Steering Paradox

[GeetFsae]

I am done doing my bit or whole part actually... but stuck with this paradoxic situation where i find no answer to it by myself and through my efforts.
The steering geometry is Ackerman when rack location is behind the front axle, (when it lies ahead ..it is Davis Geometry) but most of you have used the term Ackerman for it... and maybe applied the same concept as well... how would you do that when it is Davis and not Ackerman actually... because the I. Center lies outside of the vehicle track on rear axle...

I completely understood how this front of front axle location generates toe - in at braking and provides stability but not how you call it Ackerman an apply Ackerman geometry concepts on it when it is rather - Davis.
I seek substantial answers and there is no topic on Davis geometry in the whole of fsae forum.

[Ben Coburn]

The longitudinal position of the rack doesn't change the Ackerman calculations, they simply specify some line on which the ball joints on the steering arms must lie for a particular Ackerman value.

[GeetFsae]

how can we specify such line in this case..???
i mean if we want to have 100% Ackerman for example and keeping the rack in front ??.

[RobbyObby]

Ill give you a hint, go look in your high school geometry book.

That may seem a little harsh but seriously, we're all engineers here right?

[BMEP]

Originally posted by GeetFsae:
how can we specify such line in this case..???
i mean if we want to have 100% Ackerman for example and keeping the rack in front ??.
Draw an infinite line between the differential and the steering axis. If the steering arm joint lands anywhere on the infinite line constructed, it is considered to be 100% ackerman.

[Mehul Botadra]

Originally posted by BMEP:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by GeetFsae:
how can we specify such line in this case..???
i mean if we want to have 100% Ackerman for example and keeping the rack in front ??.
Draw an infinite line between the differential and the steering axis. If the steering arm joint lands anywhere on the infinite line constructed, it is considered to be 100% ackerman. </div></BLOCKQUOTE>

Okay fair enough. Its 100% Ackerman. What if the instantaneous center of rotation does not lie on that line, probably lies below or above that line. Then how do you calculate the % Ackerman? Even Google doesnt have an answer to that! There are various methods to do it but I dont know which one to use!

Slip angles for the time being dont matter!

[BMEP]

Originally posted by Mehul Botadra:
Okay fair enough. Its 100% Ackerman. What if the instantaneous center of rotation does not lie on that line, probably lies below or above that line. Then how do you calculate the % Ackerman? Even Google doesnt have an answer to that! There are various methods to do it but I dont know which one to use!

Slip angles for the time being dont matter!
For example, If your wheelbase is 60" and the line drawn from the steering arm through the steering axis intersects the center of the car at 120", this would be considered 50% ackerman. If the line from the steering arm through the steering axis intersects the center of the car at 30", this would be 200% ackerman.

[Crispy]

Originally posted by BMEP:
Draw an infinite line between the differential and the steering axis. If the steering arm joint lands anywhere on the infinite line constructed, it is considered to be 100% ackerman.

You need to be careful with this method. I'm pretty sure it breaks down quickly if your steering links are not perpendicular to the longitudinal axis of the car.

My preferred method is to geometrically calculate inside and outside steer angles for 100% Ackerman and plot outside wheel steering angle vs inside wheel steering angle angle. Then build a linkage in cad and run it through its range of travel (a 2-d sketch should be a good start and is simple to make). Collect inside and outside wheel angles over your desired steering range and plot them with your Ackerman curve. I also plot parallel (a straight line of slope 1) and 100% Anti-Ackerman (swap inside and outside) as references.

Then compare your curve with Ackerman and parallel. You can calculate how Ackerman your curve is at every point if you like (0% if parallel, 100% if Ackerman, varying in-between). Make sure you include toe angle.

All of this just tells you what you have, the tough part is figuring out what you want, or if it even matters.

I hope this helps!

[Adambomb]

Originally posted by Mehul Botadra:
Then how do you calculate the % Ackerman? Even Google doesnt have an answer to that! There are various methods to do it but I dont know which one to use!

Slip angles for the time being dont matter!

+1, I've also run into this problem, as I recall checking google, my old Optimum G notes, and I'm pretty sure RCVD as well, there wasn't one clearly established method, although one of those sources gave a "widely acceptable" method (unfortunately I don't remember which, and don't have my RCVD or Optimum G notes handy).

Although I will say that this is the first time in my almost 9 years in FSAE that I have heard of the term "Davis" steering geometry. http://fsae.com/groupee_common/emoticons/icon_confused.gif I've heard parallel, Ackerman, pro-Ackerman, and Anti-Ackerman, but never Davis.

[ed_pratt]

I think there has been some misunderstanding of the Davis Steering gear mechanism?

http : / / www . torqueworld. in /DAVIS_GEOMETRY.html

Ed

[Edward M. Kasprzak]

Going back to the IP: Davis and Ackermann steering have nothing to do with where the rack is located. "Davis steering" uses sliding connections between the links while "Ackermann steering" uses the vastly more common rotating joints and fixed-length links.

Crispy's post makes a lot of sense. I'll take a plot of outside wheel steer angle divided by inside wheel steer angle vs. steering wheel angle anyday. That's what matters, right? The simple geometric approximations and associated terms ("percent Ackermann") can give a reasonable starting point and a general idea of the behvaior, but cannot describe the full range of operation due to their assumptions.

