Pitch axis [Archive] - FSAE.com Forums

Fra881

01-24-2015, 07:19 PM

The fact that the body doesn't pitch about the pitch axis.

Considering the pitch axis (geometrically defined from the control arm angles in side view) as a pin joint of the chassis is even more incorrect than considering the roll axis as a pin joint. In the case of the roll axis, it is not a bad approximation at very low acceleration because the suspension response on the left and right of the car are somewhat symmetrical.

In the longitudinal case this is not the case. A RWD car under acceleration is an extremely asymmetric (front to rear) problem so the pitch axis location is absolutely meaningless.

Its more meaningful to consider the suspension loads and movements at each axle separately. The resulting body motion at each axle is the superposition of 2 main effects:
1. Load transfer - under acceleration it loads the rear axle in bump and the front in rebound
2. Jacking - can load the suspension in any direction you want but is proportional to the traction/braking force. It is typically used to load it in the direction OPPOSING that of the longitudinal load transfer and this is what cancels out the body pitch and gives the "anti" effect.

After you get your head around this, apply the same theory to the roll movements and you will already understand body movements better than most...

Hi Tim, that is actually the reasoning I used for my calculations, until a few days ago OptimumK put some doubt in my head by drawing the pitch axis so much behind the car. Thanks for sweeping it away.

I also noticed that for anti effects it is popular to tilt by an angle only one of the wishbones, leaving the other parallel to the ground. I see this solution used more often than both wishbones tilted with respect to the ground, and parallel to each other.

The differences I see are two, with the first solution with heave the wheel moves a bit less longitudinally, but you have caster gain (which is absent using the second solution). Are there other differences I don't see?

01-24-2015, 07:32 PM

What am I missing here?

Fra881,

What we are ALL missing here is a simple sketching facility integrated into this Forum that allows this to be easily explained.
~o0o~

But the short answer is given by Tim above. Repeating this for emphasis,

THE CAR-BODY DOES NOT ROTATE ABOUT THE "PITCH AXIS"!!!

(More correctly, if it does, then it is only by extreme coincidence.)

If any "experts" tell you that the body DOES move about the "pitch axis", then please ask them what this motion of the body is "WITH RESPECT TO".

Any motion of Body-A must ALWAYS be "wrt" some other Body-B.

This "Where is the Motion Centre?" (http://www.fsae.com/forums/showthread.php?6945-anti-dive-setup&p=118084&viewfull=1#post118084) post explains this from an end-view perspective (ie. Roll rather than Pitch), but the principles are the same.
~o0o~

I am implementing 30% of antisquat so my rear wishbones are parallel to each other and making an angle with the ground, pointing upwards looking forward. Flat geometry at the front.

This defines a pitch axis well behind the car.

This suggests that you think that your "side-view PC" lies at the intersection of a horizontal line through the front-wheelprint (ie. "flat geometry"), and a sloping line through the rear-wheel-CENTRE, with this line perpendicular to the free suspension motion of the wheel-CENTRE (which makes this line the "n-line" through wheel-centre). Hence you find the intersection "well behind the car".

In fact, the "PC" is at the rear-wheelprint. It is correctly found as the intersection of the two n-lines through the front and rear WHEELPRINTS (= tyre contact patches).

But, to repeat, the car-body DOES NOT ROTATE ABOUT THE "PC"!!! This "PC" is only useful as a point at which (edit: some!) front and rear wheelprint forces can be vectorially combined. And, of course, the effects of these forces can be calculated many other ways.

Z

(PS. Just saw your latest post. There is a difference. Your parallel wishbones give SAME levels of anti-squat during acceleration, and (edit: outboard-brake) anti-lift during braking. Non-parallel wishbones give different levels (typically less anti-squat). IMO your current parallel arrangement is BETTER.)

Fra881

01-25-2015, 06:24 AM

Actually well behind the car is where OptimumK puts my pitch axis.

Since with an independent suspension the driving torque is not taken by the suspension, imo it has a point. Shouldn't we use the normal line passing through the rear wheel centre?

Tim.Wright

01-25-2015, 08:40 AM

Your parallel wishbones give SAME levels of anti-squat during acceleration, and (edit: outboard-brake) anti-lift during braking. Non-parallel wishbones give different levels (typically less anti-squat).

The total anti-squat/raise effect is not purely dependent on the wishbone geometry. Brake and drive bias must be taken into account. In this case you will see that parallel wishbones give different percentages of anti squat and raise.

01-28-2015, 08:13 PM

Fra881,

Since with an independent suspension the driving torque is not taken by the suspension, imo it has a point. Shouldn't we use the normal line passing through the rear wheel centre?

It is very important to realise that with inboard-drive, or inboard-braking, THE DRIVESHAFT IS PART OF THE "SUSPENSION LINKAGE".

The driving/braking forces can be considered to originate at the road-to-wheelprint surface. They then travel through all the stressed parts of the "suspension linkage", until they eventually act on the "Car-Body" and accelerate it forwards or backwards. So if the driveshaft is stressed, then it MUST be considered part of the linkage.

Typically, because the driveshaft has CV-joints, the "wheel-leg" (ie. the part of wheel from axle down to wheelprint) always remains vertical as the suspension moves up-down. So the n-line through the wheelprint is always parallel to the n-line through the wheel-axle, at any position of the suspension.

Here are some sketches that might help. (These sketches and more words are posted somewhere on this Forum, but I have lost the link since the Forum changed hosts.)

