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Tire forces about CG

Tire forces about CG

Hello all, I need help with front/rear and inside/outside tire forces about the CG in a steady state turn.
If anyone can refer me to a plan-view drawing, that would be great. I(think I) know that the front wheels provide a destabilizing moment about the CG, while the rear tires give a stabilizing moment, as the lateral force is opposite in sense (about the CG). I'm having difficulty picturing the difference in lateral force moment arm from the front inside and outside tires. I read recently that the inside tire in a turn gives the moment INTO the turn, while the outside tire provides a stabilizing moment. Sorry, but I'm too thick to see how this works.

Thanks for any help!!

RE: Tire forces about CG

Just curious, where on Earth did you read that (or was it not on Earth) ??

An answer gets you an answer.

RE: Tire forces about CG

"I read recently that the inside tire in a turn gives the moment INTO the turn, while the outside tire provides a stabilizing moment. Sorry, but I'm too thick to see how this works."
Stop thinking 'laterally'?


RE: Tire forces about CG

The post I read is this:

"The yaw moment contribution from steer can be quite significant in situations where the turn radius is of a similar order to the vehicle track-width and wheelbase (think autocross car). There are two distinct geometric effects (ignore the tire data for a moment):

1.) Geometrically, the yaw moment arm between a tire's resultant force (lateral force, drag, drive) and the vehicle CG is not equal once an axle is steered. The outside front moment arm is at a maximum with zero steering angle and it reduces to zero when the force vector points to the CG. The inside front will change with steering depending on the ratio of 1/2 track to 1/2 wheelbase (hence it will increase slightly for nearly all vehicles but never go to zero).

2.) As mentioned by olefud, the longitudinal component (in chassis coords) of the resultant tire force will provide yaw moments about the CG. The inside tire provides a moment into the turn and the outside front tire provides a stabilizing moment. This effect is distinct from slip angle drag, it is purely geometric caused by a wheel steered relative to the chassis. In tight turns, steer is much larger than slip angle. Ackermann will change the proportion of steer and thus the proportion of this longitudinal component.

So from these (simple) effects, we can generate very different yaw moments simply by our proportion of inside/outside wheel steering; the effects become huge in very tight turns. Olefud is certainly correct that the tire slip angles are dependent upon the overall dynamic state of the vehicle. With this in mind it is important to set steering/Ackermann such that it is possible for each tire to achieve its optimal slip is certainly possible to have a steering geometry that makes this impossible. It may be necessary to use less or more anti-ackermann than what the tire data suggests."

It's from the forum, a discussion of Ackermann:
Norm, you're correct, it must be the longitudinal component that creates the yaw moments...If anyone has a clear explanation, or at least willing to drop a clue. I think I'm just over-complicating this.

RE: Tire forces about CG

Ahhhh I think I got it. Really simple: I'm visualizing the longitudinal component of the left and right front wheels negotiating a right-hand turn and their relation to the CG. I can see now where the outside wheel long. component would have an anti-clockwise moment about the CG, while the inside (right) front wheel would be clockwise.
I'll have to wait to sketch it out at different road-wheel steer angles.

RE: Tire forces about CG

The things that you have read are pretty far removed from the actual set of circumstances involve in vehicle directional control. Looks great (impresive) on paper to the self congratulatory crowd, but not acceptable to those who are familiar with simulation writing and usage, and measurement results from full vehicle tests, AND the comparison of the two methodologies.

Whether your vehicle has two or four or 18 wheels, it is subject to lateral forces induced by a steered axle or some other external force. If this force is not applied at the CG, there are other forces and moments induced. The sum of the axle forces induces a sideslip acceleration while the difference induces a yaw acceleration. The resultant of sideslipping and yawing produces the net measurable lateral acceleration. Since a vehicle speed is required for any of this to happen, the ratio of yaw component to sideslip component changes as you go faster. Those familiar with the vehicle dynamics can assure you that the longitudinal components of tire induced forces (from all wheels: inside, outside, middle, top bottom or trailered are relatively small and do not count for very much until the limit of control is approached. Even the sine component of the steered tire is relatively small simply because the steer angles are so little (lt 5 ~ 6 degrees).

Then there are the self-aligning moments. Because the tires react to slip angle inducements, restoring moments are induced on each corner of the vehicle (not just the steered axle), and these affect the transient and steady state performance (trajectory) of your vehicle. I won't mention the effects these force and moments have on net axle slip angles, but they can NOT be overlooked.

If your vehicle has a finite width and a cg higher than the road plane, load transfer occurs causing the inside and outside tires to produce different sets of forces and moments. In most cases, the inside and outside tires are mounted on the same axle and have symmetric attachements, so its safe to assume they also run at the same slip angle. A few critical thinkers will add or subtract the static alignments as slip modifiers, but its almost always no BFD to the vehicle. At the limit, the tires no longer listen to steer or slip change commands, only to camber or vertical load changes. The notion that all wheels on an axle run at completely different slip angles is nearly absurd.

This is all very easy to simulate on a computer with a program such as Matlab. On the FSAE Tire forum, I have posted a simple but educational vehicle model with tire test data lookup, load transfer and a step steer input command. A large population of tires for this series was measured at Calspan/TIRF and is available to purchase. Adding the longitudinal tire forces due to slip and camber would be no big deal. It will create a speed change deceleration which you will need to acknowledge with a tractive force addition (I.E. powertrain) if you want to run constant speed tests (step, constant steer, constant radius, etc). The power loss vectors are not all that large compared to the bigger picture.

