward cylindroid locations. Do you feel that this may jeopardise ideal driver placement to the extent that it may invalidate the concept? To get the 40/60 distribution I imagine you would have to run some very short linkages, or else run them alongside and underneath the driver (which may not be legal, and has other negative effects).

What are your thoughts on mounting the engine on the rear axle/arm with regard to driver controls? I imagine an engine moving about would have negative effects on throttle/clutch/gear control. Also there's the rule (assuming it's still a rule) that the intake must be hard mounted to the chassis. I guess one could argue that the suspension is part of the chassis but I could see it being an issue.

I don't think the front beam plus flat floor underneath would be allowed/safe. I'd imagine you'd have to have another floor over the top of the beam. Was this your intention? If so I envisage a humongous front end (they're already quite large for the most part, given the template restrictions).

Anyway, apologies if this comes across as obtuse, just trying to absorb.

11-21-2014, 10:41 PM

Jay,

"[In FSAE] To get the 40/60 distribution I imagine you would have to run some very short linkages, or else run them alongside and underneath the driver..."

All of these recent Beam-Axle drawings are meant to be quite general, and apply to a whole range of cars, not just FSAE.

For example, along with Ralph's examples from a few pages back (ie. racing on very rough tracks!), I have also got PM's from Baja students, and other more general enquiries. So, I drew the B-A(2) and B-A(3) sketches with quite long links so that they would suit long travel suspensions, much longer than is needed in FSAE.

In short, all the sketches would work fine in FSAE even if the physical links were MUCH shorter than sketched. Even with, say, 10" (250 mm) long links, the full bump or droop travel of 1" (25 mm) only changes the slope of the links by 1:10 (at most!), so much shorter links are NO PROBLEM.

And the Cylindroid itself is a "virtual" thing, so it can be placed anywhere, even off at "infinity".
~~~o0o~~~

"What are your thoughts on mounting the engine on the rear axle/arm with regard to driver controls? I imagine an engine moving about would have negative effects on throttle/clutch/gear control. Also there's the rule (assuming it's still a rule) that the intake must be hard mounted to the chassis. I guess one could argue that the suspension is part of the chassis but I could see it being an issue."

Yes ... the main problem is the Rules... :(

Again, considering the smoothness of FSAE tracks, I see NO PROBLEM with having an engine rigidily mounted to one of the "triangular" Axles, either the "Twin Beam-Wing" sketch, or B-A(2) or (3). With the engine mounted at the front of the triangle, nearer to the Body, it moves much less than the wheels when they go over bumps. And since no bumps in FSAE... (Or, looking at it the other way, many cars have won FSAE with effectively NO suspension at all...) And given that throttle/clutch/gear control can all be done via cables (and often are), I see no problems there either.

In fact, I reckon the ideal candidate for such Beam-Axle-mounted-drive would be the electric cars! Mount the heavy but compact motor(s) near the front of the Axle "triangle", just under the driver's back (ie. where the gearbox is in TBW sketch), and then take a chain or toothed-belt reduction back to the no-CV-driveshafts.

Importantly, the above amounts to "Outboard-Drive", so longitudinal n-lines have to be appropriately chosen. These are shown in B-A(1) as n2, but for good "antis-" they should have a LOWER slope, closer to that of n1. So either use a linkage similar to the TBW sketch, or if using linkages B-A(2), (3), or (4), then P should be lower, about the same level as R.
~~~o0o~~~

"I don't think the front beam plus flat floor underneath would be allowed/safe. I'd imagine you'd have to have another floor over the top of the beam. Was this your intention?"

Yes. The bottom-floor would be part of the aero-undertray. Any "cockpit-floor" above the Beam would be for the Rules.

"If so I envisage a humongous front end..."

Well, NO DIFFERENT to most Double-Wishbone FSAE cars.

Most every FSAE DW car out there today has a "stepped floor". This rises up roughly 100 mm from the seat-base to the footbox, just to provide suitable attachment "nodes" for the lower wishbones. Then there is a R&P that necessarily sits above this floor so that the tie-rods can get out to appropriate pick-ups on the upright, and keep away from the wheel-rim. And then another "cockpit-floor" above the R&P, to comply with Rules.

I figure many DW cars have this cockpit-floor at about 150 mm above ground (ie. at R&P location). Anyone care to share their numbers?