[DougMilliken]

Originally posted by Edward M. Kasprzak:
Going back to the IP: Davis and Ackermann steering have nothing to do with where the rack is located. ...

Ackermann's name is used in at least three different ways in automotive engineering --

* He gets credit (historians can debate if it is deserved) for individual front wheel steering (two pivots, one for each wheel), as opposed to horse & carriage steering with a single steering pivot in the center of the axle.

* Ackermann correction -- the topic of this thread. Steering all the wheels so they turn about a common turn center, in the absence of tire slip angles.

* Ackermann Steer Angle -- "the angle whose tangent is the wheelbase divided by the radius of turn". Quoted from SAE Vehicle Dynamics Terminology, J670e. In other words, the "theoretically correct" geometric steer angle required for a turn, often referenced to the vehicle centerline.

More history in RCVD p.713-14. Also Wm. (Bill) Mitchell (WinGeo author) wrote an SAE paper on the accuracy of various linkages that generate approximate Ackermann corrections.

-- Doug Milliken

[axe27]

hi guys...!! i m in a bit confusion abt antiackerman geometry..!! our vehicle suits anti ackerman. i m a bit cnfused abt location of icr for antiackerman geometry. where it must be located above front wheel axle unlike ackerman..???

[Marvel]

Originally posted by axe27:
hi guys...!! i m in a bit confusion abt antiackerman geometry..!! our vehicle suits anti ackerman. i m a bit cnfused abt location of icr for antiackerman geometry. where it must be located above front wheel axle unlike ackerman..???

You were able to justify that "our vehicle suits anti ackerman" but cannot locate "ICR" for anti-ackerman??? http://fsae.com/groupee_common/emoticons/icon_eek.gif

ICR for anti-ackerman must be somewhere ahead of front wheels centerline...

(method for ackerman and anti-ackerman is same..just rotate yourself 180degree upside down and proceed to get ICR!!!!)

[axe27]

marvel..i know that actually , but in a way i want to ask how i can constraint it..?? for ackerman it lies on extended line drawn through rear axle...likewise for ant-iackerman...???

[Claude Rouelle]

I gave up looking at the exact definition of Ackerman: I have see so many...

At the end I simply try to look for an answer to the 2 following questions: a) which one of the inside or outside wheel steers the most for a given steering wheel input and b) by how much.

You can find out the answer with a simple 2D model in Excel or a more sophisticated kinematics software like OptimumKinematics. I suggest you start with a simple 2D model (make it useful before you make it complicated)

5 quick remarks

1. As mentioned by other guys in this forum you can have the same Ackerman number whether the longitudinal position of the steering axis is ahead or behind of the front wheel axis. The issue will be more about packaging when you design your steering system and the front upright; if you want a pro-ackerman and the steering rack is ahead of the front axis you could have the toe link outboard rod end right in the brake disc! Every car part is linked

2. Think about the the influence that the steering rack position will have about the steering column and the steering wheel angle and how much universal joint or CV you will need. Again, every part of the car is linked.

3. Judges often ask where your front and rear roll center are. Or how much camber do you run. The question is oversimplified because it is about roll centers position and camber at static ride heights. The roll center can move laterally and vertically. Also you camber will change in heave and roll and steering. I would prefer to see CURVES of roll center and camber movement in roll and heave and steering. Similarly Ackerman number won't necessarily be a fixed number; the ration inside / outside wheel steering angle will most probably change. Better come with a curve than a fixed number

4. No need to be accurate bu 0/1 % Ackerman, when your compliance will be taken into account, this accuracy will not be relevant.

5. At the end how much Ackerman do you need, or which wheel need to be steered the most and by how much?
2 answers:
A) Use you tire models and see for a given vertical load and given camber how much slip angle each wheel needs to get the most lateral grip. The inside outside delta needed slip angle will give you a pretty good idea of the delta steering angle you need. It will give you a very theoretical answer but at least the study will help you to understand how to get for the ideal steering system. You will see that the ideal / theoretical Ackerman for tire A is not the one for tire B. Be careful; if you did a good job it could be the front grip will be much improved ad the driver will start to complain about oversteer.
B) The practical answer; TEST! Try different Ackerman solutions and ask your driver how he feels, look at the lap time and your tire temperatures (ideally with IR temperature sensors). In Nebraska I saw the Brazilian team EFI having a bracket (which hold the outside toe link rod end) bolted on the upright via shims (as used in camber adjustment) between the bracket and the upright. Not perfect in terms of compliance but so nice, cheap, useful to test different Ackerman. The student told me the initial Ackerman made the car balance very bad but by changing the Ackerman with shims they got the car better and better.

Have fun!

Claude

[Z]

Originally posted by Claude Rouelle:
A) Use you tire models and see for a given vertical load and given camber how much slip angle each wheel needs to get the most lateral grip. The inside outside delta needed slip angle will give you a pretty good idea of the delta steering angle you need.
...
... the study will help you to understand how to get for the ideal steering system.
Claude,

Clarification please. http://fsae.com/groupee_common/emoticons/icon_confused.gif

Are you suggesting that if the more heavily loaded outer tyre reaches peak lateral force (peak Fy) at, say, 1 degree greater slip-angle than the inner tyre, then the steering should be anti-Ackermann (ie. the wheels should toe-in when steered away from straight ahead)???