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

https://lh5.googleusercontent.com/-arTDwLtqt_A/TuasCHP62vI/AAAAAAAAAHk/TMOt63WgDmc/s800/MechAntiFg10.jpg
~~~~~o0o~~~~~

Tim,

The TOTAL anti-squat/raise effect is not purely dependent on the wishbone geometry. Brake and drive bias must be taken into account. (My double emphasis!)

My definition of an Independent-Suspension's "Anti-Squat" (as on a typical FSAE rear corner), which I think is similar to the intended meaning in many VD books (if they could ever be bothered giving definitions!), is roughly;

The resultant force lying on a vertical LoA through the given wheelprint, that acts on the Car-Body, and is transmitted by the suspension Control-Arms (including a driveshaft if it is stressed), as a consequence of a forwards horizontal force acting from the road to the wheelprint, and a rearwards horizontal Inertial force acting through the Car-Body's CG.

(Edit: This "Anti" force is shown as "Fca.v" in above Figure 10.)

This definition should be supported by some drawings (similar to above), which makes it all much easier to understand. Similar definition for "Anti-Lift" under braking, etc. And then more definitions for what "100% Anti-Squat", etc., means (I have a sketch of this ... somewhere...).

Anyway, regardless of the "Anti-force" that a given Independent-Suspension exerts above ITS OWN wheelprint, the horizontal forces acting on that wheelprint and the Body's CG cause OTHER corners of the car to move up or down on their springs.

So, yes, different horizontal road-to-wheelprint forces (eg. driving or braking) at the OTHER wheels do change the amount of "squat" movement at the given wheel.

But, NO, the amount of "Anti-Squat" at a given wheel, as per the above definition, DOES NOT CHANGE with different "bias". The Anti-Squat at a given wheel is set by its own Kinematics.

Bottom line (with qualifications...), wishbones that are parallel in side-view have wheelprint side-view-n-lines for inboard-drive, AND outboard-drive, AND inboard-braking, AND outboard-braking, that are COINCIDENT (ie. same lines!). So all have the same side-view "Antis".

Z

Tim.Wright

01-29-2015, 01:40 PM

Tim,

(My double emphasis!)

My definition of an Independent-Suspension's "Anti-Squat" (as on a typical FSAE rear corner), which I think is similar to the intended meaning in many VD books (if they could ever be bothered giving definitions!), is roughly;

The resultant force lying on a vertical LoA through the given wheelprint, that acts on the Car-Body, and is transmitted by the suspension Control-Arms (including a driveshaft if it is stressed), as a consequence of a forwards horizontal force acting from the road to the wheelprint, and a rearwards horizontal Inertial force acting through the Car-Body's CG.

(Edit: This "Anti" force is shown as "Fca.v" in above Figure 10.)

This definition should be supported by some drawings (similar to above), which makes it all much easier to understand. Similar definition for "Anti-Lift" under braking, etc. And then more definitions for what "100% Anti-Squat", etc., means (I have a sketch of this ... somewhere...).

Anyway, regardless of the "Anti-force" that a given Independent-Suspension exerts above ITS OWN wheelprint, the horizontal forces acting on that wheelprint and the Body's CG cause OTHER corners of the car to move up or down on their springs.

So, yes, different horizontal road-to-wheelprint forces (eg. driving or braking) at the OTHER wheels do change the amount of "squat" movement at the given wheel.

But, NO, the amount of "Anti-Squat" at a given wheel, as per the above definition, DOES NOT CHANGE with different "bias". The Anti-Squat at a given wheel is set by its own Kinematics.

Bottom line (with qualifications...), wishbones that are parallel in side-view have wheelprint side-view-n-lines for inboard-drive, AND outboard-drive, AND inboard-braking, AND outboard-braking, that are COINCIDENT (ie. same lines!). So all have the same side-view "Antis".

Z

Well then your definition is not telling the full story because brake/drive bias has a significant effect on the vehicle pitch motions.

I prefer a different definition which is similar to what Adams/Car uses. Basically it represents the anti-X percentage as the ratio of the jacking force (Fx x nLineSlope) to the load transfer (Hcg x Ax x Mass / Wheelbase). Therefore, when your jacking force is equal and opposite to the load transfer, you have 100% anti geometry.

However, the jacking force is proportional to the tyre Fx and this is related to the drive/brake balance. This is why you can't have anti-lift on the front axle of a RWD car because there is no longitudinal force to generate the jacking force (or anti force).

Here are some simulation results of a braking maneuver, 0.5g for three cases in which the only difference is the brake bias. Increasing the front brake bias reduces the pitch on the front axle:
https://lh3.googleusercontent.com/-AIR555b1T8c/VMqKcDcMmFI/AAAAAAAAAhs/gH8kJpcDUSQ/s1200/braking_pitch.png

I'm also interested to hear your explanation as to how the forces on one axle are affecting the vertical motion on the other axle. I don't agree that there is any significant effect of this kind for a traditional non connected suspension.

01-29-2015, 09:11 PM

Tim,

Well then your definition is not telling the full story...

Well, yes, IT DOES TELL THE FULL STORY, but only when you apply it to the full vehicle (ie. Car-Body plus ALL wheels)!

I'm also interested to hear your explanation as to how the forces on one axle are affecting the vertical motion on the other axle. I don't agree that there is any significant effect of this kind for a traditional non connected suspension.

I went some way to explaining this in the last post. I explained it much more fully in a Racecar Engineering article some years ago. But the dim-witted sub-editor at RE back then decided to sex-it-up by chopping up all the text and scattering it amongst racy pics of racecar bits. Apparently Sam Collins is now an FS-UK Design Judge. Go figure...

Anyway, here it is again.

Firstly, think only in terms of a side-view of forward acceleration (to simplify things). Start with RWD only, and consider the amount of Anti-Squat at the rear suspension. The most common "definition" of 100% AS (when, or, if, such definitions are ever given) amounts to having rear-wheelprint n-lines rising up-to-front so that they intersect the front-axle vertical plane at CG height.

With such n-line slopes the Car-Body has NO vertical movement AT THE REAR-AXLE-LINE under any level of acceleration (but with many qualifications!). BUT (!) it most definitely does lift a lot at its nose (edit: because of F->R LOAD TRANSFER!), and its tail (aft of rear-wheels) does squat down. So there definitely is Pitch motion. Note that with a CG at 50% F:R, these side-view n-lines pass UNDER the CG. In fact, at half CG-height.

Next, consider a car with FWD only. Such a car with 100% front Anti-Lift has its front-wheelprint n-lines intersecting the rear-axle vertical plane at CG height. Under acceleration the Body has NO vertical movement AT THE FRONT-AXLE-LINE, but there is still lots of Body Pitch (edit: because F->R LOAD TRANSFER!) (again, many qualifications here). So a very long nose does lift up at its front, and the rear of the car definitely DOES SQUAT down.

Finally, and briefly, consider a 4WD car. If the car has the above front and rear n-lines (ie. exactly the same suspensions!), and it has a 50% F:R CG, and 50% F:R bias of driving thrust, and probably a few other things I should mention but can't think of now (err, such as all equal grip tyre-road surface, linear rate springs,+++)..., then under any levels of acceleration there is ZERO HEAVE of the CG, but there is the SAME PITCH (= rotation in side-view) as if only a single axle were supplying ALL the forward thrust.

In other words, a 4WD car with suspension that has the very commonly defined (as above) 100% Anti-Squat at rear, and 100% Anti-Lift at front, nevertheless has lots of front-lift and rear-squat during acceleration (edit: again, because F->R LOAD TRANSFER!)! The resolution to this riddle comes by realising that the "%AS" and "%AL" refer ONLY to longitudinal forces generated AT THAT AXLE.

To understand the behaviour of the whole car, YOU MUST CONSIDER THE WHOLE CAR!

BTW, a 4WD car with 50%F:R driving thrust, and 50%F:R CG position, can have zero Heave and zero Pitch if both its front and rear n-lines intersect at the CG in side-view. But this zero-H&P only happens if the road-to-tyre grip is ALWAYS equal for all tyres, and the differentials are clever enough to ALWAYS distribute the thrusts equally (which is NOT a good idea, because total thrust is then limited to 4 x the lowest grip wheel, which might be off the ground!), etc., etc...

Hope that helps! :)

Pictures and FBDs make all this easier to see...

Z

(PS. To cover this more fully here...

I prefer a different definition which is similar to what Adams/Car uses. Basically it represents the anti-X percentage as the ratio of the jacking force (Fx x nLineSlope) to the load transfer (Hcg x Ax x Mass / Wheelbase). Therefore, when your jacking force is equal and opposite to the load transfer, you have 100% anti geometry.

However, the jacking force is proportional to the tyre Fx and this is related to the drive/brake balance....

And the "load transfer", and each individual wheel's "jacking force", are also all proportional to each tyre's grip at any instant, with this depending on the road surface under each tyre at any instant. So your above "definition of Anti-%" is a very fickle number that is always changing.

That is, your "definition of Anti-%" is NOT a description of an INTRINSIC FEATURE of a given suspension. Rather, it is a definition of an "output" of an analysis of the whole car. Or perhaps it is a definition of a particular "measurement" you might take when testing the whole car.

Boiling this all down, your "Anti-%" is simply measuring how much each suspension moves during different longitudinal accelerations of the whole car. Different circumstances, such as different "drive/brake balances", or different road-grip under each tyre, give different amounts of your "Anti%".)

Tim.Wright

01-30-2015, 01:01 AM

I'm still digesting the first part but in my opinion your comment that each wheel Fx is changing with its vertical load is wrong.

The braking Fx for all wheels must sum up to the Ax x mass of the car and its distribution is fixed by the brake system design only ( master cyl & caliper piston areas, disc radii and pad mu being the main operators).

Similar with the traction case, at least with a set of open differentials. The traction forces at the wheel must add up to mass x acceleration of the car and its distribution is purely a function of the gear and diff ratios of the drive train.

With the Fx split fixed, the quantity which changes dynamically is the longitudinal slip but this isn't affecting the pitch movement of the car.

Tim.Wright

01-30-2015, 03:14 AM

In other words, a 4WD car with suspension that has the very commonly defined (as above) 100% Anti-Squat at rear

This is where you are wrong. All the calculation methods that I have come across and use myself (which correctly includes the drive bias), your example car has 50% anti lift on the front and 50% anti squat on the rear which perfectly describes the resulting pitch motion.

You are, for some reason, cutting out the drive bias effect and then complaining that the result is wrong. THAT'S BECAUSE YOU ARE IGNORING THE DRIVE BIAS EFFECT!!!

The convention is to split the problem into the following terminologies:
Anti dive = Heave motion of FRONT axle due to BRAKING condition
Anti raise = Heave motion of the REAR axe due to BRAKING condition
Anti lift = Heave motion on the FRONT axle due to ACCELERATION condition
Anti squat = Heave motion on the REAR axle due to ACCELERATION condition

From this its clear that unless all 4 of those elements are at 100% the car will pitch.

"Pictures and FBDs make all this easier to see..."

Tim.Wright

01-30-2015, 03:58 AM

Another thing, explain to me this contradiction:

YOU MUST CONSIDER THE WHOLE CAR!

Boiling this all down, your "Anti-%" is simply measuring how much each suspension moves during different longitudinal accelerations of the whole car.

01-30-2015, 04:54 AM

Tim,

I am ignoring nothing, and my calculations come out right. (BTW, I added a few words to my last post to emphasize what should be an obvious point.)

Earlier you said,

I prefer a different definition which is similar to what Adams/Car uses. Basically it represents the anti-X percentage as the ratio of the jacking force (Fx x nLineSlope) to the load transfer (Hcg x Ax x Mass / Wheelbase). Therefore, when your jacking force is equal and opposite to the load transfer, you have 100% anti geometry.

Because your "load transfer" varies according to the available grip under all the wheels at any time, it follows that your above definition of "anti-X percentage" for ANY GIVEN WHEEL varies according to the grip under ANY OTHER WHEEL at any time.

If that is your preferred definition, then so be it.

But I consider a definition for the "Anti-X of a given wheel's suspension" that is always changing according to changing road conditions UNDER THE OTHER WHEELS to be somewhat pointless.
~o0o~

Regarding your last post (just popped up now), as I said before, your definition is simply giving the "outputs" of the calculations, namely the wheel vertical positions.

But to spell it out yet again, you CANNOT use your definition to say that a GIVEN WHEEL's suspension has "100% Anti-X GEOMETRY", because under most conditions of variable road grip (which is common, and amounts to the same thing as changing bias) that wheel will NOT have zero suspension movement during the "X" accelerations.

That is, any ONE wheel's "% AX" depends on all the OTHER wheels' instantaneous Fxs. That is, the "geometry" keeps changing!

Your definition does NOT describe a distinct property (or feature, or characteristic, or parameter, etc.) of a SINGLE GIVEN WHEEL's suspension. Mine does.

Z

Tim.Wright

01-30-2015, 05:03 AM

My definition is the same as yours but it includes the drive bias effect.

Please explain then how, for a given longitudinal acceleration (e.g. braking), the Fx distribution can be anything other than that dictated by the braking system pressures and geometry? Its a fixed quantity.

The Fx distribution is largely fixed, at least in a passive car - therefore the anti-X is also fixed, under all steady Ax conditions.

Also, how are your calculations coherent with the simulation result I posted which show a different steady state dive response of the front axle when you change the brake bias?

01-30-2015, 05:17 AM

Please explain then how, for a given longitudinal acceleration (e.g. braking), the Fx distribution can be anything other than that dictated by the braking system pressures and geometry? Its a fixed quantity.
...
Also, how are your calculations coherent with the simulation result I posted which show a different steady state dive response of the front axle when you change the brake bias?

Tim,

I have explained all this ad nauseum now!

The first one changes because of different road-tyre Mu under the different axles. Spend some time driving off-road, on mud, clay, etc...

The second one changes because YOU CHANGED THE BRAKE BIAS! Do the calcs by hand. Very simple!

It is Friday night, and I can hear those home-brews I put in the freezer an hour ago calling out. "We're almost frozen. Please get us out of here..."

Z

Tim.Wright

01-30-2015, 05:22 AM

Changing the mu does not change the bias brake bias. Its fixed by the design of the brake system. This is what I have been trying to explain ad nauseum now!

01-30-2015, 09:00 PM

Tim,

Last try, then I have better things to do.

Several posts ago I said.

... consider the amount of Anti-Squat at the rear suspension. The most common "definition" of 100% AS (when, or, if, such definitions are ever given) amounts to having rear-wheelprint n-lines rising up-to-front so that they intersect the front-axle vertical plane at CG height.

* In Gillespie's "Fundamentals of VD", top paragraph of page 252, there is an almost identical definition of "100% anti-squat". See also bottom of page 251 and top of page 253.

* In Millikens' "RCVD", page 619, the Figures 17.14 and 17.15 have equations giving the same definition for 100% anti-squat/lift.

* In Millikens' "Chassis Design ... Olley", page 495, Figure 9.11 and the words just above say the same thing.

Personally, I don't like the sloppy way that these things are taught (ie. as in above books). But that is the way it is. If you don't like it, then take it up with those authors.

I gave one of the main reasons that I don't like the above definitions shortly after the above quote.

... a 4WD car with suspension that has the very commonly defined (as above) 100% Anti-Squat at rear, and 100% Anti-Lift at front, nevertheless has lots of front-lift and rear-squat during acceleration!

These definitions are very misleading because they DO NOT DO WHAT THEY SAY!

Nevertheless, those definitions do have the advantage that they are a simple description of the physical geometry of each individual suspension. That is, they are a statement about the side-view n-line slope of a suspension, and of the CG-height and wheelbase of the car. This description changes a bit with suspension travel, and with changing CG-height (very common), etc. BUT this description DOES NOT change with the fickle nature of the Fx forces of any of the four wheels, at any instant in time.

Your definition does. Which makes your "new improved" definition even WORSE than the above ones, IMO.

To restress this, I hope you realise that a small patch of sand, or gravel, or oil, or mud, or plain old water, that you drive over while 4WDing, or during hard braking, can make the Fx force under that particular wheel all but disappear! Fx forces are very fickle. And "clever" ABSs and electronic diffs make those 4 x Fx forces even more variable.

It is BAD PRACTICE to use such fickle numbers in the definition of a suspension's "GEOMETRY".
~~~~~o0o~~~~~