Anyway, a B-A(5) type Beam-Axle, albeit bent into a very wide "V" for FSAE, should be able to fit under a similar height cockpit-floor. Note the Pitman-Arm and tie-rods can be in front of, or behind, the beam, and the beam cross-section can be a widish, lowish, RHS, as sketched. Add the 350 mm high foot-box template, and the underside of the steering-shaft and Bevel-Gear-Box can be less than 500 mm above ground (the template has big semi-circular cut-outs at top and bottom for the steering).

It all looks very similar to most DW cars I have seen. From a quick check of photos, these have the top of their FRH at 600-700 mm above ground. Certainly, the tops of most noses at the front-axle-line are well above the tops of 13" front wheels (= 500+ mm diameter).

Z

Kevin Hayward

11-23-2014, 10:33 PM

The raised cockpit floors are a really interesting case. If we make a rough assumption that there is around 50kg of stuff in the nose of the cockpit (drivers legs, front chassis, pedals, shocks etc.) a rise of 100mm will cause a COG height rise of nearly 20mm for a competitive car.

In perspective this is equivalent to dropping the COG of a CBR by 83mm, dropping a 5kg rear wing by 1m, dropping the drivers COG by 67mm.

I wouldn't say that it is desirable to have this stepped floor. If we accept that it needs to be there then a beam may be as good as a double wishbone setup, but maybe there are ways to avoid the step altogether.

Maybe that will come at a weight penalty, which makes for an interesting question. How much weight could you add before lowering the COG by 20mm is not worth doing?

Also please note that the usual reason for lowering COG for racecars is solely for increased tyre friction while cornering (i.e. load depenadant tyres). With FSAE there are many places on a track where the vehicle is limited by wheel lift, something that is greatly affected by COG height and very often not modelled properly by students (i.e. proper inclusion of jacking affects and transients).

Kev

mech5496

11-24-2014, 01:52 PM

Once more, thank you Erik for the (really onteresting) discussion, I believe that you give a rather useful insight, even to people not remotely interested in beam axles. Kev, the issue you raised (pun intented) is way overlooked by teams, albeit 50kg seems a bit overexagerrated IMO. Stepped floors are a bit harder to manufacture, but (for most double wishbone cars at least) offer "better" mounting points for the lower A-Arms. Moreover, I believe that one could lose a bit of the CoG height by simply putting the pedalbox/driver feet lower again, either by creating a nose-mounted "bucket" or a 2-step chassis. Another -or maybe even more- concerning issue though, and overlooked by almost everyone, is drivers feet plus pedalbox, impact attenuator, front wing etc. mounted more than half a meter in front of the front axle, and the effect of all that weight to your moment of inertia...

Kevin Hayward

11-24-2014, 09:48 PM

Harry,

50kg was a bit much, because the legs pivot at the hip. Lowering the feet by 100mm will only lower the leg COG by around 50mm. A persons COG is roughly at the top of the hips. The legs account for a lot of weight of a person. Large bones, significant muscle mass. The torso has a lower density due to the lungs. I made an assumption of 30kg for legs, 10kg for chassis, 10kg for stuff. We might end up with something closer to 15kg effective lowering of the legs, 15kg of chassis and associated. Lowering 30kg by 100mm still ends up with a pretty large COG effect. The effect of a stepped nose is more detrimental the lighter the car gets.

It is useful to do the calcs as to what a 10mm drop in COG is worth in time/points when compared to 1kg of weight. Can't do it using Optimum Lap, but just about any decent simple lap time sim will give a coarse value to go by. Tyre temps will change this, but generally works both ways for COG and weight. Because the tyres are run under the ideal temp adding weight/COG will cause less of a drop off in performance than indicated by purely the tyre load sensitivity. Poor modelling of the transients and jacking will cause an overestimate of maximum cornering which will underestimate the effect of COG height in parts of the track where the car lifts both insides. It is also very dependent on tyre load sensitivity. Engine power also comes into play. Lower powered cars are more sensitive to total mass relative to COG. By extension drag and downforce also affect the results.

From the sims it is very interesting how many kilos you can add for each 10mm of COG drop (you can add even more if you use pounds). When you compare this to the weight of the design changes required to lower the nose you get the design guidance you are after.

I would also add that any laptime sim that doesn’t include the effect of COG height is not worth running for anything but the most basic decisions (i.e. final drive).

Getting back to the orginial question, beam axles front/rear or both. From the results of calculations I have seen (and performed) I would not be using a beam at the front of a car, and not be having any step to the front chassis. If you accept that the step is required (i.e. for aero) then you might as well run a beam, with mounting points back to the front roll hoop.

Instead I think the best option is probably a well designed five link (or 3 links and a wishbone) to improve contact patch migration (relative to the car) during during steering. Harder to design than double a-arms, very easy to build. Direct acting shocks of course.