Z

[Mike Cook]

Really Z,.....
Even if the heavier loaded outside tire desired more slip angle than the lower loaded inside tire, it does not mean the tires would be toe-in when steered. I consider 100% ackerman to be the geometrically correct steer angles for low speed, no slip conditions. For our skid pad this might be about 12deg on the outside tire and 14deg on the inside. This is clearly a toe out condition. As we increase the speed of the vehicle the slip will increase equally on the front two tires. If at peak lateral acceleration we want a total of 8 degree slip on the inside tire and 9 degree slip on the outside tire, we would need to change the steering geometry so that the outside tire is steered 13 degrees and the inside is steered 14 degrees (approximates only). At this point, we would still have a toe-out condition, and more slip on the outside tire than the inside.

And looking at the tire data this is usually the case. This is why most teams run less than 100% ackerman (i.e. more slip on the outside than inside tire).

[Z]

Originally posted by Mike Cook:
Really Z,.....
...
This is why most teams run less than 100% ackerman (i.e. more slip on the outside than inside tire).
Mike,

I will wait for Claude's response before going into more detail. But I reckon any team running, say, 50% Ackermann, based on arguments similar to above, is losing a lot of performance.

Z

[Claude Rouelle]

Even if I have a feel for it, I honestly do not know what the ideal Ackerman is for a FSAE. It depends on so many factors starting by the tires, the car, the circuit, the driving style etc...

A few hints

1. You do not per say "decide" the front (and rear) tire slip angle, the car (think for example about the contribution of the rear tire to the whole car slip and yaw acceleration) and the driver do.

2. You cannot look at slip angle only on the kinematic way; you need to involve forces and moments generated by the tires. That is what the whole method of the yaw moment Vs lateral G created by Milliken is about

3. On a given car (given tracks and wheelbase, steering geometry etc...) besides the initial toe in or to out setup, bumpsteer and steer by compliance, there are 3 causes for tire slip angle
- CG slip angle Beta
- Yaw velocity r (or speed V and radius r)
- And steering delta

4. There are 13 causes for the yaw moment
- 4 tire Fy
- 4 tire Fx
- 4 tire Mz
- The aero yaw moment (If you have big wings and big side plates it will not be insignificant)

5. I have seen several cars (including very successful FSAE) winning races with anti-Ackerman. Some pictures of this website are very revealing. I can also tell you that some F1 do not use the same Ackerman at a quick track like Monza and at twisty circuit like Monaco. Best prove that ideal Ackerman is circuit dependent.

6. There only 3 way to decide what is the ideal Ackerman and each is more and more useful but you need to go though each step.

A. Analyze your tire data. Make a grid of vertical load and camber and see what the ideal slip angle (the peak slip angle) is for each condition. That should give you at least a qualitative appreciation of what your Ackerman should be. I say qualitative because there no in-lab tire testing which is spot on with the grip and moment numbers compared to a race track (well which race track, which asphalt is the closest for the in-lab Calspan test..?)

B. Create a graph Yaw moment vs lateral acceleration. That is THE method which was created by Millikan and his book described it very well. That is THE method which will tell you the influence that weight distributions, camber variation in roll and heave and steering, spring and their motion ratio, ARB and their motion ration, downforce and downforce distribution.... you name it... and of course Ackerman will have on Grip, Balance, Stability and Control. That is the method that the best FSAE teams use and that is one of the methods that makes our OptimumG customer winning races. Try different Ackerman and you will see how grip, balance, stability and control change.

C. TEST!! That is the ultimate solution. You need to manufacture a front upright where you can change the Ackerman. However, even if you find the perfect Ackerman and the quickest car, the 2 previous steps are still indispensable: in FSAE / FS the goal is not only to be quick but to know WHY you are quick.

Claude

[Claude Rouelle]

Z,


Are you suggesting that if the more heavily loaded outer tyre reaches peak lateral force (peak Fy) at, say, 1 degree greater slip-angle than the inner tyre, then the steering should be anti-Ackermann (ie. the wheels should toe-in when steered away from straight ahead)???

Yes I do (camber is not taken into account in this simplified reasoning neither the influence that higher slip angle and the Fx increased "rolling resistance" on the inside wheel will have on the yaw moment. Our balance vs grip method which take the tire Fx and Mz into account shows the same trends.

That is what I believe in and that is what i have experienced on race tracks. For example when I race engineered F3 on Michelin tires (in 2 years we won more than 50 % of the races we competed in and both championships) where the tire models and data clearly showed that the more you loaded the tire the more slip angle you needed to get the most Fy, we always got quicker with anti-Ackerman geometry. In fact the front became "too good" (driver comment) and we had the work on the rear to use this additional front grip and get back to the same balance; same yaw moment, more grip. That was even more true on tight circuits like Pau or Monaco. Quantitatively, the amount of need anti-ackerman needed was a function of the track grip and a bit the driver style. I went racing with the same car in Germany where the mandatory tire was a different one and where the more you loaded the tire the less slip angle we needed; there a pro Ackerman worked better.