To OP or others interested,

Most of this "anti" VD-behaviour can be understood simply by knowing the longitudinal and lateral N-LINE SLOPES at the wheelprint of each suspension (ie. in side-view and end-view).

For a really simple start, assume massless wheels and suspension, and a POINT MASS Car-Body (ie. it has Total.Mass and CGx,y,z). Better yet, and not much harder, is a Car Body with DISTRIBUTED mass (ie. add the 3 x MoIs on 3 x Principle Axes, for 10 numbers in total).

Now, determine in some way the 4 x Fx and 4 x Fy road-to-tyre forces acting at the wheelprints. You can assume these for a car not yet built, or measure them when testing a real car. Similarly, determine the CG's X, Y, Z gravitational and inertial forces (for point mass) and inertial couples (for distributed mass) acting on the Car-Body. Possibly also throw in a non-flat road profile.

Next, knowing your spring-rates, either of the 4 x corner-springs (+ 2 x ARBs?), or else of fully-interconnected-springing (simpler, better!), you can determine how the forces above are distributed between the springs and suspension control-arms.

Finally, this tells you the 4 x Fz wheelprint forces, and the 4 x wheel-heights wrt Body (or, equally, the Body's Heave, Pitch, and Roll positions wrt some ground reference frame).

Then, for bonus points, add the fact that the wheels and suspensions are distributed masses, so extra 10 x numbers for each of those. And since the wheels are rotating they have gyroscopic effects. As do the engine and driveline...

And ... don't forget aero! :)

Z

Tim.Wright

01-31-2015, 05:14 AM

Z, you are hard work mate. I get the impression that you are arguing just for the sake of arguing. The first half of your rant blasts me for using a fickle number like Fx in my calcs then in the second half you use them yourself in a practically IDENTICAL model to the one I use for my ride/pitch/roll ride calcs.

The fact that you are either ignoring or not understanding is that you always have a BASE split of longitudinal forces in braking and acceleration which is very stable (the opposite of fickle) under normal driving conditions and is a function of the brake system and the powertrain NOT the contact patch condition. These can therefore be included in a simple pitch model like I have described (and like you describe in the second part of your post) to give you and IDEA of the pitch movements of the car and its sensitivity to brake and drive ratios.

Regarding the contact patch condition. If the Fx disappears on one axle due to a low friction surface then either one of two things happen:
1. The driver or reduces brake pressure or throttle application - which reduces the forces on BOTH axles but the RATIO remains more or less the same therfore the pitch movements predicted with my model are still valid.
2. The wheel locks - at this point your your pitch angle is the least of your worries

You are throwing too many red herrings into this discussion in the form of sand, gravel, oil, mud, water ABS and E-diffs, which are all BS conditions that account for probably 0.001% of driving conditions and in the end it makes no sense to analyse with a simple model like this. Consider also, that with any appreciable longitudinal velocity, and mu split between the front and rear axle is a temporary condition lasting a few hundreths of a second at most. Anything that happens to the front mu will very quickly also happen to to the rear mu.

If you still disgree, then I expect that you also concede that all of your previous lateral calculations where you have assumed lateral forces distributions left and right to prove your points on roll centre theory are also meaningless for the same reasons.

Claude Rouelle

01-31-2015, 05:41 PM

Z arguing for the sake of arguing....?..... Nooooo :)

CWA

02-01-2015, 03:35 AM

Not meaning to take the thread off topic, nor detract from the value of the current discussion. But can anyone describe a real world case where it has been so important to ensure that your axle pitch movements can be so accurately predicted?

If it is important to predict the wheel travel for the sake of knowing resultant camber angles, doesn't compliance added in with the kinematics discussed completely dilute the importance of what has been described? Or perhaps these approaches are similar to those which must be used to quantify torque-steer on a powerful FWD car? Maybe accurate approaches like these are more important / correct in other industries, but their transfer into vehicle dynamics theory is not so?

How much of what has been described so far is going to be of benefit to an FSAE student, who likely can't even quantify the amount of friction in their suspension system, which is sure to ruin all these numbers?

If anyone can contribute something along the lines of "well this one time, in industry, we had to really focus on the drive-shaft torque's contribution to rear wheel travel, because of [bla bla bla...camber gain, wheel recession, induces tramp...bla bla bla] but in most other cases we've found the contribution to be negligible", for me at least, this would be a lot more inspiring and useful.

I do feel slightly uninformed considering this discussion as 'mental masturbation', but I'm rather sure an old tutor of mine who I consider to be very experienced in the industry would describe the discussion as something close. At least for the sake of FSAE.

Claude Rouelle

02-01-2015, 11:16 AM

CWA,

I can give you at least one example of why teams like to know where their pitch axis is (and/or move): on cars whith a significant amount or aerodynamic downforce and that are very front and rear ride heights sensitive (such as F1, GP2, F3, LPM1, LMP2, DTM, Nascar, some GT, Japanese GT 500 and 300 etc and FS/FSAE cars the day students start to use ground effect the proper way .... and here is more, unexploited, underwing freedom in FSAE/FS cars than other race cars I know), engineers like to know where the instant "hinge" of the car is; it gives them an idea of about what axis the car will pitch (or roll). That helps to predict the amount of downforce, drag and even more front - rear aero-balance. They try to keep that axis not moving too much. In fact on several close cockpit cars you can sees that the "hinge" is close to the front splitter and the engineers play with both the rear static ride height and the rear suspension stiffness to have the car "attitude" (pitch) and altitude they want when they want it. And this target is different at different range of speed and longitudinal acceleration.

I would like to use this post to specify to the usual whiner of this forum that I never, ever said that the car was rotating around the kinematics pitch axis. He seems to invent or modify some of my statements to give himself another opportunity for controversy. As I said earlier there are people who are not happy....unless they are not happy.

More on pitch and roll axis comments.... After all when a car pitches (or rolls of both) there must be somewhere, somehow one axis around which the car is instantaneously rotating..... Knowing where this instant axis is (and moves) can help you to better exploit the car tires, aero, kinematics, brake and acceleration torque distribution etc....