Kev

mech5496

11-25-2014, 07:55 AM

Kevin, thanks for your thoughts. Indeed CoG height vs. mass is an interesting debate and something we worked quite a lot on last year to quantify (as well as other parameters). I still believe though that a "double step" chassis (or a way to get feet/pedalbox low) is the best compromise, as your A-Arm mounting points would be placed to offer more straight load paths.

A bit offtopic, but an interesting resource, is the following link, especially towards the end:

http://msis.jsc.nasa.gov/sections/section03.htm

I know that there are enough teams out there trying to model all car parts/weights but often "forget" the driver as part of the game.

mdavis

12-02-2014, 11:01 PM

mech5496

12-03-2014, 03:59 AM

Matt would you mind sharing some of these drawings here? To be honest, a lot of things package well if you design with them in mind in the first place, even the much-hated longitudinal Z-bars. The thing is that most FS team members start thinking out of the box shortly after they have left the team...the old "marrying your favourite design" thing...

12-03-2014, 07:22 PM

A few weeks ago, myself and a fellow UC alumni put together some rough conceptual drawings for a frame that had the top tubes maybe 20mm above the OE of a 10" FSAE tire, that would package direct acting dampers at both ends of the car, use pitman arm steering and a whole host of other fun things.

Matt,

Yes, I would like to see those sketches too. Or similar from other ex-FSAEers. (Apparently that sort of thing is acceptable on this Forum. I've been getting away with it for years!)

As Harry noted, the average student's time in FSAE is barely enough to understand "The Standard Car", let alone really push the envelope on an unusual design. And words do not convey the gist of these ideas nearly as well as sketches.

So, with the goal of advancing the state of the art ...

... more radical "out-of-the-envelope" car sketches, please, from everyone! :)

Z

mdavis

12-04-2014, 09:19 PM

I don't think the cad work was ever completed, so it'll have to be hand sketches. I'm not nearly as good at drawing as Z, but I'll give it a whirl this weekend.

-Matt

mdavis

12-08-2014, 08:16 PM

Alright, hopefully these images work reasonably well.

Basically, the front takes a bit of inspiration from the BCMS 2011 car, where the lower inboard points are very near the centerline of the car. With a real and pinion, this makes for a very small rack. Or, kart steering could be used. That's the way I would do it here. The front lower points are shown with the 2 dots above the front lower frame rails. The front upper point is attached to the front node. The rear upper point is loaded into the front roll hoop. The other node is for a direct acting damper. I'm not 100% sure exactly where that node should be in 3d space, but that point should be close. Detail stuff to be sorted out later.

Rear end would be a bulkhead, with all rear suspension points and the damper attaching to it. Beyond that, this frame should be more than stiff enough for whatever suspension stiffness is desired, even with sprung mounted aero and the increased spring rates that would come along with it.

This frame was simply reusing a lot of our geometry from 2013, so there is certainly room for some improvement there. I think the ideal way to do it would be a swing axle in the rear, as that would allow moving the dampers further forward on the trailing link. The way the rules are written, the has to be a lot of structure right behind the roll hoop, so you may as well use it for more than just checking the rules box.

I should also note that the engine model is not 100% accurate, it's of the older yfz450 engine rather than the newer 450r that we ran in 2013.

Thoughts/feedback/discussion welcome.

-Matt

mech5496

12-09-2014, 03:20 AM

Cool, thanks for sharing Matt! I believe there is a tad too much triangulation but other than that I like it and I agree on all your points. I am also searching my conversations with Rob Woods for a draft CAD I did for a twin beam interconnected e-car back in 2012 to share.

Tim.Wright

12-09-2014, 08:51 AM

...I believe there is a tad too much triangulation...

What are you talking about??

http://cdn.meme.li/instances/250x250/52866977.jpg

rjwoods77

12-09-2014, 01:18 PM

If it works for the wall of death then it should work for FSAE...

http://fb-troublemakers.com/wp-content/uploads/2013/07/1003653_602864306410578_669610362_n.jpg

mech5496

12-10-2014, 07:52 AM

OK, so here is a draft design of mine dating almost 2 years back. Chassis is a dead simple monocoque (flat panels for ease of manufacture of the mold). Beams are at an initial stage, albeit in the fourth picture (the one with wheels) they are a bit more detailed, manufactured by an oval filament winded CF tube and bonded, sheetmetal inserts. It was done mainly as a packaging exercise on how to package a twin beam and how simpler teh subframe would be. Longitudinal Z-bars were running the length of the car, with splined ends to accommodate rockers. No DASD because pullrods were needed to package the twin Z-bars. Motor is our electric YASA 750, diff would mount inside the hole as it is now, no gearbox. Batteries are on both sides of the cockpit for low MoI and rearwards mass distribution.

