[Torcs-users] Wheel Slip Angle

[David S. <dsa...@te...>]

Dear Sirs:
                Wheel Slip Angle
Sine(slip angle) of a wheel is not a measure of slip.
Lateral slip = Sine(slip angle) * |Sine(slip angle)|
Here is why:

Imagine pushing a wheelbarrow straight ahead at 0 degrees and
sqrt(0.75) meters/second from the origin. At the same time
another person pushes straight ahead at 90 degrees and 0.5 m/s
on the wheel axle.
What results is: The wheelbarrow moves at an angle of 30 degrees
at 1 meter per second with 0% wheel longitudinal slip, and
100% wheel side slip (lateral slip).
Now you can draw a diagram with the vector: 30 degrees, 1 m/s.
The vector x-component is sqrt(0.75) m/s. , x = 1m/s*cos(30 deg)
The vector y-component is 0.5 m/s.        , y = 1m/s*sin(30 deg)
The x-component slip is 0% (wheel rotates)
The y-component slip is 100% (wheel slides)
The wheel slip angle with respect to the vector is -30 degrees.

The vector (30 degrees, 1 m/s) represents the combined longitudinal
and lateral velocity, so what is the wheel slippage with respect to
this vector? Well, this vector sees a wheel rotating at sqrt(0.75) m/s
at a slip angle of -30 degrees. The wheel is off-angle from the vector.
The component of wheel speed that is in line with this vector
is: sqrt(0.75)m/s*cos(-30 deg) = 0.75 m/s. Thus, the wheel speed is
1m/s * cos^2(30degrees) and the ground speed is 1m/s.

Now to determine the longitudinal slip for the vector (slip angle = 0 degrees):
longitudinal slip = (1m/s - 1m/s*cos^2(slip angle)) / 1m/s = 1 - 0.75 = 0.25

Note that all of the slip is lateral slip applied to the wheel axle.
lateral slip = 1-cos^2(a) = sin^2(a) ::  sin^2(30 degrees) = 0.25

Lateral slip is positive or negative for left or right, and independent of
forward or reverse. Thus, lateral slip has the following formula:

lateral slip = sin(a) * abs(sin(a))

            An experiment on TORCS

change line 275 of:
https://sourceforge.net/p/torcs/code/ci/r1-3-1/tree/torcs/torcs/src/modules/simu/simuv2/wheel.cpp
from: sy = sin(sa);
to:   sy = sin(sa) * fabs(sin(sa));

Sincerely,
David Savinkoff