The location of the real pitch (or roll) axis will never be very precise (but that is not an excuse to try to more accurately locate it) and depends on many factors and the kinematics is only one of them; the suspension stiffness (and in transient the damping and the masses inertia), the compliance, the aeromaps, the tires' stiffness, the tires' forces and moments, the weight distribution, the suspended and non suspended CG locations, the torque distribution (front-rear for a 4 WD and/or or inside outside for a FWD or a RWD), the brake distribution etc.. have also also to be taken into consideration. But the multitude of factors doesn't make the kinematics obsolete. The best prove is that on a K&C test rig, when you change only some suspension pickup points by a few mm, all other car parameter and car and tire force inputs remaining the same, the "real" roll or pitch axis position can significantly changes.

Somewhat linked to the same topic: the n-line is a good but not sufficient idea. As Tim Wright very well pointed the tire forces (and moments) need to be taken into account. Without an accurate and relevant tire model, the n-line theory will remain what it is: pure academic theory.

Same story for the jacking forces: the inside and outside tire lateral grip (and/or longitudinal front and rear tire grip), the tire Mxs, the difference in altitude between the non suspended masses CG and their instant center (where is this center on the n-line?) plays a significant role in the jacking forces and the ride heights changes (and guess what the instant pitch and roll axis).

Interestingly the Rambo Zero of this forum has never mention these...

CWA

02-01-2015, 11:49 AM

Thanks Claude, great write-up, exactly what I was looking for

DMuusers

02-01-2015, 11:50 AM

BillCobb

02-01-2015, 12:20 PM

Although I agree with your entire post, it's always hard to relate all these parameters to one accurate model. I always wonder how much laptime/points you can get from these more complicated models vs. a simplified one which gets you in the right ballpark. The amount of effort to gain must have a peak somewhere. I guess the only way to find out is to actually make such a model ;).

BTW, you will have to include at least the brake bias into the calculation since it does make a significant difference, and if you have some downforce and drag, a sensitivity analysis over the velocity range is also advised. In my opinion.

The presence of an accurate model by itself does not generally increase the chances of an optimal product (race car). The exercise of it in controlled, systematic tests, accompanied by directed post processing of simulation run(s) is where the big reward is. Influence coefficients, team specific terms and optimal control points are the high value products of these models. This allows the designated team member assigned to a vehicle design to accept and maintain responsibility for their part of the project. This effort must be accompanied by some simple lab tests (to get model input parameters) and some on the road tests (Not lap times) to validate trends and objectives. Road tests must be open loop (robotic inputs unrelated to race course operations) and closed loop (inputs related to race maneuvering).

In my career, a team without an Adams, CarSim, SimMechanics or some other of the many multibody analysis programs is just playing in a racing sandbox or counting on the bad luck of some of the other teams. They are just filling the field.

Looking for a career in Vehicle Dynamics? Get at least one of these skills. Otherwise you are just a mechanic. ("I need you to change a flat tire.")

JT A.

02-01-2015, 01:24 PM

I have also wondered for a long time why there is such a fuss about knowing exactly where the pitch center (or roll center) is. Lets see if I can explain the source of my confusion.

You want to be able to predict the attitude of the the car, front ride height, rear ride height, jacking forces, etc... as accurately as possible to best exploit your aerodynamics and tire loadings. So far this makes perfect sense.

But the "pitch center" or "roll center" as they are drawn kinematically do not define the true pitch & roll center of the car and do not predict the true motion of the chassis platform.

To find the true pitch and roll center, you need to use K&C testing, multibody models, and/or on-car testing to measure how the car platform really moves in response to inertial forces & forces at the tires.

Then once you have simulated or measured the heave, pitch, & roll response, you can use that information to calculate where the true "center" that everything is rotating about.

But if you already have measured/simulated the front & rear ride heights, and therefore pitch and heave, and roll, and tire loads, etc...then what is the point of going back and figuring out where the pitch/roll center is? You already have what you wanted in the first place. Finding the pitch center really just seems like intellectual masturbation. Is there some purpose of locating the true pitch/roll center that I'm not seeing?

Tim.Wright

02-01-2015, 04:59 PM

To answer CWAs very valid question, I can also confirm what Claude said that for motorsport work at least, the roll centers and anti geometries are used while keeping an eye on front and rear ride heights for aero performance reasons.

A more general reason which applies also to non_aero cars is that you should be running the chassis as low as possible without grounding out in order to keep your CG as low as possible. The amount that you can lower the chassis is dependant on the precision that you can predict the body movement under braking, accel and cornering conditions. As well as the slope of your n-lines, significant contributors to this include brake/drive bias (as has been discussed), tyre vertical stiffness and aero loads.

To reiterate what Bill said, unless you are looking at the full vehicle implications of your choice of anti-pitch/roll geometry otherwise you are just doing a lot of handwaving.

Though Claude, I would like to take the opportunity to ask you; in your opinion, for a 2WD car, what is the physical significamce of the geometric pitch axis? To me it seems to be a useless construct given that without drive on one axle it cannot be uniquley defined. I am of the opinion that the degree of asymmetry of the longitudinal pitch dynamics basically rules out the use of this construct and that its more correct (or less wrong) to look at the front and rear in isolation in terms of the vertical movements due to braking and traction loadcases.

P.S. JT A, what you say, is in my opinion, completely correct. A pitch axis can be defined from a given vehicle design but it should be treated as a reference number (for comparing designs) but it is NOT the mechanism causing the pitch movement.

Claude Rouelle

02-01-2015, 08:03 PM

Daniel,

We have such model. We use it with our performance engineering consulting customers in Indycar, GT, Australian V8 Supercars, LMP1 and LMP2, South American V8 Stockcar and at least one OEM passenger car manufacturer. Is is perfect? No and we know the limitation of such model and simulation. Is it useful? You bet! Our customers win races and championship because of it. They win but here is the best: They and we know WHY. That is where the fun starts.

Garbage in, garbage out. The most difficult is to get accurate and relevant tire models, K&c data and wind tunnel models (best results are from scale one rolling floor wind tunnel with roll, pitch, ride heights, yaw and steering input). If our engineers are on the track (most of the time that is the case) to acquire analysis data and work with thetam to close the loop with the simulation the we start getting good confidence in our simulation tools.

PS check your mailbox. I will send you a personal message in the next few days

Tim,

I agree with you with no aero, CG height importance and influence of kinematics on those.

Want another example: on a Indycar, on ovals (only left end corners) on low banking / relatively low speed, the engineers will put the roll axis on the left side of the car to get the car as low as possible with lateral acceleration. But on high banking they will put the roll axis on the right side of the car to create some jacking to counteract the high banking vertical G. The fun comes when you see that the roll axis is on the left or the right of the car but not necessarily parallel to the car longitudinal axis but lest's no go that far... Some well funded teams who have access to K&C data and tire models and good aeromaps will speak about the force base roll and pitch axis and the ones who do not have access to K&C and tire models and good aeromap will limit their simulation to pure kinematics. The first group will get a more accurate and useful simulation and will develop the car quicker. But it is not as if the second group work will be futile and unsuccessful; it just will be less precise.

To all and here more specifically CWA and JT A,

1. Pitch (or roll axis) location = kinematics + compliance + tire model + brake distribution + etc.... When the only thing you have is a kinematics software, AND YOU FULLY REALIZE THAT "PURE" KINEMATICS IS ONLY A PART OF THE STORY, at least you work in delta. Not perfect but useful

2. I do not like the notion of antidive, antilift, antisquat, When you look at antidive you look at the front of the car as if the rear did not exist. When you look at antisquat you look at the rear of the car as if the front did not exist. If we go this way in front view we should look at the anti bump of the outside wheel and the antidroop of the inside wheel. The car has 4 wheels and is a whole entity and need to be regarded as such.

3. Besides the aero "hinge", there is another essential reason while you need to know where the roll and pitch axis are: if you want to make transient simulation you will need to know what is the distance from the roll or pitch axis to the suspended mass CG is. The suspended mass inertia is, within other parameters a function of the square of this distance (parallel axis theorem).

02-01-2015, 10:56 PM

Why IDIOCRACY, and The Next Dark Ages, are Just Around The Corner.
================================================== ===

Fra881 starts this thread asking about his implementation of,

"30% of antisquat so my rear wishbones are parallel to each other ... pointing upwards looking forward. Flat geometry at the front."

Fra881 is a little worried by this because Claude's OptimumK tells him,

"This defines a pitch axis well behind the car.
In an ideal and symmetric situation the car is supposed to rotate around it during longitudinal acceleration."
~~~o0o~~~

I then give explanations based on VERY SIMPLE MECHANICS. I even throw in some DEFINITIONS of the terms commonly used by the Automotive VD industry. I even give references to industry sources of those definitions of things like Anti-Squat/Lift.
~~~o0o~~~

But Tim spends the first two pages telling me I am wrong.

"... your definition is not telling the full story ...
... your comment that ... is wrong ...
... This is where you are wrong...
... YOU ARE IGNORING ...!!!"

However, by the bottom of page 2 Tim concedes that my explanation is,

"... practically IDENTICAL ... to the one I use ..." (Make up your mind, Tim!)

The main difference is that Tim uses a much more complicated meaning to Anti-Squat/Etc., without giving a clear definition of it, or even acknowledging that it is VERY DIFFERENT to the other meanings used by the industry for EXACTLY the same words.