Comments are kindly welcome! :)

443 444 445 446

rwstevens59

12-18-2014, 09:32 PM

Question for those who have used the late Bill Mitchell's WinGeo kinematics software, what solid axle suspension layouts are supported? I have only briefly played around with an older demo version of this software which as I recall only had templates for a three link and a NASCAR truck arm style layout.

Thanks,

Ralph

01-11-2015, 01:25 AM

FRONT BEAM-AXLE, Suitable For Car With Front-Overhang.
==============================================
Here is another sketch of a Beam-Axle, this time suitable for the front of an FSAE car that necessarily has some front-overhang. This might be because an off-the-shelf engine prevents the driver sitting further back, so their feet end up forward of the front-axle.

(As stated many times before, I believe a driver-entirely-within-the-wheelbase design is best VD-wise, although I accept that this is not always possible when working under some Team constraints. In fact, this sketch was prompted by Christian's similar design on his thread. Because this sketch is in part a derivation of Christian's work, it is not necessarily what I would do if starting entirely from scratch...)

Also squeezed into the sketch are some ideas that might be useful for very different cars. For example, the "Side-Mounted-...-Brake-M/Cs", that allow the Front-Bulkhead to be positioned immediately in front of the pedals. More below...
~o0o~

OVERALL CONCEPT - This is a "Model-T-Ford" style, low-mounted (ie. underfloor) front-beam. The major dimensions can be found, roughly, from the small three-view detail at the bottom-left of the sketch. The wheels and tyres are nominally 10" x ~6+" wide. The Steer-Axis geometry is "centreplane" and should package with the maximum steering-locks shown.

The beam feeds the major road-to-tyreprint loads to its main "Apex-BJ" that connects to chassis at floor level and close to the middle of the car. Thus any heavy chassis structure needed to carry these major loads is low and centrally positioned, thus giving overall low-CG and low-Yaw-Inertia. The beam has only four connections to chassis in total (not including steering). The two main Kinematic constraints are low down and on the car centreline, so allow easy chassis jigging and fabrication.

Spring-Dampers are Direct-Acting, and feed their loads in a close-to-straight path from the wheelprint to a mandated strong part of the frame in the FRH to upper-SIS node. Note that different lengths of DASDs can be accomodated by having the upper-SD-BJ connect to a "frame-bracket" that looks like a frame-tube cantilevered down-and-out from the FRH-SIS node. As long as this tube is aligned with the SD-axis it will be strong and stiff enough, even if it is quite long, say ~15 cm. At most, some small "gusseting" of this tube to the FRH or other frame tubes might be required. Create this bracket with Craftsmanship, then check with Engineering-Analysis, or better yet, do a real Load-Deflection test.

Lateral control of the beam is via a "wishbone" and "Ball-In-Tube" joint, detailed at top-right of sketch. Note that the similar front-beam on the first of my sketches back on page 2 could also have used a similar, but longitudinally much shorter, form of lateral constraint. The Peg-&-Slot used in the page 2 sketch is perhaps simpler in that case, because its Front-Bulkhead is just BEHIND the beam.

Here the B-I-T joint is simply a conventional "spherical joint", with its "ball" bolted firmly to the front of the wishbone, but with its "outer-race" allowed to slide longitudinally in the cylindric housing attached to the chassis (ie. attached to the mandated very strong FB here). The cylindric housing might have an internal bronze sleeve for a "proper job", but not really necessary in FS/FSAE. In fact, the "ball" just has to be reasonably stiffly constrained laterally, but allowed to move a small amount longitudinally. A rubber bush inside the cylindric housing would do the job.

The combination of the B-I-T joint at front, and the Apex-BJ at rear, gives the beam as a whole an 0.8 metre wide "base", along the centreline of the car, to resist any "yaw" (ie. "steer") motions of the beam. This gives very stiff directional control of the beam.
~o0o~

https://lh3.googleusercontent.com/-YBFHsF8Lp5c/VLIUZzT94nI/AAAAAAAAASQ/79qc6T0V_eU/s800/Beam-Axle-Front-BIT.jpg

BEAM STRUCTURE - The entire beam is fabricated from folded sheet steel, typically 1 - 3 mm thick. With the dimensions sketched I would suggest mostly 1.6 mm thick (= 1/16" or 16 gauge). This is thin enough to easily fold, and thick enough to easily weld. Some details of the fabrication techniques are shown at the bottom-right of the sketch.

