rec.autos.simulators

Afaik, whenever the tire operating condition (slip angle, slip ratio, etc)
is changed, it takes some distance (the relaxation length) for the
resulting forces to transition from one condition to the next.  The
distance is usually assumed to be constant, regardless of speed...so the
response time is very short at high speeds.  If you think of the tire as a
stretchy thing, this makes more sense physically -- a change at the hub
will first change the shape of the tire before the forces get through to
the ground.

The relaxation length for slip angle (steer angle) is some fraction (could
be 1/2, more or less) of the tire circumference, depending on the tire
construction.  For slip ratio changes, the tire is a lot stiffer and I
noticed that in SAE 950311 they are using 1/10 of the distance that they
use for slip angle...but they admit that they have no data.

-- Doug

                Milliken Research Associates Inc.

  I'll be darned, it works.  Thanks, Ruud.  I didn't realize that it was the
tangent of the slip angle the paper referred to, rather than the slip angle
itself.  I'll play with the slip ratio part and try it in my model shortly.  

  Thanks again,

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

The power of the open source development model aptly demonstrated.

KFG

(phew, great fun discussing stuff with your idols ;) !)

That part about lengths is certainly true and should happen in a very
accurate model, but the close to 0 speed behaviour, according to the
very specific model Ruud and I are using, should cause oscillations in
the rotations of the wheels (when the dampening is close to zero), and
not really freeze the slip ratios when brakes are released. The model is
(pseudoequation):

d Slip/ dt = 1/L_relax (|u| Slip - V_slip) (1)

where |u| is the longitudinal component of velocity, V_slip is the
corresponding component ofslipping velocity and Slip the slip ratio or
Tan(slip angle).

However, I am using a slightly different model myself,

d Slip/ dt = 1/L_relax (|V| Slip - V_slip) (2),

where |V| is now the absolute value of the total velocity, and for the
lateral direction I do not deal with Tan(slip angle) but Sin(slip
angle). The difference between the two models is, that if the car is
sliding fully sideways (|u|=0), there is no relaxation going on in the
longitudinal direction in the case (1), and the slip ratios can increase
indefinitely, while in the other model it is, I believe, slightly better
behaved.

That's why I asked if the slip ratio 'freezing' is only present in the
sideways sliding case.

Just a comment; the above model is also good for stopping on a banked
surface, as the 'slip' variables will settle automatically and give
nonzero forces which will balance the car. The only 'problem' is, the
car will shift for about the order of magnitde of L_relax, which is a
bit more than what the tire flexibility should allow for. Nevertheless,
it's great fun to see your car jitter in yaw when stopping after a
sideways slide!

Thanks for the input on the lateral vs. longitudinal relaxation lengths,
it will sure come in handy!

-Gregor

As for Todd, and myself (and other interested people), yesterday I did
a test run on Monza, and I noticed something about the SAE950311

frequency).
I noticed that since eq. 20 is like:

deltaSR=(u-Rw)/B-(u/B)*SR

Where 'u' is positive and is the velocity of the wheel vs. track. Now
when 'u' gets big, the term (u/B)*SR will become larger and larger, no
matter how fast or slow the wheel itself is spinning.
So the system becomes unstable at large 'u'. I upped the frequency to
250Hz and things got better again. However, estimating I want to go as
far as 400km/h, this might be a deciding factor that I don't want in.

Check out SAE980243 as well, which uses a 3D spring tire method. It's
not pretty since it doesn't deal with aligning moment (force feedback)
and camber (Nascar anyone?), but it doesn't seem to have an unstable
factor like the 'u' from SAE950311, *at first glance*. Haven't
actually implemented the model.

It seems like for low speed, a slipvelocity model will do nicely. That
was the first attempt in Racer0.1, remember? ;-)
Problem is that you don't get slipAngle lags; that may be used from
SAE950311 still. As tan(SA) goes to infinity, unstable delta's are
less of a problem there (since the atan() catches up on that).
I never had low-speed problems in Racer0.1, which used a RARS method,
which is:

  F=-slipVel*friction

Add in here an added spring model on top to get the 'my car drives
back when I stop and then lift the brakes quickly' and it might do
nicely (note I did an extra: if(slipVelocity<1)F*=slipVelocity for the
road reaction force, something like that). I think I'll have a good
think about my own tire model (mixing lots of those out there)
somewhere soon. For now, I'm giving my brain some relaxation length,
eh, time, ;-) and am working on a first no-brainer AI car (grandpa
driving around the track, should be fun as target practice).

In conclusion, I think for SAE950311 you're better off not using the
slipRatio equations, because of the large 'u' problems (and damping).
For slip angle it shouldn't be that bad.

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Free car sim  : http://www.marketgraph.nl/gallery/racer/

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Free car sim  : http://www.marketgraph.nl/gallery/racer/

Ouch, make sure you read my other post about the SAE950311 slip ratio
model. I'm not too fond of it anymore (drives frequencies higher).

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Free car sim  : http://www.marketgraph.nl/gallery/racer/

(esp. at B=0.091, a large forward speed, u, makes for large d/dt(SR)
values, because of (u/B)*SR, so if your dt is too large, you get the
same problems as with braking tire forces etc etc).

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Free car sim  : http://www.marketgraph.nl/gallery/racer/