THIS LACK OF CLEAR DEFINITIONS IS ONE ROOT CAUSE OF THE DESCENT INTO IDIOCRACY!
~~~o0o~~~

Tim then says,

"... [Z, your] previous lateral calculations where you have assumed lateral forces distributions left and right to prove your points on roll centre theory are also meaningless ..."

Two points.

Firstly, on a technical note, my very simple "Old-School Classical Mechanics" explanation of a car's lateral behaviour works CORRECTLY with ANY "lateral force distribution" AT ALL! This is trivially easy to understand.

Secondly, I DO NOT HAVE ANY "ROLL CENTRE" THEORIES, AT ALL!!!

In fact, I pointed this out in this "Many Definitions of RCs" (http://www.fsae.com/forums/showthread.php?4390-Roll-Center-Migration&p=16320&viewfull=1#post16320) post from 2011, when I came back to this Forum to try to correct some of this nonsense. And since then, I have been at pains to point out that the biggest cause of the misunderstanding of these things is the complete LACK OF CLARITY OF THOUGHT that pervades today's society. A particularly good example of this is the Automotive-VD-Cottage-Industry and their complete disregard for CLEAR DEFINITIONS, as is evident right here on this thread!

How the hell do you expect to understand what you are talking about, when you never bother to clearly define the meanings of the things that you are talking about!?
~~~o0o~~~

Then Claude chimes in with these pearls,

"... teams like to know where their pitch axis is ...
... engineers like to know where the instant "hinge" of the car is; it gives them an idea of about what axis the car will pitch (or roll)...
... In fact on several close cockpit cars you can sees that the "hinge" is close to the front splitter..."

This then followed immediately by,

"I would like to use this post to specify to the usual whiner of this forum that I never, ever said that the car was rotating around the kinematics pitch axis."

HUH! So what (TF!) is that "pitch axis/hinge" in your above quote!!!??? And why, Claude, has your OptimumK software told Fra881 that his "pitch axis" is well behind the car? And why does Fra881 think his car will rotate about it?

The answer to above questions will likely NEVER be known. Because, despite my asking many times, Claude REFUSES TO GIVE ANY CLEAR EXPLANATIONS of this nonsense.

EG 1. Claude tells students to calculate a critical damping ratio about the KINEMATIC P&R "axes", using "parallel axis theorem for MoI". Why? NO ANSWER!

EG 2. Claude tells students that using pushrods&rockers can "reduce the non-suspended mass". How? NO ANSWER!

And on and on it goes.

EG 3. "More on pitch and roll axis ...
... when a car pitches (or rolls of both) there must be somewhere, somehow one axis around which the car is instantaneously rotating..."

More than a dozen years ago I made considerable effort to explain to Claude that any relative motion of two 3-D bodies is always about an INSTANTANEOUS SCREW AXIS! This concept of an ISA has been common "Classical Mechanics" knowledge for ~250 years. I sent Claude detailed references so he could do his own further research.

But no, Claude never bothered learning these things. He is STILL STUCK IN HIS 2-D WORLD.

EG 4. "Without an accurate and relevant tire model, the n-line theory will remain ... pure academic theory."

"Normal lines" (aka "right lines") have been common knowledge, and central to the simplest Mechanical problems, for centuries. In fact, CLAUDE USES THEM EVERY TIME he talks about Pitch or Roll centres/axes. But sadly, because he DOES NOT KNOW WHAT HE IS TALKING ABOUT, he now pretends they are some kind of new-kid-on-the-block, UNPROVEN, "academic theory", with no relevance to real racecars.

And, as always, the best way to muddy the waters and obscure the fact that you don't know what you are talking about, is to bring up Claude's favourite red-herring, the "accurate and relevant tire model".