Most of the tubes are folded into octagonal cross-sections, about 60 mm across flats for the main tubes. In fact, the main-beam would be marked out with folding lines ~30 mm apart for the horizontal/vertical faces, and ~20 mm apart for the "bevelled corners". These octagonal cross-sections mean more corners to fold than square or rectangular sections, but the folds are only 45 degrees rather than 90 degrees, and more folds better stiffen the flat faces against buckling.

Also shown are two "reverse folds" at the edges of the sheet where the tube's "seam" is later welded together. This requires extra folding work (I would clamp the sheet so it overlaps the edge of heavy steel table, and use hammer to make these small, sharp-edged folds), but it makes TIG welding of thin sheet, say <1 mm, EFFORTLESS! NO filler rod used, just melt the two lips into each other. A conventional butt-weld can also be done, perhaps with an aluminium backing-bar to prevent burn-through of thin sheet.

The two tapered torque-arms are made with the folding lines converging at the narrow end to ~half the distance given above. So near the Apex-BJ these torque-arms are ~30 mm across flats. A nice gusset can be welded into this Apex-"V" to stiffen everything up. Use a BIG BJ here, perhaps 10 mm ball-bore. Smaller will save negligible mass, and will soon wear-out and start rattling.

The most highly stressed parts of this beam are the "elbows" where the SD-lower-BJs attach to main-beam-to-torque-arm nodes. Here the torque-arms are merged with the main-beam so they meet the outboard part of the beam, which rises up at ~45 degrees, at a mitre-joint cross-section of about 100 mm wide, x ~80 mm high. The rising part of the beam then tapers to meet the next outboard horizontal section, which is ~60 mm octagonal inboard, morphing to 60 mm SQUARE outboard. Folded sheet structures allow lots of fancy stuff like this!

IMPORTANTLY, all the mitre-joints (aka "lobster-backs") MUST have internal webs! Well, you can try without, but the structure is greatly weakened. These webs prevent the corners from crushing under bending loads. (Do some force diagrams of the skin-stresses!) The webs can be the same thickness sheet as the outer skins, or can be twice as thick with a lightening hole in the middle. The thicker webs can make the welding procedure easier, or not, depending on details...

The amount of gusseting required at the various joints is best determined as follows. Make rough trial-run beams, then LOAD TEST TO DESTRUCTION! Note where the skins first start to buckle, or buckle the most. Gusset said weak points. RETEST TO DESTRUCTION ... until whole structure is giving up UNIFORMLY. So, NO WEAK POINTS.

BTW, I made a half-scale, half-beam (ie. only one side of centreline) out of about half a cereal-cardboard-box + sticky-tape, in about one hour while watching telly. Hot-melt-glue-gun does a better job of "welding", but is messy, and, err..., kids have "hidden" it! This sort of Cardboard-Aided-Design makes it very easy to decide where "faces and edges" should go, and gives a quick and accurate indication of how the structure will fail, so where more section-size/webs/gussets are needed.
~o0o~

STEER-AXES - My preference is the Inverted-Tractor-KPs as detailed on this SLT-Swing-Arms (http://www.fsae.com/forums/showthread.php?8950-Suspension-Design&p=45363&viewfull=1#post45363) post. Compact, strong, stiff, low-friction...

Alternately, a more conventional upright can be used, as shown at top-left of sketch. This has Camber-Adjustment by shims between the beam and a small "Top-BJ-Carrier". This gives Camber-Change = Steer-Axis-Inclination-Change, which is OK. Castor-Adjustment is made via swapping different Top-BJ-Carriers, which move the Top-BJ fore-aft. Castor should only need to be adjusted occasionally in early testing, so "change-part" restrictions in the Rules are NOT a problem.

A big-ish question here is do you carry the vertical Fz loads of this conventional upright via the lower-BJ, or the upper-BJ, or both? I know what I would do... but I prefer the Tractor-style... :)
~o0o~

Last bit next (10k char limit!!!)

Z

01-11-2015, 01:26 AM

(Last bit from above...)

SIDE-MOUNTED BRAKE-M/Cs - These are carried on an "L"-shaped pedal-tray bracket, which can slide fore-aft and is fixed in position by a single spring-loaded pin at the base of the left-side FRH. The front of this bracket also carries the throttle-pedal (not shown) and is located sideways and up-down by some simple "slide-rails".

