Kinematic curveball - tire rates

As you probably know, the balance of a car's wheel rates (front-to-rear and on diagonals in particular) play a big part in cornering feel and over/under-steer. Tire spring rate is a component of wheel rate... so any change in how tire rate is distributed has the potential to change the feel of the car.

Before I go any further, I'll share one of the tunes I'm rockin tonight as I get my vehicle dynamics on. Don't worry about the Friday night in... tomorrow night will likely have shenanigans afoot down in Columbus.

Anyway. Obviously tire rate is going to change with air inflation. Good way to make small tweaks. Tire rate also can change with camber - significantly. Typically it goes down the more you lean a tire. This in itself isn't anything earth shattering. It's public domain knowledge, and I remembering even hearing about it at a talk on tire testing & modeling at Colorado State right as I was finishing up undergrad. Never really stopped to think about the implications.

Let's assume we have some tire rate versus camber curve like below. Note: the numbers are totally arbitrary, just to serve as an example.

We'll consider some simple car with equal corner weights and identical installation rates (Ks). Kt denotes the tire rate, Kw the wheel rate.

Now we can give the car some arbitrary ride-camber rate and an arbitrary pitch input.

Fronts are going to gain negative camber, rears are going to move toward positive. Aka, fronts will soften and rears will get stiffer. How significant is a 1.4% change? That's up to you and your driver to decide. You'd be surprised what subtle changes you can notice - even playing with 0.5 - 1.0 psi increments on different corners of the car to play with tire rate.

Can also make up some arbitrary roll-camber rates and input. Let's say in this case, a car with more roll-camber change in the front than the rear (Mustang?).

In this case there's a very slight front/rear change, but a noticeable change in cross. Yeah, and you thought cross weight was only for oval racers. In this case, going up in cross during a left hand turn I believe tightens the car up mid corner - putting extra load on the RF and LR hurts front cornering capacity but helps drive-off.

Of course this is a really simple example with identical, linear tires on all corners. In reality it's a bit more involved. Opens a whole new can of worms in kinematic design - which wasn't exactly fuckin' easy to begin with! One option is to make use of rising rate motion ratios. Presumably if you knew enough about the tires you could use that to offset the change in tire rate and keep a relatively constant wheel rate.

Alternatively it may be beneficial to take advantage of some dynamic change in cross or lateral load transfer distribution - depending on how you want your balance and braking or power-on capacity to change at different parts of the corner. Trick stuff.

Of course none of this probably makes a hell of a lot of difference on FSAE teams that decide to throw heaps and heaps of spring rate in their car, in the misguided notion that it will increasingly make the thing more responsive. Brick the suspension and you don't have to worry much about kinematics, or low speed damper tuning for that matter.