Chassis roll and yaw rate, lateral velocity

[GSpeedR]

I definitely share RideRate's viewpoints regarding mechanics. The engineering universe (non-relativistic and non-quantum) is force-causal with motion a resultant effect. Newton's 1st law applies not only for rigid bodies, but for continuous systems as well (fluid mechanics is pressure-causal and flow-resultant). The trick is keeping track of which forces are acting on which body, and then the resualtant motions make more sense. This can be difficult to accept for many race engineers because force is extremely difficult to measure, while motion is comparatively easier. Even when measuring "force" we are often actually measuring motion which has been calibrated, such as with a strain gauge. A good engineer will understand when using motion to determine forces is valid and when it is not...it becomes time for assumption or to modify the system.

Back to WilO's question, the relative phasing between roll and yaw are coupled and dependent on the vehicle system components (tires, spring, shocks, geos, etc). As mentioned by others, it is probably impossible to entirely determine their relationship without full knowledge of the system. If I was tasked with figuring out your question personally I would 1.) build a simulation, or 2.) test an instrumented vehicle. Both options might be out-of-reach for a club race budget. If you went to test route, it is imperative that you use controlled conditions. Develop a roll\yaw transfer function from a step-steer test; OEMs have been doing similar standard tests to determine response characteristics for many years.

[WilO]

GSpeedR,

Many thanks, as always, for your input.
I recognized while I was typing the original post that roll was a result of applied force, and not causal. However, while driving my own vehicles, and in observing the roll motions of other vehicles while cornering, it seems to me that roll may well be underdamped: that the sprung mass may oscillate slightly in roll.
I suspect it is the result of the bin full of rubber bushings that are stashed at every possible point in the suspension and drivetrain, as well as residual energy in the tire sidewall.
Initially I wondered what effect this (oscillation) might have on the yaw and lateral acceleration response of the vehicle, which lead me to the relative phasing question.
Thanks for the recommendations and insight too.
Wil

[GSpeedR]

Typically, severely roll-underdamped cars that are not under-damped in heave will have most roll stiffness contributed from swaybars. Your corner damper are still responsible for controlling roll movements, but your normalized roll stiffness will likely be higher than heave stiffness and pitch stiffness (assuming your track-widths are close-ish to your wheelbase). This is all for a conventional suspension. The presence of numerous bushings adds compliance as well as hysteretic damping, both of which may actually increase overall damping levels in roll; though it will cause the vehicle to roll more (larger magnitude). As others have said, tire alignment is probably the most significant handling effect from avg roll angle.

Roll oscillation can have a strong effect on tire load variation particularly on stiffly sprung vehicles, where vibration modes will transfer energy at frequency bands that the tires are sensitive to. If you suspension is locked (bumpstop, bottomed-spring/shock, ridiculous jacking) then you are very likely to be underdamped in all modes, and there's little you can do about it.

So both the roll angle and roll variation can affect vehicle handling. Since the yaw response and roll response of a vehicle occupy different degrees of freedom, it is possible for either to lead or lag at any frequency. One could argue that yaw is a more direct response to tire force, and roll is a direct result of the vehicle acceleration which must lag the tire force. It's all about the tire forces.

[gixxer_drew]

Also, its possible to have a car that doesnt roll. If you set the IC of each suspension high enough you will have a jacking force that equals the load transfer and the end result is no movement of the suspension. This is commonly seen as "putting the roll centre at the CG". It is never done. Ive never heard a decent explanation why though.

Tim

I hope you all don't mind old thread bumps? Since I am new here i'm reading through archived discussions and I realize this question went unanswered. I believe I may know the answer. Disregarding things like driver comfort or feel, tires don't like extremely rapid changes in loading. It's the same issue with very high amount of anti.

When you get into extreme aero stuff, this will diminish in relation to raw Z load in terms of the best tradeoff.

I'd like to ask someone like JT to explain "tire shock" better, my imagination is that you get shockwaves through the tire. I imagine hitting a water balloon fast and slow, same amount of work, but at different rates, one simply deforms it, the other makes a shockwave.

[Jersey Tom]

Nothing so dramatic as that... tires just take time to transition from one equilibrium to another. Not much time, but some.

The whole vehicle system has sensitivities to rapid ("shock") dynamic inputs, not just the tires. You could have a consumer vehicle with a trim of steady state understeer for example and spin it out (and/or roll it in the process!) with the right steer inputs, like a Scandinavian flick.

[dcasey]

I have a question about yaw stiffness. I have been doing some research on vehicle dynamics and came across an equation for yaw stiffness. I am using values from our FSAE car and I get a yaw stiffness (dM/dB) of approximately 0.95, but I'm not sure how to interpret that value. I'm assuming a positive yaw stiffness has characteristics of very responsive turn-in characteristics with less steady state straight stability, and the opposite is true for (-) values.

[Greg Locock]

So, what's M, B and what are your units?

Guessing p353 in Dixon, M is mz, and B is beta, the body slip angle. So it is the restoring couple on the car, if it is understeer. It's a linear range bicycle model property. If positive the car is unstable, if negative the car is stable. It's not a very interesting number in itself but leads on to the static margin, which is more interesting.