Maybe I was right but for the wrong reason(s) and I am always ready to listen but so far that is what my reasoning and experience is. A few successful Le Mans and F1 engineers I discussed this with also thinks this way, although if all of them agreed on the principle some of them also say that "it is not that simple..they are other factors starting with tire temperature and tire temperature distribution. These guys have extremely sophisticated tire thermal models. I agree and that is why using tire IR temperature sensors while testing different Ackerman will teach you a lot. But these engineers and I could all be wrong. What is your take?

Claude

Claude

[Z]

Claude, (and anyone else interested http://fsae.com/groupee_common/emoticons/icon_smile.gif),

For what follows, let's define "Ideal (or 100%) Ackermann" to mean that when the steering-wheel is turned away from straight ahead, lines drawn through both front axles always intersect the extended rear axle line at the SAME POINT. So for low speed, no-slip cornering this point is the "Instant Centre" for plan-view motion of the car body wrt ground.

Furthermore, note that for a typical wheelbase/track FSAE car to be able to corner "between kerbs" ~6m apart, with no tyre slip, the outer-front wheel must steer ~30 degrees, and the inner wheel ~45 degrees. This puts the car in the middle of the track at a FSAE hairpin, which in the rules has 9m OD and 0m ID (ie. outer-front wheel follows path ~6m dia., and inner-rear wheel ~3m dia.).

Mike Cook suggested above that based on typical tyre data the front wheels should steer ~1 degree less than required by "Ideal Ackermann" (Mike, correct me if I misunderstood). So at full-lock perhaps only 14 degrees of "dynamic toe-out" is required, rather than 15 degrees. However, given Mike's example of the Skid-Pad where only 1 deg toe-out was required rather than 2 deg, it might be interpreted (by lazy students!) that only half, or 50%, Ackermann is required.

Claude, in his post, seems to categorically recommend that the wheels should be toed-in when steered, giving anti-Ackermann (again, Claude, correct me if I misunderstood). This means that at full-lock there is MORE than 15 degrees difference between the "Ideal" and actual steer angles.

I say that "tyre curves" are largely irrelevant to FSAE steering geometry, and the maximum practical amount of pro-Ackermann (dynamic toe-out) should be sought. Here is why.

1. During high speed (ie. large radius) cornering, the front wheels are hardly steered at all. Therefore, their relative toe angles are determined mainly by the "static" setting, and only slightly modified by any Ackermann geometry. High speed sweepers are typical of high profile race series, such as F1, and the F3 mentioned by Claude. Here toe-in of the front wheels can reduce the "slip-angle drag" from the inner wheel, and allow more efficient use of the outer wheel, and so increase speeds. BUT! I am not aware of any really high speed sweepers in FSAE.

2. The rules of FSAE state that there will be (possibly many) hairpins as described above, on any AutoX and Endurance track. Assume that when going through these hairpins, the rear, and outer-front wheels have, say, 6 deg slip-angle for their peak Fy. Then with parallel-steer the inner-front wheel might be forced to run at well over MINUS 6 degrees. That is, it pushes the nose of the car OUTWARDS with all its available force! Admittedly, the more heavily loaded outer-wheel wins this fight, but still not good. Even worse with anti-Ackermann.

3. Tyre "Fy vs Slip-angle" curves don't have sharp "peaks". Typically they have broad, rounded tops. Some just gently reach a plateau and stay there (correct me if wrong for FSAE tyres). This means that when running at +/- 1 degree away from the "peak" the tyre has almost as much Fy as at the peak. However, the change in steer-angle makes a much bigger difference to the car-rearward component of Fy (ie. slip-angle drag, which increases 20% going from 5 to 6 degrees). Repeating this, the cornering (centripetal) force changes very little, but car-coordinate drag force (not tyre rolling drag!) changes a lot. This can be a problem in that it can upset the yaw balance between the two front wheels. However, I don't think this is a big issue on FSAE type tracks (see 5 below).

4. Most R&P steering linkages can NOT track the Ideal Ackermann curve to less than +/- 5 degrees (ie. they are ~5+ deg "wrong" at some steering position). This swamps any +/- ~1 deg effect of tyre "peak-Fys". So get the geometry right first...

5. And I haven't even got onto "transient" effects yet (ie. yaw acceleration), which is important in FSAE because of all the changes in direction. Briefly, more dynamic toe-out (pro-Ackermann) is better. And there is also the issue of yaw stability in steady-state cornering, where again it is better to have the inner-wheel "saturated", or past its peak (this perhaps only relevant to Skid Pad, because not much steady-state in AutoX or Enduro.)

