Thoughts on roll centers & geometric load transfer

Some discussion at F1 Technical got me thinking about this some more. Depending on who you talk to, there are a variety of opinions on how best to determine geometric weight transfer and jacking forces. Unfortunately none that I've seen back anything up with hard data.

How accurate are kinematic roll centers for use in WT calculation? Are individual instant centers better? How do these deviate from force-based approaches? How important is it to use a tire model to get lateral force split between the tires?

What I do know is the following: On an SPMM I can measure the effects of geometric load transfer.



The SPMM (Suspension Parameter Measuring Machine) is a kinematics & compliance rig. It is not very dynamic, like a 7-post shaker rig is. You can measure any number of things... your true, as-built kinematics... compliance rates... roll rates... damper friction... mechanical hysteresis in your suspension joints, etc. The machine clamps onto the sprung mass, and the tires sit on force pads. You can either move the sprung mass and measure corner forces (ride, roll, and pitch rates), or keep the sprung mass in place and apply tire forces and measure compliances.

In a compliance test where the sprung mass is fixed, if a lateral force is applied at the tire... the Fz changes without the suspension moving! I couldn't derive how this happens in a SLA suspension, much less something like a NASCAR rear suspension, but it happens nevertheless. If I do a lateral force compliance test with the forces in opposite directions, those force vectors intersect at the force-based roll center, which I'm thinking should be close to the kinematic roll center. I don't have data on that.

Anyway, we can use that knowledge to then figure out geometric force effects. Below is how I think it all shakes out.

The interesting items to note are that using RC's and IC's give the same result for non-rolling overturning moment, as do symmetric forces versus asymmetric (at least in the case of a symmetric suspension). What does change is the amount of jacking on the sprung mass, which admittedly will slightly change total lateral load transfer in general. In this example though, even if my axle rate is as low as 200 lbf/in, that +6 lbf jacking force amounts to... jack.

And even with regard to jacking or anti-jacking forces, who is to say they're bad! On a FSAE car, you're not very ride height sensitive. It may not be a big deal to have some jacking force. On a full aero car on a fairly open track (Lime Rock? Watkins?), maybe you want lots of anti-jacking mid corner to really squeeze the ride height down and get maximum downforce out of the underbody? Plus at a track like that, corner entry isn't very abrupt, so a more sluggish roll response may not matter.