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