Bottom line is that anti-Ackermann might suit "real" racecars on full-sized circuits, but that ain't FSAE.
~~~o0o~~~

Now, all the above probably sounds like a load of "theoretical" codswallop. http://fsae.com/groupee_common/emoticons/icon_smile.gif

So I leave it to Carroll Smith, who I recall at his last FSAE event publicly saying to the teams something like "FSAE cars should have as much pro-Ackermann as you can get from a conventional steering linkage, because even that is not enough."

Z

[Claude Rouelle]

Claude, in his post, seems to categorically recommend that the wheels should be toed-in when steered, giving anti-Ackermann (again, Claude, correct me if I misunderstood).


NO I never said that! I said that Ackermann choice is mainly tire specific. Some tire (mainly race radial tire new generation) requires more anti-Ackerman and some like cross play require pro Ackerman. It depends on your tire.

More to come

Claude

[Moop]

Originally posted by Z:
Then with parallel-steer the inner-front wheel might be forced to run at well over MINUS 6 degrees.
I'm not seeing this - what makes you say this?

I can say for sure that in my simulations I've never seen anything like this happen, even with only about 5 deg ackermann at 25 deg inside wheel steer angle. At least, not anywhere to yaw moment = 0

[Mike Cook]

Like he mentioned, in a hairpin the inside might need to be steered 45deg and the outside 30deg. With parallel steer, they get steered the same. If the outside tire has 6 deg of slip, then the inside tire would have 45-30-6 = 9 degrees of slip in the wrong direction (i.e. pushing the car out of the corner).

[Z]

Thanks Mike, that's what I was getting at.

Students might try slowly pushing their car, with steering at full lock, around a hairpin with a sandy surface. If the steering has insufficient Ackermann, then both front wheels will "snow-plough", ie. slide with lots of toe-in.

Z

[Marvel]

Originally posted by Mike Cook:
Like he mentioned, in a hairpin the inside might need to be steered 45deg and the outside 30deg. With parallel steer, they get steered the same. If the outside tire has 6 deg of slip, then the inside tire would have 45-30-6 = 9 degrees of slip in the wrong direction (i.e. pushing the car out of the corner).
I am not sure but still...will that matter when (in the sharp corners), you try to completely unload your inner wheel or try to get some greater amount of lateral load transfer?? http://fsae.com/groupee_common/emoticons/icon_confused.gif

[Z]

Originally posted by Marvel:
... you try to completely unload your inner wheel...
Marvel,

Yes, that is one solution. Lift the inner-front-wheel and it doen't matter what Ackermann you have.

BUT! now you have lost one means of adjusting handling balance (under/oversteer). Furthermore, if you are running a "spool" differential, then typically you want to lift the inner-rear-wheel, which means similar vertical loads on both fronts.

Don't paint yourself into a corner. http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z

[The Stigg]

Hi Guys and especially Z,

here are my 2 cents on this topic:

Slip angle drag through kinematic steering design at the inside front tyre for FSAE is one of the most underestimated tuning factors I've ever seen.
We tested this over the last 3 years and it provided at least the biggest lap time improvement for us. BTW - by far more than any roll-center displacement optimization at all.

And here is why:

1. FSAE is about yaw acceleration. slip angle drag and therefore fx can be build up more than a 1th(depends on tyre) of a second faster than fy!!!!

2. The heat generated by this can have an immense impact on your laptimes especially in the first 2-5 laps.

That's why I would totally agree with Carroll!



Originally posted by Z:

So I leave it to Carroll Smith, who I recall at his last FSAE event publicly saying to the teams something like "FSAE cars should have as much pro-Ackermann as you can get from a conventional steering linkage, because even that is not enough."

[zh]

so finally, can we say that amount of ackerman percentage we choose depends only on tire graphs

[Luniz]

...and on yaw acceleration, CoG height, wheelbase, track width, roll stiffness distribution...

[Dettle]

Hi,

my little contribution to that topic:

I do it pretty much the same like Chris Patton mentioned. I would like to sum up a little bit..

In the end it is all about which outside/inside steering ratio vs. ackermann steer angle (see def. from Doug page1) is best for your lap time. This obviously depends strongly on the track layout since with conventional steering systems, you cannot design the relationship between outside/inside steering ratio vs. ackermann steer angle as free as you might need to favor every type of cornering situation on a track. The Ackerman percentage discribes nearly all the possible design configurations for the relationship of outside/inside steering ratio vs. Ackermann steer angle. Hence it makes sense to talk about Ackermann percentage to fully describe the steering configuration. But it is still very difficult to conclude from an Ackermann percentage on the actual relationship between inside wheel slip angle and outside wheel slip angle as this is also a function of the vehicle geometry, the weight distribution, the rear axle slip angle and most important the cornering radius! Ackermann percentage alone is just not that descriptive! What could help is to plot Ackermann percentage curves as outside/inside steering ratio vs. ackermann steer angle and then also add your "ideal" or lets say wanted relationship of outside/inside steering ratio vs. ackermann steer angle for a given tire characteristic. By investigating the differences between the ideal and the available ackerman percentage curves it might be easier to find the right ackermann percentage which fits your requirements best. Again, your requirements will be made up by the type of tire you use and the characteristic of the track in terms of amounts and contribution of small, medium or large radius corners.

In this point I see what Z is talking about: FSAE corners are considerably smaller in diameter and Ackermann correction angles become more imporant for proper inside tire slip angles! The interpretation of Ackermann percentage on front tire slip angle can be irritating compared to medium and high speed corners. In very tight corners, you must ultimately have a considerably amount of Ackermann if you want to maintain a positiv slip angle on the inside wheel.

By the way.. I never saw an FSAE car beeing able to steer as much as 45° on the inside wheel. Do you design your steering system for a 3m radius turn like this?? My last car had about 3.6 m min. turn radius I guess. My thoughts on this: Isn't that tight turn mainly about rotation!? Yaw angle, yaw rate, yaw acceleration! Yes, you name it: Yaw Moment! How important is lateral acceleration in this? And lateral forces? How can longitudinal forces contribute? Or how can even the absence of lateral forces help to turn the car around the yaw axis!?
How often do you find such tight turns on a competition? Mostly (in Europe) it's a turn in the autoX at the end of a slalom to re-entry the slalom, isn't it? I know one fast way for this turn without steering too much (search for video of Stuttgart in AutoX UK 20XX for example).. I believe there is a reason why they do it in Rally.. maybe because it's much more fun! http://fsae.com/groupee_common/emoticons/icon_wink.gif