So there you have it. VD 101.

RE: Tire forces about CG

Cibachrome, Thanks a ton!! Great of you to write that up. Next time I ask a question, it will be better, promise.

RE: Tire forces about CG

Note: I'm the author of the F1-Technical post, but my normal username (GSpeedR) has registration issues.

Cibachrome: I think that you've (inadvertently) taken the post out of context, and completely ignored/missed the first sentence: "The yaw moment contribution from steer can be quite significant in situations where the turn radius is of a similar order to the vehicle track-width and wheelbase (think autocross car)." That post was in response to a general question about Ackermann steering geometry and produced yaw moments ('pointing couples') about the CG. Perhaps giving a qualitative reply on a forum makes me a member of the self-congratulatory crowd, but I would then claim that your posts here confirm your membership as well. :) Anyway, I'm very familiar with both simulation writing and full-vehicle instrumented tests, so it seems that our professional experiences have led us to very different conclusions.

I hope you realize that a small autocross car (like an FSAE car) will require steering angles much larger than 5-6 degrees in tight turns, and in extreme cases as high as 30deg. Thus the sine components of these angles can certainly be significant, and result in relatively large longitudinal forces about the CG when resolved in vehicle coordinates. As for points #1 and #2 brought up in the F1-Tech post, both effects are easily seen from a plan-view free-body-diagram. Eric Zapletal (Racecar Engineering contributor) has published articles describing the effects in better detail than I can do here. Sure, the magnitudes are directly dependent upon steer magnitude, but I don't see why anyone would be so dismissive regarding the concept. Perhaps such details aren't necessary in a simple stability analysis, but they are present in a real vehicle and present in a properly setup mult-body model. Whether they are significant depends on the vehicle conditions, which I was careful to describe in the F1-Tech post.

RE: Tire forces about CG


I owe you a huge apology, I clearly failed to put your post into proper context. Hope you can forgive that, 'cuz your posts are always great, and written in a way that makes the topic easy to understand (which shows you really know what you're talking about). I take full responsibility.

RE: Tire forces about CG

ttx40, nobody owes me an apology. You asked a question, probably wanting to tap into the wealth of knowledge and experience of the members on this site. I think Cibachrome's answer is fine, but I felt that the context was missing and I wanted to clarify...he/she may still disagree anyway. Hopefully, I didn't come off as combative. I rarely post here, but I do lurk in some of the forums.


RE: Tire forces about CG

Interesting stuff. To be honest, I'm one of those who would have thought that tires on an axle would have somewhat different slip angles while cornering due to LLT. The fact that, at the limit the tire no longer 'listens' to slip or steer is not surprising I suppose. The fact that it does respond to camber and vertical load changes is though. Leads me to wonder what things modify slip angle (which to me is just the distortion of the tire carcass due to lateral force)?
Obviously slip angle is independent of steer angle, so vertical load and camber must be the big players (all other factors such as tire construction and pressure held constant).

RE: Tire forces about CG

One way to think about is that once that sheet of rubber is sliding across the road surface the precise orientation of the sheet of rubber makes little difference to the sliding force. It is more of an asymptote than a complete disregard for SA.


Greg Locock

New here? Try reading these, they might help FAQ731-376: Forum Policies

RE: Tire forces about CG

ttx40: In addition to Greg's example you can picture a Force-Slip Angle curve. At the force peak the force sensitivity to slip angle (slope of curve) necessarily drops to zero (definition of a peak), so the tire will not respond to small changes in steer. It may or may not be sensitive to camber, it depends on the tire and the conditions same things applies. However, a tire will respond to vertical up until silly amounts of vertical load are applied where the tire construction begins to fail.

It is certainly possible for tires across an axle to have different slip angles. Slip angle is defined as a relative angle between the wheel plane-ground intersection (wheel orientation vector) and the contact patch velocity vector. Because the tires are kinematically coupled by the chassis, the CP velocity vectors will be mostly controlled by the vehicle path. If there is a large discrepancy in steering between two tires (either from steering geometry, compliance, etc) then each tire's orientation vector will be different and their slip angles will be different. So this doesn't really matter for a nice, rigid, non-steering solid-axle, but certainly could for a front independent suspension (especially with asymmetry!).

RE: Tire forces about CG

RigTest, that was a huge help.

So in a rough summary of sorts;
The tire forces are a function of the loads supported by that corner of the car at any given instant. The force causes the tire carcass to distort, resulting in a slip angle. The slip angle at the tires gives rise to a body sideslip (Beta), determining the attitude of the car while cornering? (Note that this is stated as question, not fact).

I've just gotten a copy of Milliken's book, and along with it the companion Problems, Answers, and Experiments. I have to say, it is NOT an easy book by any means. And the workbook? Forget it. It's great stuff, but it's not a simple book, at least given my background. I have Gillespie's book as well, but that doesn't seem to deal with transient cornering as much. So all the help you guys have given me is great, really helping me make sense of this subject.

RE: Tire forces about CG

Of course ackerman, static toe, wheelbase/track/path radius also affect slip angles across an axle.

Incidentally I just looked at the most recent production tire I had tested, and the change in Fy/Fz for a -6 degree change in camber at high slip angles is around 0.03 , but the same amount of positive camber is twice as bad. I looked at one Fz only.


Greg Locock

New here? Try reading these, they might help FAQ731-376: Forum Policies

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