A tyre is just another mechanical component like all the rest. But you students will only see that when, or IF, you ever LEARN MECHANICS!
~~~o0o~~~

SUMMARY - Too many people here peddling too much nonsense.

Too much use of fancy, technical-sounding, but ultimately obfuscating terms like "the % Anti-X of", with too little attempt at CLEAR DEFINITIONS of said terms.

Too many pretend-Engineers still stuck in a kindergarten world of 2-D "axes" and "centres", with said people TOO LAZY to learn anything 3-D.

Worse yet, an education system that has so ROTTED the minds of several generations now, that hardly any University level engineering students can do the simplest of FBDs. And as for any hope of them understanding any 3-D Dynamics, such as the 250 year old Euler Rigid Body Equations, well Buckley's chance of that.

Worst of all, an army of Automotive Industry "Experts" who are determined to accelerate this DESCENT INTO IDIOCRACY. Firstly, with organistaions like the FSAE who ask students to enter their car's "Front and Rear Ride Frequencies" (!!!) into the Design Reports. Then, with "experts" like Claude doing their best to convince students that Classical Mechanics is merely an untested "academic theory", not fit for the design of real racecars, even though said experts haven't the foggiest understanding of it.

Classical Mechanics, and the CLEAR THINKING it is based on (ie. the axiomatic-deductive approach epitomised by Euclid's Elements, and starting, Book 1, Page 1, with DEFINITIONS!), was a mature subject a century before the first horseless-carriages rattled out of their garages.

Classical Mechanics took Man to the Moon.

Classical Mechanics gave you all the lifestyle where you can achieve morbid obesity by age ten.

But Classical Mechanics has been TOO SUCCESSFUL. Because nowadays nobody can be bothered thinking about anything anymore, because STOMACH TOO FULL!

Yep, eat up now, because "TNDA" is just around the corner!

(Well, my estimate is ~300 years, give or take 200. Based on above, sooner is more likely.)

Z

Tim.Wright

02-02-2015, 02:29 AM

The main difference is that Tim uses a much more complicated meaning to Anti-Squat/Etc., without giving a clear definition of it, or even acknowledging that it is VERY DIFFERENT to the other meanings used by the industry for EXACTLY the same words.

Apart from the exact definition that I gave including a formula?

Its pretty clear that you are reading what you want to hear rather than what anyone actually saying, both for my post and Claude's. Whether we are right or wrong, you need to give more than a token effort in understanding what we are trying to convey then you won't look so stupid responding to arguments that we are not making. We waste large amounts of time picking through your diatribes to understand what you are saying so we would expect at least the same in return.

Anyway, I think I will leave it there for the moment since the discussion clearly isn't going anywhere.

BillCobb

02-02-2015, 06:38 AM

[B]Classical Mechanics took Man to the Moon.
Z

Not exactly. The Russians tried to use Classical Mechanics to solve the Lunar Orbital Injection problem but it clearly failed because the Moon is not a homogeneous solid. (It's not all just green cheese).

Instead a whole line of computer hardware (IBM's System 360 Multi-Processor) was needed and developed to solve the nonlinear Lunar Mission simulation from the ground up (so to speak).

In fact, as a student at RPI, I helped with a peculiar catastrophic mission ending problem solution that made use of a technique soon to be named "Finite Element Method". The Saturn 5 Booster suffered from what was called Engine 5 Backfiring Issue. Engine failure resulted in the heavy steel Motor Base plate MELTING during liftoff before staging. A computer program was developed to study the thermal characteristics of the Booster Motor baseplate using classical heat transfer methods but on a much grander (FEM) scale. The program was called "NASTRAN' (NASA Structural Analysis). First used as a thermal analyzer, it became apparent that the constitutive equations for a heating solution could be formulated for mechanical analysis. Thus, another problem could be solved: The so called "Stick Balancer". The Saturn 5 Stack could NOT stand up by itself (fully fueled). Classical mechanics was used to represent the Stack as a set of hinged, solid beams and a control algorithm was developed to balance the stack using active motor gimbals (lots of hydraulic power needed). RPI Control Engineering Students (like myself) were faced with a series of class problems involving a toy railroad car with 3 types of meter sticks mounted on it" 1) solid beam stick, 2) 2 sticks hinged at a center joint, 3) a flexible stick. Note that 2 and 3 situations were conditions in which the meter stick would not stand up by itself (sound familiar ??). Oh, and I finally got to write an SAE paper about how to model a CAR with NASTRAN to determine the chassis compliances of the suspension and the body with a frame. Ignore the body and frame and you get the wrong answer (crash into Moon).

Students were challenged to develop a control algorithm using a TR3 analog computer to take base angle displacement and velocity measured signals and pull the rail car back and forth until the top of the stick (with a capsule mass on it) was balanced. You run out of brain cells when the flexible stick is introduced. Especially one with characteristics like a "tape Measure" (ya know, a curved one that falls out of straightness just before you want to take a measurements). So, new incremental control mechanics formulations (State Space) theories were developed. My Controls Professor (C.N. Chen) who wrote the book on this (wish I had saved the textbook) worked on the Saturn Stacker solution and saved the day.

BTW: The Base Heating problem was solved by discovering that the center #5 engine was starved for oxygen because the O2 turbo-pump hp was insufficient. Increasing the pump capacity 20% or so produced a clean burn and no longer melted the 5" thick steel support plate.

We knew that the moon was not a point mass so the Orbital Injection process had to be solved ON THE FLY using ground based real time simulation to guide the final approach. Otherwise, it was hit the surface or lost in space. It is these situations that the space race competition could not solve or rectify. Vostok could not be turned into a bunch of rigid sticks. The attempts to steal the 360 architecture, hardware and software, were many (one did succeed but the S.U. scientists could not get it running in time).

One thing you got for free with a SYSTEM 360 computer was a program called CSMP (Continuous System Modeling Program) written in Fortran IV. I became a CSMP guru (still am) and often applied it to other Vehicle Dynamics (no longer flight dynamics) situations.

And THAT, as they say, is the rest of the story ! Newton was a great guy, but sometimes Mother Nature slips you a Mickey to separate the Men from the Boys ...

Claude Rouelle

02-02-2015, 07:19 AM

Zee clown of this forum continues his show.... Most of his knowledge and valuable arguments and perspectives are melted away by his desire for controversy. Is the goal of this forum to exchange ideas in a respectful way or is it for one person to be right and the rest to be wrong and to go on and on in futile circles. Both laughable and sad. In the circus of life the clown is often the saddest man......

Claude Rouelle

02-02-2015, 07:54 AM

Another perspective about instant axis of rotation: yaw axis.

We have been working with simulators it our "office" (we got one a bit less than one year ago) and with other simulators. I can tell you that when you make the simulator (and the driver) rotates about its CG or you make it rotate about the yaw axis (which is the axis at which the tangential yaw speed is zero and can be calculated with the front and rear chassis slip angle) the driver has a different feeling. The "feelings" are unfortunately very driver dependent (remember we do not try to reproduce the reality but what the driver feels the reality is; that is a challenge) but most of them feels the simulator more "real" when the car rotates around the "real" pitch axis instead of its CG. And during the different corner phases the yaw axis never stop moving....

Again the the accuracy of the calculation (should I dare to say the "estimation"?) of where the yaw axis is is dependent of the accuracy of the inputs. Garbage in, garbage out. Same thing as for the roll and pitch axis.

In FS/FSAE design judging I times to times ask students where the yaw axis is. Often they told me that it is an axis perpendicular to the ground and going through the car CG. that is what some text book show in the first simplified version of their explanation. I then ask them this: "If the force F= Ma due to the lateral acceleration is represented by a force vector of which the origin is at the car CG (counteracted by 4 tire grip Fy) and the yaw axis passes through the car CG ...... how do you create a yaw moment? Without a yaw moment how does the car enter (or exit) the corner? " Often that makes them think (which is one of the goal of this competition and this forum).

In transient you will need to know (or, OK, "estimate" the best your inputs accuracy and calculations can give you) where the yaw axis is because the yaw inertia will be a function of the car yaw inertia about its own CG and the SQUARE of the distance from the yaw axis (yaw center in 2 D) to the CG.

Similarly, the car suspended mass does not rotates in roll or in pitch around its CG. The square of the distance between the suspended mass CG and the roll and pitch axis will influence the suspended mass roll and pitch inertia.

Mitchell

02-02-2015, 05:02 PM

Hi Claude, since you mentioned it, I was wondering if you could help me out with the following yaw axis related problem?

Imagine a car negotiating a right hand bend. Not in hot and sandy Egypt, but in the cold and icy North. The car oversteers and spins off the road and onto a large frozen lake. There the car's CG keeps sliding in a straight line, at a steady 10m/s directly North, while the whole car keeps spinning (yawing) at a steady 1 rev/s, clockwise in plan-view. (Think recent James Bond movie...)

There are three points painted onto the car's centreline.
Point "A" is 1 metre in front of the CG.
Point "B" is 1.6m in front of CG.
Point "C" is 3m in front of CG (the car has a long nose).

Q7. At any instant, where is the "Instant Centre" for this essentially horizontal, planar motion of the car's body, WITH RESPECT TO (= wrt) the frozen lake?

Q8. Describe the paths of points A, B, and C, wrt the car body.

Q9. Describe the paths of points A, B, and C, wrt the frozen lake (draw and post these here, if possible).

Q10. What is slightly special about the path of point B, wrt the frozen lake?

Q11. What would be the EXACT position of point B (on car centreline) to make this path EXACTLY special?

Q12. What are the fancy sounding mathematical names for the paths of points A, B, and C (wrt frozen lake)?

Assuming the frozen lake is an "inertial reference frame", and neglecting aero forces:
Q13. If your body has a mass of 100kg, then what are the major forces acting on your body when you sit at points A, B, or C???
Give magnitude and direction at any instant.

Q14. Is it possible to determine all the forces acting on your body in the above question, if you know the exact postion of the IC for the car's (and hence also your) motion wrt frozen lake, but you only know this IC position AT THE INSTANT?

Look forward to your answer

Mitchell

Claude Rouelle

02-02-2015, 07:28 PM

Mitchell

02-02-2015, 08:11 PM

Mitchell,

I saw a post like that long time ago. I think I remember where it came from

Just for me to understand the goal of this exercise...

Did you create this exercise? if not where does it come from? What were questions 1 to 6?

1 to 6 are not relevant. It was a series of questions asked to you by someone over a year ago which you must have overlooked. I have always been curious as to how you would answer it.

I am not the creator, but you can probably guess who is.

Claude Rouelle

02-02-2015, 08:31 PM

Mitchell

02-02-2015, 08:43 PM

"I am not the creator, but you can probably guess who is." It was obvious from the style

Why in that case didn't you play open book and tell me that from the beginning?

I could take the time to go through it; there are a few basic equations but I won't because a) I am not retired. I am running a company, have seminars and consulting project to work on b) whatever I answer will be the source from another round of unproductive controversy with the clown c) Lets' say I answer you; how would this help you to understand and build a better car?

Because the creator of the questions is not relevant. Sometimes it is useful to see somebody else approach a problem to see different methods. I am very curious to see specifically the Claude approach.

There will be no controversy, it is a straight forward VD question with a single answer.

02-02-2015, 08:55 PM

Bill,

Not exactly. The Russians tried to use Classical Mechanics to solve the Lunar Orbital Injection problem but it clearly failed because the Moon is not a homogeneous solid. (It's not all just green cheese).

I enjoyed your post (really!) but I am not sure about that failure...

Firstly, Classical Mechanics works regardless of whether the body is a homogenous solid, or lumpy green cheese, or anything real, so far..

Put simply, CM works for EVERYTHING except the extremely small stuff, where QM takes over. Interestingly, even Relativistic effects can be directly deduced from CM with the addition of an extra postulate (ie. "measured-C = constant") to Newton's Three.

CM is the best explanation we currently have for describing the behaviour of ALL the macroscopic stuff around us.

Secondly, and putting this as gently as I can, the Russians put the first rocket into space, then the first satellite, then the first man, and the first dog, woman, etc. Having won these pissing-contests, and, more importantly, having gained the first foothold on the military high-ground, they set about consolidating their advantage there (see movie ref. below).

Meanwhile, the Americans tried to save face via the rather useless exercise of being first to put a Man on the Moon. But very shortly after they did (roughly one and three years later), and so as not to be upstaged, the Ruskies sent up two SUV-sized Luna-Cars to cruise around the Moon. This demonstration of remote-controlled complex machinery was quite impressive. Apparently the result of this, ahem... "scientific mission" was,
"Robot-kar sez iz nyet grin chiz! Iz yust rocks. All yust rocks..."

Oh, yes..., and nowadays any 'Mercuns who want to go to space have to hitch-hike with the Ruskies...
~o0o~

... to separate the Men from the Boys ...

That last line has a hint of Clint Eastwood's movie "Space Cowboys" in it, which I quite enjoyed. A reasonable portrayal of changing times, IMO. :)

But what happens in another 40 years, when the characters suggested by that movie are all gone?
~~~~~o0o~~~~~

Claude,

... the goal of this forum to exchange ideas in a respectful way...

Agreed, and I would be fascinated to hear more on your home-brewed ideas/theories of Vehicle Dynamics.

In particular, any of these below concerning the Pitch/Roll/Yaw axis. I would especially like to learn about this business of "squaring the distance" as per the "Parallel Axis Theorem".

Can you please give a worked example with as many relevant details as possible?

... if you want to make transient simulation you will need to know what is the distance from the roll or pitch axis to the suspended mass CG is. The suspended mass inertia is, within other parameters a function of the square of this distance (parallel axis theorem).
...
...In transient you will need to know ... where the yaw axis is because the yaw inertia will be a function of the car yaw inertia about its own CG and the SQUARE of the distance from the yaw axis (yaw center in 2 D) to the CG.

Similarly, the car suspended mass does not rotates in roll or in pitch around its CG. The square of the distance between the suspended mass CG and the roll and pitch axis will influence the suspended mass roll and pitch inertia.

Or perhaps you could just exchange your ideas on those questions Mitchell posted?

Perhaps just a one word answer to Q14?

Z

Claude Rouelle

02-02-2015, 09:26 PM

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

BillCobb

02-03-2015, 08:05 AM

Hi Claude, since you mentioned it, I was wondering if you could help me out with the following yaw axis related problem?

Look forward to your answer

Mitchell

I'd say about 1.55 m, eh ? (I get the point....)

C=15 is every water skier's nightmare.

BillCobb

02-03-2015, 09:12 AM

Most fun though, at 2.2 m/sec.

BillCobb

02-03-2015, 11:06 AM

It's "The Helen of Geometers".

And, There were NO differential equations used in the generation of these results. Anybuddy wanna see the graphs ? They are kinda cute in 3 colors....

02-05-2015, 07:25 PM

Anybuddy wanna see the graphs ? They are kinda cute in 3 colors....