The foot loads on the brake-pedal are transferred rearwards by two pullrods connected to the side of the pedal. Note that this puts the pedal structure under considerable torsional loads, so it should be fabricated as a hollow sheet steel structure (as above!), NOT as a pretty, but flimsy and expensive, billet-machined 7xxx part. The pullrods actuate two "pull-type" M/Cs, which in turn connect to a vertically oriented balance-bar, just in front of the FRH.

The advantages of this system over the more conventional "M/Cs in front of pedals" are:
1. Significantly shorter chassis for less overall mass, and MUCH less Yaw-Inertia because the heavy Front-Bulkhead is as far rearwards as possible.
2. The M/Cs and balance-bar are moved rearward for lower Yaw-Inertia again.
3. The brake-pedal, M/Cs, and balance-bar are all a planar mechanism so can use low-friction revolute joints (eg. needle rollers) everywhere, rather than higher friction sphericals, thus giving more accurate brake-balance.
4. Adjustment of brake-balance is within easy reach of the driver (ie. under his left knee), without the need for the usual messy cables, etc. (BTW, the detailed balance-bar design has been thought through (it is simple and easy to make), but no room to sketch it...)
5. The large brake-pedal loads (ie. ~2 kN) are fed back to a central and strong part of the car, namely the base of the left-side FRH.
~o0o~

Enough for now...

Z

CWA

01-11-2015, 10:56 AM

Z, it's slightly off topic and I'll admit I haven't read all of the text in your posts above. But I'm very curious to know, how much time you spend on your sketches? I really think they are fantastic. Do you sketch in pencil first and make adjustments, or do you get it all right first time in ink? Your talent for drawing is quite indisputable.

Jay Lawrence

01-12-2015, 01:05 AM

Z,

What are your thoughts on the possible compliance with the sliding joint at the front bulkhead? I imagine this to be something that would be difficult to get right in practice (perhaps why you've suggested rubber bushes instead?)

Also, given how critical it is to have a solid brake pedal I find it hard to believe that your system would create confidence for the driver. I would think that the "L"-shaped bracket would also want to be bolted/retained up close to the pedal pivot (less practical for adjustment, but I just can't picture a lightweight solution according to your concept)

01-12-2015, 10:08 PM

With Oz-14 comp and Xmas I missed some above posts...
~~~o0o~~~

Matt,

Thanks for the frame images. I have dozens of similar little spaceframe sketches floating around here. Unfortunately, all the good looking ones are ... illegal!

It seems that whenever I find a way of "connecting the dots" that works really well, there is at least one (stupid!) little Rule that gets in the way. For example, equilateral triangles work well in spaceframes, but one of the Rules has words to the effect of "... in side-view the FRH must be within 20 degrees of vertical". I want to put it at 30 degrees from vertical, for nice equilaterals...!

Another of my sketches has the MRH and FRH at 45 degrees in side-view, and meeting at their bottoms. So the MRH follows the driver's back, and the FRH follows the driver's thighs, for really good side impact protection and a neat and very stiff frame. But the above "20 degree FRH" Rule again makes this illegal. Probably also illegal by the SIS Rules. Aaarghhh...
~~~o0o~~~

Harry,

It looks quite close to ECU's current car, at least at the rear... :)
~~~o0o~~~

Ralph,

Sorry, no idea?
~~~o0o~~~

CWA,

... Do you sketch in pencil first and make adjustments, or do you get it all right first time in ink?

Very briefly, it is NEVER, EVER, right, even the umpteenth time. Which is why pencils have erasers, biros have white-out, FSAE students have angle-grinders, etc... (And yep, damnit!!! Missed one tube...)

Several other people have also asked, so here is the general process.

I start with "an idea", then flesh it out with a lot of roughly drawn freehand sketches. These are typically quite small and drawn in the margins of the TV times while I am watching some junk on telly. So lots of time to do these! :) The sketches are taken from whatever "view" makes the idea easier to see or understand.

When I decide to turn one of these "ideas" into a sketch for this Forum, I usually do a few more rough drafts on small post-it notes (ie. about credit-card sized). This way I get an idea of how much information I can put into the finished sketch. In a way, these "small pictures" clarify the amount of "Big-Picture" thinking that can go into the final sketch. This is a bit like writing a point-form summary of some big subject, or stepping back from whatever you are working on to get a better over-view of it.

For the more complicated sketches (like the last one), I then do a rough, freehand, draft-sketch on A4 paper. This gives me a better idea of how much detail, both drawings and text, I can fit into the final sketch. Next I stick the draft onto a drawing-board I have, and start the actual sketch, also on off-the-shelf A4 white paper.