But let's stay serious.. here's one way to design the "ideal" outside/inside steering ratio vs. ackermann steer angle relationship. I'm not saying that it is 100% correct and super accurate, so at this point I would like to refer to Claude's saying: "make it useful before you make it complicated" ..I guess I never got to the point of complicated! http://fsae.com/groupee_common/emoticons/icon_biggrin.gif
But it should be something to start with..

I've done a simple 2D sketch in a CAD software of a four wheel vehicle (top view) for a turn situation. I prefer to start with the SkidPad radius as it seems to me that it is the most relevant situation for the steering geometry of a FSAE car. In tight radius steady state cornering you might need as much front axle grip as you can get (in tight turns a torque sensitiv limited slip differential will most likely cause significant understeering without the proper adjustment of suspension and weight transfer distribution..remember it's also and mainly about Fx and resulting yaw moments.. never mind a spool..).

Now that I have made a sketch of a vehicle with 1650mm wheelbase, 1250mm front track, 1200mm rear track & 48:52 weight distribution and draw all the necessary lines etc.,
I can start analysing the things going on! First information I looked up is: a 6m turn in diameter will require about 25 deg outside wheel angle and 36 deg inside wheel angle according to 100% ackermann!

If we want to see the real deal, we need rear tire slip angles. For the sake of simplicity I look up the slip angle for peak lateral force at the rear outside tire. A look at my tire model for the condition 1280N load and -1.5 deg camber says 5.5 deg (of course this is lab data and I second Claude's thoughts on this point - but we need to assume that as reasonable as we can).

Now for an instant turn radius of 9m we have following "boundary conditions":
Body Slip Angle: 0.84 deg (front end of car pointing into the corner)
Rear Inside Tire Slip Angle (no rear toe out/in): 6.25 deg

My front "neutral" steering angles (!without! any slip angle) are:
4.16 deg outside wheel, 4.76 deg inside wheel! We have a delta of 0.6deg!

At this point & for this exact steering situation I can already say that if I apply this delta of 0.6 deg to my steering system, I will have the same slip angle at both front tires. Consequently, with parallel steering my inside tire is going to have 0.6 deg less slip angle than the outside! Well isn't that all the information I am going to need!???? I have to know the geometry of the car, the slip angle at the rear axle and the turn radius! Than I will have to decide how much delta slip angle I want to have between the inside and outside front tires and last but not least I'm going to add the individual slip angles to the "neutral" steering angles at the front. From that I calculate my outside/inside steering ratio for given amount of steering input.

For our SkidPad radius the calculation would proceed as follows:

Asking the tire model I find that my optimum slip angle for the outside front tire is about 5deg. For the inside tire it is also 5deg! Than I add this angles to my "neutral steering" angles and end up with an inside steering angle of: 9.76deg and an outside steering angle of 9.16deg. This is an outside/inside steering ratio of 1.0655.

Now to compare this to ackermann, we need the ackermann angles for this amount of steering. I assume that the outer wheel is absolutly dominant and stays at 5deg slip angle and thus 9.16deg steering angle: the inside steering angle according to 100% ackermann is: 10.51 deg. The 100% Ackermann steering ratio is 1.147!

So in this exact case, 100% Ackermann will produce an inside tire slip angle of 5.75deg! That's much more than 5 deg! So I want much less than 100% Ackermann!
With parallel steering the inside slip angle decreases to 4.4 deg. Hence, the geometry that I run is somewhere in the middle between these two! (Don't want to calculate the exact value right now). If I would like to run the inside tire with less than 4.4 deg slip angle, I would actually run reverse-Ackermann!
This Ackermann percentage will change for different turn radii and different steer angles!

If we repeat this for different turn radii we will be able to make a plot of the "ideal" outside/inside steering ratio in dependance of turn radius or more sensible, the ackermann steer angle (see Def. from Doug page1). Of course you could also consider different tire slip angle delta's for different turn radii! This "ideal" relationship would be the characteristic you want to design your steering system to. The question is how much does that "want to have curve" derivate from the possible real world steering configurations which are identified by the Ackermann percentage.. and which Ackermann percentage is the best to choose. One that suit very tight turns or one that suits wider turns!? To favor the SkidPad Performance for example, I would choose an Ackermann percentage that matches the ideal curve best in the range of SkidPad Steer angles.

You can do this also for different rear axle slip angles to get a feeling how this influences your inside vs. outside steering ratio! Or try static toe settings or whatever. This is of course a very simple approach as you basically don't check for anything - e.g. no equilibrium of forces & moments and so on.. but this would end up in a messy iteration anyhow and will be as good as your tire-data's correlation to real road surfaces etc.

Of course it would be nice to plot the "ideal" outside/inside steering ratio and the Ackermann percentage outside/inside steering ratios. And of course add your final characteristic and bring all this stuff to design judging. This way you show the whole picture without any confusion! And I'm talking from experience as I messed up in Design Judging with Claude at FSG2010. We had quite some missunderstandings talking about Ackermann as I didn't had such a nice graph back in those days and struggled to explain my thoughts on Ackermann.

Anyhow, in the end the major questions still remain: is a large slip angle for the inside wheel beneficial or not!? Can it improve tire temperature? Does it effect tire wear and hence performance? Does it increase tire drag & increase yaw moment? Does the increased jacking force effect the handling? And of course "by how much" http://fsae.com/groupee_common/emoticons/icon_smile.gif? This list goes on and on and will be different for different track characteristics! There are so many interacting factors that there seems to be only one easy and accurate way to set-up the steering geometry: by TESTING!
But in the end you should understand why it works.

Regards

[BillCobb]

A question on Ackermann steer.
Not answered without a great fear.
A cause for concern,
The front tires will burn.
You forgot about those in the rear.
(Just what will THEY say about this ??? )

