New way to set target roll stiffness

How the hell are you supposed to come up with a starting point for designed roll stiffness of a racecar? There are ballpark figures given in RCVD, which I'll admit we had used before (in FSAE) and even a couple years ago (wow! Here, and here) when I did some real preliminary estimates. Ballpark values are nice for reference and a sanity check, but you should know by now - that's not how we do legit engineering.

Let me tell you - this is how we do it:

(Not really, this song is awful)

What do we (relatively young, relatively inexperienced engineers) generally associate with changing roll stiffness? I'll admit - turn in responsiveness (overall stiffness) and balance (front to rear balance). I'm not ashamed to own up to it! It works - it's the right association - but not entirely for the right or really complete reason.

If you recall my earlier thoughts on top-level engineering, in my mind there's only a one step difference between a rigid body model with instantaneous load transfer, and an elastic sprung mass model with delayed load transfer. In effect, as you put stiffer and stiffer springs (and eventually hard links) in your suspension, you're just turning your car into a rigid vehicle - like a go-kart. As such, that rigid model is the upper bound on cornering or turn-in responsiveness (fine, maybe barring some roll-steer shit and what have you). That is not to say that it's instant, because there is still only a finite amount of yaw acceleration and there's definitely yaw inertia, but it is an upper bound.

As we add a suspension and start softening the car up, it's obviously going to add a degree of laziness to the rate of load transfer. In addition to having to wait for the car to start yawing and building lateral acceleration, we also then have to wait for the sprung mass to roll, engage the springs, and transfer load across each axle. Less roll stiffness (or more roll inertia) makes the car lazier and lazier to sharp steering inputs. In one of this SAE papers, Chuck Hallum seems to mention that he thinks (thought - RIP) a conventional tire model doesn't necessarily show this, but I disagree given the rudimentary sim outputs below. I've picked a certain parameter which indicates responsiveness, and have removed the actual numbers - do your own work.

As we reach "stupidly stiff" spring rates, we get close to bumping that response limit which ultimately is a function of yaw inertia and tire properties. Want to raise it? Get new tires, or more downforce. It is absolutely eye opening when you do back-to-back tire testing (FSAE kids take note). The math behind it isn't too difficult and is both in RCVD among the concepts of stability and control derivatives. Conceptually it's really not too difficult to grasp. You can keep adding spring to car and eventually there's a limit of what it does (likewise with chassis stiffness). The trick is finding that limit.

How does this tie back into design? By doing some up-front engineering I can determine what that upper response bound is, and how quickly I approach it. From there I can say I want a responsiveness level of 'X' by a variety of ways - even if I say I want the car to be within 10% of the rigid body response. Once that target level is established, the required roll stiffness falls out, and from there the appropriate levels of spring and/or bar. QED. Science: It works, bitches.