The drawing-board makes the isometric drawings a bit easier (ie. these have a vertical Z axis, and X and Y at +/-60 degrees from vertical). However, the old fashioned straightedge with a built-in roller works just as well for these parallel lines. I also have an ellipse stencil for drawing "isometric circles" (eg. the wheels, etc.). This stencil is a piece of plastic with elliptical holes in it, which cost ~$1.00. I also use similar "round circle" and "french curve" stencils, which are easier than a compass for small circles, although I have a cracker of a homemade compass for accurate large radius curves.

For the drawing proper, first comes the border, in black medium-point biro (ie. "ballpoint" pen). Then a bunch of pencil "construction lines", mainly the ground level centrelines, verticals through wheelcentres, etc. Once there are enough pencil lines to give a good idea of where everything goes, I fill in the details with a standard biro. Thicker lines are simply multiple biro lines next to each other. Also used very often is the "aaarghh!" white-out (ie. aka correction-fluid/~white-paint).

Text comes last, usually on a normal table because the drawing-board is in an inconvenient corner where I can't lay it down flat, Then all pencil construction lines are rubbed out. And maybe a bit more white-out and touch-ups...

Next comes the hard part! I have a really old scanner (last century? :)) that works well and has a reasonable editing program (ie. allows files to be easily touched up, compressed, saved in different formats, etc.). This is still perfectly functional, but is on an old computer with no USB ports. So I now have to use a new scanner (admittedly only ~$59), which is a right PITA! Aaaaarghhh!!! Editing options include "Try your luck"... Honestly!

I have recently downloaded "Gimp" for last minute touch-ups, but its "ergonomics" are, well, at the poor end of the FSAE scale. I use it so I don't have to go through the scanning process a second time. I prefer a purely "black & white .tif" file, but the current scanner insists on "greyscale", and between that and the Google upload procedure the background to the sketches gets a bluish shadow. I guess I could try more trial and error to fix this, but...

All up, the last sketch (at the high-content end of the scale) probably took less than four hours from blank paper to scanned image. The initial rough drafts a lot less, but these are done in "free time", and are the most enjoyable. But the touching-up in Gimp takes an almost arbitrary (bordering on infinite?) amount of time. The purely B&W images were much easier for this, but, honestly, the ergonomics of even simple tasks like erasing little blotches is TERRIBLE. Even navigating with Zoom and Pan is a right PITA.

However, the hardest part of all, is deciding what to put in, and what to leave out. Given that I use A4 paper, I am probably erring on the side of trying to fit too much in. More different sketches, each with a simpler, bolder, message, is probably better. But that would mean more scanning, gimping, and uploading, which I don't like...
~o0o~

Anyway, bottom line is that the above sketching process is quite similar to the design & build of a whole FSAE car.

1. Start with many, many, rough draft ideas.
2. Decide what to put in, and what to leave out, and proceed to flesh out the details.
3. Execute the details, turning them into reality via the long, slow, grind.

Finally, never be satisfied with the end product, but acknowledge that it must be delivered sometime...

Z

01-12-2015, 10:18 PM

Jay,

What are your thoughts on the possible compliance with the sliding joint at the front bulkhead?

NO problems at all. It is a joint like any other. I image an extremely poorly made one might have 0.5 mm of slop, but much less "compliance" (ie. flex). This slop gives a steer-change of the beam, over its ~800 mm "centreline-base", of 1/1600 or less than 0.04 degrees.

Compare that with the slop + compliance of most FSAE steer-arms, which are typically much less than 100 mm long, so with ~ten times the steer-change, or more. And then all the extra slop that comes from a conventional suspension's dozen or more BJs.
~o0o~

Also, given how critical it is to have a solid brake pedal I find it hard to believe that your system would create confidence for the driver. I would think that the "L"-shaped bracket would also want to be bolted/retained up close to the pedal pivot (less practical for adjustment, but I just can't picture a lightweight solution according to your concept).

Tsk, tsk, tsk...

I should have added as one of the advantages that it would give a MUCH STIFFER installation than many of the conventional pedal-trays and brake-linkages.

Think about where all the forces go. Do some FBDs! Here is a start...

1. FBD of Driver while braking.
Vertical: Gravity pulls down, Seat-base pushes up (~1kN each).
Horizontal: Left-side-seat-back pushes forward on Driver's-back (2kN ->). Brake-pedal pushes rearward on Driver's-left-foot (<- 2kN).

