Let's take a gander at the following force / moment equivalence.
There is a force (Fy) and moment (Mz) generated by each tire during cornering. I can sum all of that up and act as if it's a total force, and total moment, acting at the CG. Then, if I want, I can take that force and moment and resolve it into two different forces acting at the front and rear axle. The effect should be apparent. Mz effectively "robs" the front axle of cornering power and will always generate an understeer moment. On "real" racecars the magnitude of extra Fy needed at the front can be quite significant. I haven't run the numbers on a F1000 or FSAE car yet, but on the latter it might be significant just based on the fact that a short wheelbase really amplifies the effect.
The other important thing to note is how Fy and Mz behave in the tire's linear range and at the limit. The picture I have here isn't the best.. I found it on the interwebs.. but it will have to suffice.
The above plot becomes VERY asymmetric with high camber, but for simplicity's sake...
In the linear range (within a couple degrees of slip angle) both Fy and Mz build up at a constant rate, and the two are related by the "pneumatic trail" of the tire (Mz/Fy). So as the driver is approaching a turn and beginning to "feel out" the entry the effect is a normal buildup of slight understeer. At the tire's peak grip where the footprint is transitioning to full slide, Fy saturates but Mz drops to zero. The picture doesn't really show it well but generally Mz will peak and start to fall off much earlier than Fy does.
My suspicion is that cars shod with tires with high aligning torque will feel good on entry and with initial steer angle, but then at the limit will transition (gradually or snap) to something much more free. Aggressive camber curves probably play into this as well as they have a big effect on peak and slide Mz.
Generally the wider the tire footprint is the less Mz you have to deal with. Wider rim widths on a given tire will tend to make the footprint wide, and higher pressures will tend to shorten the footprint up as well.
1 comment:
Hi! It was really nice reading your blog, a lot of interesting things here! (and definately a good source for learning)
I was just thinking about another way that you can quantify the effect of aligning torque on vehicle handling/dynamics.
Just think of what happens in real world. You can model this simply by a Fy on the wheel trailing the tyre centre by the distance of the penumatic trail. (as you said in the later part of your blog)
From TTC tyre data, the penumaitc trails(My/Fy) is about 3cm(ish). While normal FSAE cars have distance from the front axle to CG of about 80cm(ish). This reduces the anticlockwise moment on the car(by the front tyres) by about 3.75%. Simlilar argument goes to the rear so the clockwise moment on the car exterted by the rear tyres increase by 3.75%. The net effect in the yawing moment ont he car is the sum of the two.
How significant is that? hmmm, to be honest, I don't really know.
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