Subj: Re: Missing r.a.s. post
Date: 5/24/00 8:14:46 AM US Mountain Standard Time
From: JTW62074
To: kevin...@gateway.net
Kevin,
I apologize for over reacting to your initial response to my post. I do
appreciate your input. So you understand where I'm at, here's how my model
basically works at this point:
----
* The car is one solid mass, completely unsprung.
1. The slip angles (all four tires are done seperately) are calculated based
on the positions of the wheels in relation to the center of gravity, the
vehicle's x and y velocity, rotational velocity, and steering angles.
2. When these slip angles are found, the cf is computed from a simple
equation as an approximation. The equation gives a peak cf of 1.2 in the 5-9
degree slip angle area, similar to what a Nascar tire test showed. I realize
that the cf changes with vertical load, camber, tire pressure, temperature,
etc., at all of these slip angles, but I was keeping it simple to get the
basics down and see if my approach would work as anticipated. Either way, this
variable is the only part of the model that needs to be updated to allow these
other factors to be taken into account.
3. There is no suspension model yet, so the static weight on each tire,
plus any fore/aft weight transfer and front/rear wing downforce respectively,
is multiplied by this cf to get the lateral force. Lateral weight transfer is
not included, as there is no cf variance with vertical load in this model yet.
Since the weight transfer happens almost instantly in this model, it drives
like a car with the chassis bolted directly to the wheels and with super hard
tires (wheel rate is infinite here).
4. These lateral forces are then broken into x/y and rotational components
and added to wind resistance to change the x/y and rotational velocities and
postions of the car.
5. Loop back to 1, calculate again for the next .005 second or whatever
----
That's basically it. As you may see here, slip angles are determined by the
model from the motion of the car, rather than the other way around (your
explanation of the arcs a vehicle will follow is the kind of info I needed BTW,
thank you, Kevin). In step 2, throttle and brakes are used to produce a
longitudinal force for each tire seperately. Your approach was one of two I
had tested and it works perfectly, as far as I can tell. It follows the paths
you described when changing longitudinal forces, and all other things happen as
you and Doug Milliken have described so far.
Step 2 also had to limit the lateral force produced by each tire. My "tire
model problem" was in how to do this correctly. I thought of two methods,
yours was one of them.
**Method 1-Your way**- Using your method, the total available force (in any
direction) at each tire is calculated, based on their maximum cf and total
vertical force on each tire. Then, based on step 2 above, the lateral force at
the tire is calculated (slip angle's cf times vertical force). The lateral and
longitudinal forces are run through the Pythagorean Theorem to limit the
lateral force if necessary, so the vector sum of the two forces will not exceed
the total traction force available (as you also described).
So, in essence, with this lateral force limiting method, a very small slip
angle of 2 degrees producing 200 lbs of lateral force will keep producing 200
lbs of lateral force after the longitudinal force changes (unless it's enough
to exceed the total traction available at that instant, in which case the
lateral force gets limited, and the fun power slides begin). As you said, the
car continues to follow the same arc when the longitudinal force is increased
(as long as we stay inside the total traction available). Slip angle and
everything else will change along with it as the vehicle's speed, weight
transfer, etc., changes. This happens automatically through the other steps
and is why I wanted to isolate the basic tire behavior from these factors to
see if the approach was basically correct.
The method just described produces the results you spoke of. There are no
problems with the car refusing to straighten out with throttle or brakes on,
regardless of whether the self-aligning torque model is implemented or not.
**Method 2**- The other lateral force limiting method, the one that would not
let the car straighten out with the throttle or brakes on even the minutest
amount, was similar. Slip angle of a tire was calculated the same way, the cf
was calculated, and the initial lateral force was calculated for the tire the
same way.
Now, I read that hitting the gas in some cars while cornering causes the car
to yaw a bit more quickly (of course, my '79 Firebird didn't do this, come to
think of it), and couldn't recall from How to Make Your Car Handle exactly
whether or not this happened when the tires were nowhere near their traction
limit.
You pointed out that *** "...if you could find your copy of How to Make Your
Car Handle you would find that it would say that if you add longitudinal load
it will reduce the force AVAILABLE to generate lateral load." ***
Then the effects on yaw rate due to throttle changes (getting on the gas to
get the back end out a little more) are due to exceeding the AVAILABLE
traction, and Method 2 is incorrect.
I thought I had read in this book that the rear slip angles changed whenever
the rear wheels were fed more torque (i.e., the lateral force was reduced by
ANY amount of longitudinal force, even though the tire wasn't near the traction
limit, therefore, the car yaws slightly more quickly for a moment, the slip
angle increases until the old lateral force returns, it stabalizes at this new
slip angle, the yaw rate slows back down a little, but the car is now following
a different arc after a brief wobble.) As you described, this is against the
very definition of traction limit force and must be incorrect. This also made
it impossible to straighten out the car if any throttle or brakes were applied
to the rear wheels.
I too, thought that using self-aligning torques would solve the problem, but
it did not. When all the tires produced a counter-clockwise torque in a right
hand corner, the forces they produced on the center of gravity of the car more
or less cancelled each other out (depending on the geometric details of the
chassis and cg location).
The left front tire pushed the cg forward and to the right, the front right
tire pushed the cg backwards and to the right, the rear right pushed it
backwards and to the left, and the rear left pushed it forwards and to the
left. It does change the handling of the car slightly (not enough for me to
tell from the in-car view), but had roughly zero effect on straightening the
vehicle, even with nearly zero grip tires on the front end, so this wasn't the
problem.
So I asked the initial GPL question, "What happens in the first instant when
you hit the gas in GPL when using the softest suspension settings?"
By using the softest suspension settings, the weight transfer would have very
little effect in the first couple of instants, as the springs would need to
compress and/or the dampers would need to rise in velocity in order to plant
more force on the tires (how the sprung weight's weight transfer really
happens, right?). Of course, the unsprung weight would transfer more quickly,
but believe I could still get an idea which lateral force limiting method GPL
was using, if either, from someone's answer.
If someone said the car "kind of yawed in a little, wobbled, then moved
outside the turn more", or "it turned in a little tighter at first, so I had
to back off the wheel for a split second until it set into the turn, then give
it more steering than before to keep my line", I would suspect GPL was using
something like the second method (the one that didn't let my car straighten
out). If they said the car immediately started pushing towards the outside of
the corner, I would suspect that weight transfer caused this, and since there
was no sudden increase in yaw rate, the first method (your method) was more
correct.
I received one email that said " ....[In GPL] it seems that adding gas before
nearing the traction limit simply pushes the car away from the corner without
changing it's attitude. Letting off on the gas, however, turns it in a little.
Of course, things change when you hit the traction limit."
This, in combination with my assumption that GPL cars can drive straight ahead
with some throttle or braking applied, unlike my model when using method 2,
tells me that your method (method 1), is more correct, just from reading this
description of GPL handling. What this email indicates to me is that weight
transfer off the front tires and onto the rear caused it to push away from the
corner. The attitude didn't change, so the rear slip angles probably didn't
get a sudden boost when a small amount of throttle was applied. If the emailer
had indicated a sudden wobble and subsequent push, I'd have second thoughts.
This answers my question, and method 1 (that follows yours and Doug Milliken's
descriptions of vehicle behavior) is now being used.
Cheers,
J. Todd Wasson
http://PerformanceSimulations.Com