Go check your architecture boys and girls. You have a rear drive, rear wgt biased vehicle which inherently already has more front grip potential than the rear and you want to 'optimize' i.e. 'maximize' (increase) your front side bite ? Dr. House thinks there's a problem here with line of reasoning. Dr. Cutty thinks a brain scan might help, Dr Chase thinks its end-around-me triosis and the ducklings are totally confused. Dr. Chassis Sim will have mis-diagnose the patient because he's neglected the Mz's major contribution to the rigid body mechanics. Time to put your thinking caps back on (visor forward please). We're all trying to look like professionals here ...

[Charles Kaneb]

Bill,

Excess front grip and Mz overloading the rear tires might be a problem at steady state, but on turn-in when you need a whole bunch of Mz to get some I*alpha to make the damn thing point in a different direction, it's something you aim for rather than worrying about.

[EPMPaul]

About bill s comments, i ve run into a similar provlem during simulation basically anti ackerman helps front grip too much... the solution ehich will move things around the most will probably be some rear bump steer... although that has some risks in other situations.. as for actually chosing an ackermn number( or rather relative evolution of inside and outside steer ange) you re probably better off being a little more to down and look at overall laptime vs ackerman then do a checkup on the stability side... while milliken moment diagram is extremly powerful, it gets really long to sweep the whole design space of multiple corner radii. Not only that but it somewhat detaches you from the end game ie going fast around a fsae specific track. As was said earlier this stuff is radius dependant and while skidpad couldbe a decent place to start when u look at the points you get for it s it s a bit of a fart in the hurricane. You re probably better off trying to be decent in autocross and endurance.... finally a word about roll centers.and load transfer in general... once youset weight % and tires you re gonna have a hard time changing much with those so building some adjustability in to your slip angle modifiers is probably your best bet in case you get it wrong... justmoving your driver is going to change a lot weight distribution wise.. and finally a good comprehensive reference for all these top level choices is a paper by a guy from the u of t called vincenzo libertucci... i got most of my funy ideas about lapsim in that paper...

As for how peaky tires are i d take a hard look at the data from the contine tals... as i recall a degree did a fairbit to fy

[Dettle]

@ BillCobb:

I totally agree. But let me tell you about one compromise you will run into when you have to run a steady state cornering maneuver with a 9 m turning radius (aka skid pad):

Many teams are runing limited slip / torque biasing differentials! If we take a look at the yaw moments generated by the longitudinal tire forces we will have the following situation:

1. A very large drag component on the front outer wheel!
2. A comparably very small drag component on the front inner wheel!
3. A very small drive force on the rear outer wheel!
4. A very large drive force on the rear inner wheel!

This is pretty much amplified by the very tight turning radius. So our major concern in the Skid Pad Event is to reduce (or counteract) the "understeering" yaw moment created by mainly the front outer tire drag and the limiting slip action of the differential! I will not adress the Mz's of the tire's for simplicity as I guess that they have less influence compared to the above. And this yaw moment can be huge! In fact it is so huge that the lateral force capability of the front axle is far away from being sufficient.

To give you some feeling:
Our car (with the endurance setup) will use appr. 300 to 500N of the front axle lateral force only to compensate the "understeering" yaw moment by the longitudinal tire forces! This holds true for more and less rear weight biased cars.

There are many different ways to handle this. But one measure I would at least think about is increasing the front lateral grip by as much as possible and hence adress ackermann!

I admit that there is one reasonable and obvious measure to handle the differentials negativ influence in tight steady state cornering (even though I noticed many teams don't do it).
One hint: It will give you one more agument for a driver adjustable anti roll bar as you will have to do some serious fine tuning for different road surfaces (especially Wet-Pad in FSG).

This of course adresses only car's with limited slip differentials. But still front outer tire drag is of concern! If not compensated with drive torque on the rear axle it has to be compensated by front lateral forces or maybe with front inner tire drag (which might be sufficiently increased with more slip angle and hence more ackermann!?)!

Regards

[Dettle]

As for how peaky tires are i d take a hard look at the data from the contine tals... as i recall a degree did a fairbit to fy

Yes it is a good example. But even there you will see that at low loads there is not much of a peak.
The Continentals are a good example to adress reasonable interpretation of tire data too. At high loads and high slip angles the tire began to chatter which definitely influenced the strong reduction of Fy after the peak. But still they are radials so it is a characteristic for them to have a pretty early and clear peak in Fy, making them efficient in terms of slip angle drag, wear rate and permitting lower heat generation (both from slip and from internal friction), otherwise maybe making it more challenging to exploit the maximum lateral forces (for the driver as well as for the suspension designer). Also, in general the lower the stress and temperature the less peaky the tire will be, so it is possible (or likely) that the Fy vs. SA curve is a totally different in real world (at least after the linear range, but even cornering stiffness will be slightly influenced by temperature etc.).
That said a tire like the continental will be most likely much more stressed running the TTC test than for example a bias ply which peaks at 9deg slip angle.

Regards

[Z]

The perennial Ackermann debate resurfaces. This subject is a perfect example of why this forum needs a drawing facility. For example:

What is meant by "tyre drag" above? Is this the tyre's rearward component of force in the wheel's coordinate frame (Fwheel.x)? Or is it the rearward component of the wheel's lateral force (= Fwheel.y, = axial force), as seen in the car's coordinate frame (so, Fcar.x)? These are hugely different forces. Fwheel.x can vary from Fcar.x by +/- ~45 degrees.

Confusing the above reference frames can lead to some interesting aberrations. Taking the dot product of the tyreprint's Fcar.y force (ie. the tyre's "lateral" force wrt the car), with the tyreprint's velocity vector wrt ground, gives positive power output during cornering! Yes, the tyre is GENERATING POWER, indeed pulling the car forward, even though the car has no front driveshafts. Yahooooo, ... perpetual motion at last!!!

Errrr, ... uummm, ... well ... except for those pesky other force components kinda not mentioned... Dammit!

And what is "Mz" above? Does this refer to the car as a whole, or just an individual tyre?

Ohhhh, for some nice, neat, FBDs ........ http://fsae.com/groupee_common/emoticons/icon_smile.gif
~~~~~~~~~~o0o~~~~~~~~~~