2. FBD of above Side-Mounted-Pull-Type-Brake-Pedal-Tray.
Vertical: Small gravity, etc.
Horizontal: Driver's-left-foot pushes forward on Brake-pedal (2kN ->). Double-shear-pin-at-left-side-FRH pushes rearward on Pedal-tray (<- 2kN).

3. FBD of Frame.
Vertical (...).
Horizontal: Driver's-back pushes rearward on Left-side-seat-back (<- 2kN). Pedal-tray pushes forward on Double-shear-pin-at-left-side-FRH (2kN ->).

This would be much easier with a simple sketching facility, but put simply,
ALL THESE FORCES TAKE THE MOST DIRECT PATHS POSSIBLE!!! All forces are in a straight(-ish) line from Left-side-seat-back to Brake-pedal!

For anyone who still can't see this, picture a rope (roughly equal to the brake pull-rods) tied to left-side-FRH and looped around driver's left-foot while he pushes it forward HARD!

Ahh... education system... groooaaann... :(

By comparison, some conventional pedal-trays use leverage to create much larger forces (ie. 3++ kN) that act vertically, trying to rip piddly little bolts out of a flimsy floor! (Do FBD of the "almost vertical M/Cs" that are quite common.)

Z

Jay Lawrence

01-13-2015, 09:51 PM

Z,

Thanks. I guess with the slop I imagined a fairly short length of bush being subjected to that variety of forces would cause any slop it may have to 'catch an edge', which would be bad for nice suspension movement (kind of like a poorly designed wishbone fouling on a pickup or something). I'm probably just imagining problems because I haven't tried this solution myself, hence the question.

As for the brake system: I'm aware of where the forces go, it was more the mounting method that concerned me. Do you intend to hammer the locating pin in so it's a nice fit with zero compliance? Or am I missing something?

MCoach

01-14-2015, 10:35 AM

Yep, can vouch for forces that could almost rip bolts out of the floor from "almost vertical MCs". However, 3/4 that hold our pedal assembly together are in compression. So it's no big deal.

One thing that may be more related that bothers me that is more related to suspension design that most people don't seem to take into account is lengths. I'm not talking about mechanical leverage, yes, that should be a given. But rather how much material is used to create these connections. For example, Z, your brake MC placement seems very logically sound, but if presented to me I'd ask the understudy to compare this design's compliance to the conventional pedal in bending (MCs at bottom) and the now "conventional" (oh crap, am I calling something very unconventional outside of FSAE, conventional???) near-vertical MCs.

I'll tie this back into beams and suspension in a just a minute...

The reason being that however sound your load paths may be, I'm concerned about the load lengths. A pedal with near vertical MCs, if designed correctly, can essentially render the main section of the brake pedal nearly loadless, loading mostly into the MCs, thus making the analysis of deflection relegated to the transferred forces to the floor which could be innumerable in material choices and design as well as brackets, so I'll leave it alone. I could go into the comparisons of the load paths further, but essentially it boils down to a comparison of the total deflection of the parts. Is it worse to have a 8" 1"x1" steel box tube pedal in bending (conventional design) or to have two 30" ~5/16" solid steel(?) rods that connect to the brake pedal at the same point (and the pedal is still in bending)? It would be beneficial for someone to check with their own braking forces to compare the three I'd be curious at the result and most likely your design judges will, too :) . If Claude is going to make sure you know the compliance from your brake pads, you better know the compliance from everything else up to that point, too.

So, back to suspension things. One more time with feeling. Our team used to be very big on titanium for everything, it's the material of race cars and mach 3 recon spy planes. It's awesome stuff, right? Oh, yeah it is. Our '09 car used titanium suspension links that saved us a lot of weight that were all designed for strength so that it would survive the suspension forces. However you could always tell if the car was driving in pictures because if the rear suspension was not positively cambered, you were obviously stopped when the picture was taken...and a cone killer...facing the wrong direction on track...like me :P . I did a study last year on how camber compliance from the suspension design and assembly may have affected our total camber gain. To summarize, things start to show their nasty side when you imagine that the rear links were about a meter long and weighed less than the 1/2" x 0.028" steel stuff people use now, so LOTS of compliance. It turns out that from our design, yes, we effectively had positive camber gain with the links contributing more than the wheel. It was geometrically sound, of course, but was basically held together with fishing line and long sections of it. It just didn't work the way the designer intended.

So, now the kicker. If you double the length of your part to "optimize" it's load path and reduce the resultant load by 20% or something arbitrary, if reduced at all, what has really been accomplished? One step forward, and two steps back...