Bill,

Yes, I would like that! I think they might be helpful here... :)
~~~o0o~~~

Claude,

It has been a few days now since Mitchell asked you those questions. Answers to those questions will help students gain deeper understanding of this topic.

Such answers from you may also help clarify your particular interpretations of "Pitch/Roll/Yaw-axes" and the sort of VD calculations you do with these axes.

So, PLEASE, could you give us a worked example of your methods, perhaps using this example of the spinning car?
~o0o~

To be specific, I am especially puzzled by your suggestion that a "Second-Moment-of-Inertia" has to be calculated about these axes. (BTW, I am familiar with the Parallel-Axes Theorem. It is a very standard tool of CM. But, like all tools, it is only useful when used correctly.)

I would really like to know where, or how, or why, you use these MoIs?

To take just one example, does a Car travelling around a very gradual curve, such that its Yaw-axis is at an extreme distance sideways, have an extremely-extremely high Yaw Inertia, because of the "distance squared"? And in what sort of calculation would you use this extremely-extremely large number?
~o0o~

Anyway, given that you are a professional educator (ie. giving all those seminars to students, race teams, OEMs, etc.), don't you have a responsibility to ensure that your teachings have some basis in fact? Namely, that the predictions of your "theories" give more accurate answers than the predictions of those old-fashioned "academic" theories of Classical Mechanics?

Z

(PS. Bill, "C=15 is every water skier's nightmare. ". Well, ... no problem ... IF he can dead-lift 6 tons! :))

BillCobb

02-06-2015, 08:46 AM

By your command... (My colors look better than these, WTF?)

Z: 6.65 tons Water ski with a chain tow 'rope'.

stever95

02-08-2015, 12:52 PM

Man. Wish I had the time and brainpower to sit down and try to understand so much of what's being discussed here.

Who's with me?

BillCobb

02-08-2015, 06:33 PM

Ok, what can you Muses say happened here ?

CWA

02-08-2015, 07:33 PM

OK, so the coaxing and cryptic clues have got me thus far, some observations but no conclusions:

~1.6m (1.55m? - I haven't run my own sim, just looked at BC's plots) is the radius of the cycloid that leaves finite points during stages of the vehicle's rotation. These finite points could be called 'instant centres' at these particular times of the event, if an 'instant centre' is to be defined as the point around which the vehicle body's reference frame rotates w.r.t the global reference frame.

The vehicle body's forward speed and rotational speed in the ice lake reference frame define the radius of this cycloid. I haven't sim'd 2m/s as BC has mentioned, but I imagine if 360deg/s is maintained, the radius of the cycloid is much smaller, the 'instant centre' at certain times in a rotation will be closer to the vehicle CG than for the 10m/s case.

So far, this scenario, and BC's plots only track the movement of the front end of the car. If we were to add similar curves generated by similar points positioned on the rear of the car, we would see a similar instant centre be alluded to 180 degrees of rotation after what is currently shown in BC's plots. This instant centre would not only have a different longitude value due to forward speed of the body, but would have a different latitude value too.

So, for every full rotation, we have AT LEAST two instant centre locations, implying that the instant centre is constantly migrating in this situation, and is not just the 'vehicle CG'.

As for how to properly define/track this instant centre's position for the rest of a rotation, I'm not sure yet. Am I on the right track?

BillCobb

02-08-2015, 08:13 PM

What's your Simulink cape-ability ? (Available/familiar, available unfamiliar , non-existent, not applicable, none of the previous).

02-08-2015, 09:44 PM

Am I on the right track?

CWA,

Well, first few paragraphs were going well, but things fell apart near the end.

Namely, "TWO" ICs? For ONE body (= the car), wrt ONE reference frame (the lake)???

Maybe try an old-school simulation.
1. Cut out a piece of cardboard that represents the car reference frame (say 10 cm circle of cardboard, car CG at centre, car drawn at 1cm = 1 metre).
2. Punch little holes (~1 mm diameter) through car's centreline at the CG and A,B,C positions.
3. Place the car on a bigger sheet of cardboard representing the frozen lake.
4. Draw straight line on lake representing the path of car's CG.
5. Do "time-stepping" at, say, every 1/10 second, so car-CG advances 1 metre (= 1cm on cardboard), and car rotates 36 degrees (or other linear/rotational velocities).
6. Mark on the lake (with pen pushed through car-holes) the positions of A,B,C at each time-step.
7. For each PAIR of time-steps, Tn and Tn+1, find the point where you can push a pin (= thumb-tack) right through car and into lake, such that rotating the car back and forth about the pin takes it back and forth between the two time-steps. (Hint: Draw perpendicular bisector of two successive CG positions at Tn and Tn+1 (easy!). Also draw perpendicular bisectors of successive A,B,C positions at Tn and Tn+1. ALL these bisectors should intersect at the SINGLE, unique, "Centre" for this small but finite n->n+1 motion. Reducing timestep dT to zero gives "Instantaneous Centre" at Tn.)
8. Say, "Wow, ... bleeding obvious really!!!". :)

Or you might Search for "frozen lake James Bond" (Open section of Forum)...

Z

Goost

02-09-2015, 09:47 AM

which is the axis at which the tangential yaw speed is zero and can be calculated with the front and rear chassis slip angle
[...]
And during the different corner phases the yaw axis never stop moving....

I'm still trying to understand your definition of 'yaw axis'. Under what conditions is the statement 'tangential yaw speed is zero' true?

A) what is this tangential to ___?
B) by 'speed' do you mean (m/s) or (rad/s)?
C) is this 'axis' a point on the chassis X-axis center-line from a top view?

I will tell you what I think you mean, tell me how this is wrong. Either:

1) you have chosen a new term for 'Neutral Steer Point' (related the concept of 'static margin') that may be more intuitive than those words (even with SAE definitions, the words themselves don't tell us much without study, it's true)

or

2) This is a point which (exactly during steady state / approximately otherwise) is the perpendicular projection of turn center onto the chassis X-axis center-line. This point 'feels' like a center of rotation if the (steady) lateral acceleration component is removed?
It's also perhaps similar to the n-line / instant axis concept for a 4-bar linkage (chassis center-line is the 'upright', lines along tire lateral forces are the 'links'), hence your term 'axis'?

I think (2) is close, since you suggest that the 'yaw axis never stops moving'?

Is this concept important other than for the simulator 'feel'? i.e., is this concept useful for design ('I want next year's car to have XYZ yaw axis location during skidpad')? Is there a more standard term that matches your definition?

Sorry it's a lot of questions, perhaps an equation could clear things up? You asked a teammate this question once; we still can't figure what it means such that it needs its own term.

Cheers,
Austin G.

CWA

02-09-2015, 10:25 AM

Say, "Wow, ... bleeding obvious really!!!". :)

Ah - I'm here now!

When I said this ..

If we were to add similar curves generated by similar points positioned on the rear of the car, we would see a similar instant centre be alluded to 180 degrees of rotation after what is currently shown in BC's plots. ....would have a different latitude value too...so, for every full rotation, we have AT LEAST two instant centre locations...
..I incorrectly assumed there would be a symmetry about the longitude axis (vehicle direction) when the curves for the rear were drawn. There is no symmetry about the longitude axis due to the asymmetric direction of the vehicle's rotation. In short, I shouldn't have assumed this, I should have a-sim'd. I now know how this is all wrong. Moving on:

The direction of the CG-to-yaw centre vector is always 90 degrees from the CG forward velocity vector (this 90 degrees is constant in the global/ice lake reference frame). The magnitude of distance of the yaw centre to the CG is dependent on the combination of forward speed and rotational speed, or the 'cycloids' described by the vehicle's motion on the lake (this graphic helped me a lot - http://en.wikipedia.org/wiki/File:Cycloid_f.gif).

Mathematically, this distance magnitude, defined as a radius from the vehicle's CG, 'R' = forward speed (m/s) / rotational speed (rad/s) = 10 / 6.282 = 1.59m.

In this case, where there is forward (north) speed and clockwise rotation, the yaw centre is always to the right (east) of the CG's travelled path in the lake reference frame. If the vehicle happened to be yawing left (anticlockwise) whilst still travelling forwards, the yaw centre would always be to the left (west) of the CG's traveled path.

As a result, the yaw centre's position in the vehicle's own reference frame is constantly changing as the vehicle spins. The yaw centre seems to prescribe a curved path around the vehicle CG in this reference frame, and is a constant distance/radius from the CG as described above ('R').

So now I just need to get it clear in my head how useful / useless a knowledge of a vehicle's 'yaw centre' can actually be.

BillCobb

02-09-2015, 10:37 AM

But what happened here ? You're still on an ice rink or snow covered lake. (Which reminds me, I have a hockey game today at 5:00 p.m.)

Not the same as if you were under full tire adhesion control in a parking lot or race track.

CWA

02-09-2015, 11:19 AM

BC in answer to your previous question, my Simulink capability is available/familiar, but not familiar enough for me to trust my results for proving this one out to myself. I felt much more comfortable with my sheets of paper for this one.

But what happened here ? You're still on an ice rink or snow covered lake. (Which reminds me, I have a hockey game today at 5:00 p.m.)

Is this question directed to me as a follow on from my last post BC? The arrowed lines you've drawn against your curves are not what I was expecting / have drawn myself. Can you re-phrase your question? Are you implying that my last post shows misunderstanding? If so, I can't yet see how.

Not the same as if you were under full tire adhesion control in a parking lot or race track.

Sure. So is this statement in support of / against the idea of knowledge of the yaw centre being useful? I'm still not sure what is being implied I'm afraid.

BillCobb

02-09-2015, 12:10 PM

In my last post, there is a distinct difference between the path curvatures shown in my previous plots. This is because speed and rotational velocity is no longer constant over the course of simulated time. Even for ice, you don't slide forever. In this case, a real (but small) mu of the surface causes speed and yaw velocity to drop as time goes on (like so many other things). Here the two motions are constrained to stop coincidently.

On a dry surface with rolling, non-sliding tires, a vehicle does not turn around its CG unless it has equal cornering compliances front and rear (That's even regardless of whether its mass center is mid-wheelbase. Instead, a vehicle turns about a point in space located by the intersection of perpendiculars to the front and rear slip angle vectors. So, the turn center and the mass center (with all of It's properties) are usually not coincident. (Go look up "Static Margin").

What causes the most fumbles in the Vehicle Dynamics game is the ignorance of all of the other front and rear compliances present in the chassis. This includes the roll steer, the lateral force steer and aligning torque steer (especially that in the front steered axle) and some camber stuff. When you add these real, finite and sometimes very large terms to the front and rear tire contributions to slip angles, there is a dramatic change in the predicted/actual trajectory or path that it takes in a turn. To determine all of these compliance terms, you need some type of chassis measurement facility or a really freakin' good suspension and chassis modeling software product. In spite of your best efforts, even body flexure will alter your estimates and this can be missed by the current methods of clamping vehicles to K&C rigs: They are artificially constrained.

Anybody hear that Bruce Jenner's car crash was caused by a tranny problem ?

02-09-2015, 08:45 PM

CWA,

Full marks on IC-finding this time! :)

So now I just need to get it clear in my head how useful / useless a knowledge of a vehicle's 'yaw centre' can actually be.

As hinted earlier, answers to above question can be found on a thread discussing a Frozen Lake (http://www.fsae.com/forums/showthread.php?7572-Vehicle-Moment-Axes). (Not much on page 1, some Z-ranting page 2, many questions asked page 3, and, as usual, answers at the back of the book, page 4.)
~~~o0o~~~