Originally posted by Hannes:
So in this exact case, 100% Ackermann will produce an inside tire slip angle of 5.75deg! That's much more than 5 deg [required for peak tyre Fy]! So I want much less than 100% Ackermann!
With parallel steering the inside slip angle decreases to 4.4 deg. Hence, the geometry that I run is somewhere in the middle between these two!
Getting back to Ackermann, imagine your team has narrowed the choice down to either 50% Ackermann, as suggested by Hannes above, or maybe 100% Ackermann. Using roughly the figures from Hannes post we can compare the two choices for different types of corners.

SKID-PAD or LARGE RADIUS CORNERS.
==================================
100% Ackermann.
----------------------
This requires less than 1 degree of front-wheel toe-out. By Hannes calcs this puts the front-inside-tyre about 0.75 degrees past its "peak" Fy.

But how much tyre Fy is lost? 50%? 10%? 1%? I guess less than 10% LOSS of inner-front-tyre cornering force. (If anyone can give more accurate figures, then PLEASE DO. http://fsae.com/groupee_common/emoticons/icon_smile.gif )

50% Ackermann.
---------------------
By Hannes argument this puts the inner-front-tyre right on its peak-Fy, so NO LOSS.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~

HAIRPIN or TIGHT RADIUS CORNERS.
================================
100% Ackermann.
-----------------------
By several earlier calculations (mine and Hannes) this requires about 10 to 15 degrees of front-wheel toe-out. Real steering linkages are unlikely to get the inner-front-tyre exactly on its peak, so let's say again less than 10% LOSS.

50% Ackermann
--------------------
The inner wheel now has 0 to MINUS 2.5 degrees slip-angle (draw the FBDs). So about 100% to 150% LOSS (!!!) of inner-front cornering force (ie. 150% loss = tyre pushing OUTWARDS with 50% of its peak force). Parallel steer is even worse.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~

Bottom Line for Steady-State Cornering.
=============================
If you "optimise" for Skid-Pad as above (= 50% Ack), then you're screwed on the tight corners.
~~~~~~~~~~~o0o~~~~~~~~~~~

More Important Bottom Line.
======================
There is very little "steady-state" in FSAE. Mostly it is transitioning between corners, like the slaloms. Fast transitions require large Mcar.z. (BTW, Mcar.z = 0 for steady-state cornering). Large Mcar.z is helped by having as much pro-Ackermann (100++%) as you can get (eg. see Hannes' post two up, or do the FBDs!).
~~~o0o~~~

Ah, but this would be soooo much easier to explain with a simple drawing facility.... http://fsae.com/groupee_common/emoticons/icon_smile.gif

Z