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Car Physics: Lateral force sign
Hello,
First I wanted to thank you all for your posts to this group. Reading through them all has helped me significantly in developing my simulator. Nevertheless, I have a question about the sign of the Pacejka lateral force. I'm using the Pacjeka model for the lateral forces on my tire, as per Brian Beckman's tutorial. The coefficients are from Genta's Ferrari, and I've checked my output against Ruud's Pacejka player. However, it seems to me that either the sign of the lateral force isn't correct, or I'm calculating the sign of the angles incorrectly. Since you've all used the Pacejka formula successfully, I'm guessing it's the latter, so perhaps you can tell me what I'm doing wrong. Let's assume we've got a tire rolling along, and a velocity vector that is pointing to the northeast from the contact patch, i.e. in the positive X and Y directions in the tire's SAE coordinate system. From my reading of RCVD, it would appear that this is a POSITIVE slip angle, which would result in a POSITIVE force, i.e. to the right, tending to move the tire along in the direction of the velocity vector and spinning the car to realign with the velocity vector (I know there's such a thing as a realigning torque that we feel through the steering wheel, but I'm pretty sure this isn't it). This doesn't make sense, because if we look at this situation as that of a car moving to the north-east and steering its wheels to the left, we should expect a force to the left on the tires, and thus a torque that would tend to turn the car to the left. Assuming I've got the coordinate systems right and the signs correct, I can think of one way to reconcile a positive slip angle and positive lateral force, and that's by going back to the contact patch. If we add up the car velocity vector and patch's velocity vector, we'll get a net contact patch velocity vector, which Beckman call's L. Now my intuition is that the direction of the force on the tire is opposite to the direction of this patch. My reasoning is that the contact patch itself (assuming no slippage) is stationary with respect to the ground, while it 'wants' to be moving in the direction of L. Therefore, there must be a force put on the tire from the ground opposite to L that keeps the patch stationary. Calculating the angle of this force, i.e. atan(L.y/L.x), would give a negative slip angle for the case where the tire has a positive slip ratio and the velocity vector of the car suddenly turns to the northeast. This would then result in negative Pacejka lateral force, as expected. What do you think? I'm wary of changing signs just to get things to work, so I thought I'd run it by you to get some idea of the reason behind a possible sign change. Thanks in advance, Sina |
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