Wheelbase, stability and control derivatives, etc

There was a thread over on F1 Technical earlier discussing the merits of a short versus a long wheelbase (incidentally one of many parameters I haven't nailed down). When I was thinking of how to reply it dawned on me that I had little objective or rigorous data to back up what my initial thoughts were. As a start, some might think that long wheelbase implies stability, whereas short wheelbase implies being nimble.

As a generality, I'm not really convinced that's true, at least thinking about it to a degree in 'derivative notation.' Milliken goes over this idea around page 149 of RCVD. In a nutshell it wraps some basic tire and basic vehicle concepts together into a fairly powerful but simple way of describing vehicle dynamics.

All other things being equal, a longer wheelbase should imply higher 'static' directional stability; if you split the axles apart further it should require more torque to 'dislodge' the car from a particular attitude. It should feel planted and secure.. but that's not to mean unresponsive. At the same time as you increase the distance from the front axle to the CG you bump up the control moment derivative; the front tires have a larger moment arm with which to act about the CG, and create higher yaw moment for a given steer angle.

Given that most of my regulars here have FSAE experience, the following example may be enlightening. If there's a series that needs sharp, fast, predictable response almost all the time.. FSAE is it. If you were to test the Goodyear D2692 and D2696 back to back on identical cars, you'd find some big differences in how they drive. The '96 generally should have higher response rates (cornering stiffness) overall, while in the same construction, size, etc. As such, the static directional stability is higher. The car can feel more settled and planted. At the same time it is much more precise and responsive to steering inputs, since the front response is also up! The '92 by comparison, with lower control and stability derivatives, can feel both vague and lazy. (The '96 also has higher ultimate grip, comes in faster, and has unbelievably good wear. Pretty good improvement.)

On the other hand, while the control moment derivative increases linearly with "a" (distance from CG to front axle), if you think of that front axle as a point mass it's contribution to vehicle yaw inertia increases with a^2. In theory then you'd think a car with a short wheelbase would offer higher yaw acceleration capacity. My question is - how much yaw acceleration do you fuckin need? "More" of anything is not always better, except for beer and scallops. I may have to see if I can dig up some old DAQ to see just how much you need. If you already have 2x the acceleration potential that you could realistically need.. why add more when there may be benefit elsewhere?

I'll let you marinate on that.

New mini project

This will be a good one, if / when I get it to work. One of my better ideas recently.. as usual, spurred by a couple beers. If you want a refreshing, mentally inspirational taste that's as cold as the Rockies, reach for a frost-brewed Coors Light.

Anyway, the idea is.. it will work like OptimumK in reverse... and consequently much more practical for the design engineer.

More to follow if I put something together.