Bill,

But what happened here ?

I'm thinking stunt driver does really cool parking manoeuvre?

The car starts off at left of shot, pointing and moving rightward (= North) at V = 10 m/s, and it also has clockwise yaw rotation of 1 rev/second, as before. The tips of the arrowheads and the red trace represent the point C, 3 metres in front of CG, and the tails of the arrows are the CG.

For the most part, the arrows can also represent the Inertial CENTRIFUGAL (= "centre fleeing") force acting on the person sitting at point C. So this force is trying to "push" said person off the front of the car.

After about 270 degrees of spin, the clever stunt driver manages to get tyre friction working again. So both forwards (= right/North) motion and spin slow down, and the car eventually stops, perfectly parked with nose pointing True North.

What would make such sims even more helpful, IMO, is more detail and more MOTION. So addition of some kind of graphics of a plan-view of the car (and maybe screeching sounds ... and the smell of burning rubber?). All presented in variable speed motion, with "Fwd/Rev/Slo-Mo/Pause" buttons, etc. And with overlaid arrows showing whatever forces you want to track.

The moving Cycloid linked by CWA is a start, but needs more "video-game"...
~~~o0o~~~

Posted by Bill:
... a vehicle turns [Yaws] about a point in space located by the intersection of perpendiculars to the front and rear slip angle vectors.

Earlier I said pretty much the same thing (but in many more words!).

7. For each PAIR of time-steps, Tn and Tn+1, ...
... draw perpendicular bisectors of successive A,B,C positions at Tn and Tn+1. ALL these bisectors should intersect at the SINGLE, unique, "Centre" for this small but finite n->n+1 motion. Reducing timestep dT to zero gives "Instantaneous Centre" at Tn.

Adding even more words...

Consider point A on the Car (which could be where your "front-slip-angle-sensor" is mounted).

At time Tn, A is at position At, in the Frozen Lake reference frame (= "global coordinates" if you want).
At time Tn+1, A is at position At+dt, wrt FL.

So, in this short time interval, A's average "direction of motion" is along the vector At->At+dt, and A's "average position" is midway between At and At+dt, all wrt FL (= in "global coordinates").

It follows that the (edit: "PERPENDICULAR" =) "NORMAL-LINE" through the midpoint of At->At+dt is also the "direction of NO motion" of A, during this short time interval. That is, the "perpendicular bisector of successive positions" of A (as in my above quote), is A's "Normal-line", or "n-line" as it was called several hundred years ago. (It was also called a "right-line", because at right-angles to direction of motion).

In 2-D Kinematics, whenever ANY TWO such n-lines of a Body intersect at a certain point, then ALL n-lines of the Body MUST ALSO intersect at that point, with that point called the Instantaneous Centre of Motion. (To make this more rigorous the above time interval dt has to go to zero, and the "Axiom of Rigidity" is used. Also, in 3-D Kinematics, in general, only a tiny fraction (one infinitieth) of ALL the Body's n-lines intersect the ISA, but there are still infinity-squared n-lines doing this. So infinity-cubed n-lines in total.)

Bottom line, Claude might think that "n-lines" are only of academic interest, but they are used in a great many places (as above), even though their users may never know they are using them!

Z

BillCobb

02-09-2015, 09:47 PM

That's a pretty fair set of observations on my sim plot. I would have used thumbtacks at work, but not on my own kitchen table. I would be killed.

The drift is a pretty fair description of my own travels with a Yamaha 4 wheeler on a smooth covered pond at the back of my property. You get going and spin and spin and spin. Then, I spun down to about 5 kph and the tires developed an immediate mu of two or more and the Yami rolled over on top of me. My family audience was apparently laughing their azz off 300 meters away until they realized I wasn't able to move any limbs.

While I lay there paralyzed, I had a chance to review the Laws of Unintended Consequences (there's more than 1. The locked wheel tracks in the ice would have made a stunning aerial photo, but a whole flock of confused spectator geese messed them all up. Geese don't make very good carrier landings on ice that looks like open water...

Actually, Matlab has a Virtual Reality Toolbox that would nicely do what you want to see....

DougMilliken

02-09-2015, 11:56 PM

The drift is a pretty fair description of my own travels with a Yamaha 4 wheeler
Sounds like your next 4-wheeler might be a side-by-side with roll cage?

Here is an interesting website that takes a novel (to me) approach to computing and displaying dynamic systems, http://worrydream.com/KillMath/ note the animations attached to the text. This sub-page uses a very simple car model as an example, http://worrydream.com/LadderOfAbstraction/

mech5496

02-10-2015, 06:26 AM

Doug, this website is awesome. Thanks!

BillCobb

02-10-2015, 08:24 AM

Sounds like your next 4-wheeler might be a side-by-side with roll cage?]

My next 4 wheelers turned out to be golf carts. Much more fun and practical. Turned up the governor on the gasser. Added an inverter generator standby to the electric one for that comfy "extended range confidence" feeling. I call it my "JOLT".

I'll bet these carts can out perform more than 1/2 the FSAE field.

To lose the fear of tipping over, I recommend a mobile crane. This one was hit by lightning so I got it "on sale". Lightning never strikes twice in the same spot, right ???

BillCobb

02-10-2015, 07:47 PM

Just when you thought it was safe to go outside. (I really like the added visual showing the real time steering wheel position as well as yaw , bounce and pitch motions). Yes, you can mouse around in the VR world to look from the top. Sorta like my Phantom Vision 2 Plus Quadcopter dog chasing video.

This is a VR Toolbox example, but easily adapted to FSAE car shenanigans.

02-10-2015, 07:57 PM

...This sub-page uses a very simple car model as an example, http://worrydream.com/LadderOfAbstraction/

Doug,

EXCELLENT LINK! Highly recommended!

I haven't read it all yet, but strongly support the idea of continuously climbing UP AND DOWN the ladder. Up the ladder to get the big-picture view. Back down the ladder to better see the details. Make changes. Repeat.

Z

Kevin Hayward

02-10-2015, 09:10 PM

Doug,

I add my thanks for the link, although it kept me up quite late last night reading through what I could.

The car example is a very good one and raises one of the big issues of data representation (in this case the data being the results of the model). This tends to be pretty straightforward for up to about 3 or 4 variables, but becomes much harder as the variables increase. Thinking about new ways to represent and analyse the solution space rather than a particular point is valuable.

I have run up against this teaching dynamics. Students prefer to solve problems that have specific inputs and the answer comes out as a single number. Coversely they generally complain about problems where the answer comes back as a relationship. This year the students I had the students solve a problem about projectile motion that involved moving through the layers of abstraction as presented here. The first solution involved the trivial solutions, the next layer moved towards a more complicated dynamics model, then on to optimisation and searching of the solution space, and then finally to something involving real world validation and a very difficult model involving impact and transition from bouncing to rolling (bonus marks awarded). Almost without fail the students were fine with the trivial solution and even the more complicated dynamics model. There was plenty of available documentation for this. The big difference in students ability came when optimisation and searching were introduced. Some were unable to do it at all, some when for a brute force approach and spent way too much time on it, And there were few elegant approaches. Graphical representation of the set of available solutions was also presented from anything from horrible looking tables, very imprecise graphs, to only a few that managed to present it quite neatly.

Our problem solving training tends to almost exclusively focus on the particular rather than the general. This is quite odd given that in any competitive field optimisation is the primary activity, which invariably requires people to effectively model and search solution spaces. This requires an understanding of important relationships.

The links you provided have given me a few more ideas to present in lectures and tutorials.

Between you, Bill and Z (and a few others) the content on these forums (and the type of discussion) has improved dramatically recently (excusing some of the arguing). It is a humbling experience to read some of these posts, and see the depth of understanding that some of you have.

Kev