Stephen Ferguson wrote:
> Depends on the level of realism. I should first say that I went to the
> opposite extreme to ymenard in my response, only because we constantly hear
> what a perfect simulation GPL is. Overall I am very impressed with GPL, but
> I imagine a lot will have to be added to it to start modeling NASCAR or
> CART. Many months ago the subject of aero came up, and some of us said it
> would be perfectly adequate to have a simple lookup-table based aero model
> that then applies the appropriate downforce and drag to the rigid connection
> point where the wings meet the chassis. Others (the purists perhaps, or the
> zealots) started huffing and puffing and claiming that nothing less than a
> full CFD analysis (running in real time, on a PC!) would be worthy of
> inclusion in the GPL model. Actually, you and I agree; I just found
> ymenard's response to the other fellow a little patronising.
Now I see your point more clearly. The people wanting a full CFD model
do not know what they are asking for. I agree with your approach to
aero, the full real time CFD model is far, far beyond the reach of the
top 1GHz home processors we use today, and the results of both
approaches would not be distinguished by us mere mortals, at least not
in the normal regimes which matter the most.
> Trust me, I have a decent understanding of it. I have dabbled with most of
> the commercial rigid body packages, although most of my work now is modeling
> the non-linear behaviour of human soft tissues. My point here was mostly
> anecdotal, and based on observations of others (Richard Clegg perhaps) that
> strange things start to happen when the car spins too far, which should not
> happen with a properly functioning rigid body simulation. Of course you're
> right that such a model is the best way to tackle the complex behaviour of a
> car that is seriously out of shape. In the end, I think the conclusion was
> that some of the goofy behaviour was due to graphics slowdown caused by all
> that thick rubber smoke in the air. Again, just a little exaggeration on my
> part.
First of all, this is not a problem of the rigid body dynamics
situation, but with modelling the forces on the tyres. Second of all, I
don't think it is wrong at all.
I think that what most people complained about was the fact that of you
went into a corner, developed a yaw and then tried to correct it by
dialing in some opposite lock, the spin would start to develop further.
If this is not what was the issue, then the following explanation can be
skipped.
This is actually the correct behaviour and is in some sense simmilar to
the post-stall regime and aileron reversal with aeroplanes. It happens
when the front tires are way past their optimal slip angles, and two
effects contribute to it.
The first is the fact that while in the regime of small slip angles the
lateral force increases with the slip angle, but after the optimal slip
angle is reached (where the lateral force is the highest) the lateral
force starts slightly decreasing with slip angle. Once you overcook it
you are by default in this second regime. You need to decrease the force
on the fronts in order to stop the spin. If you decrease the steering
lock (and hence the slip angle), the grip on the fronts does not
initially decrease but actually increase, because you are in this
'reversal' regime. Only after you reached below the optimal slip angle
by dialing in further opposite lock and actually found yourself back in
the normal regime (where the lateral force increases with the slip
angle) does the opposite lock start doing it purpose of actually
decreasing the lateral force on the fronts. Sometimes, there is simply
not sufficient opposite lock possible, and even when there is, the
transition time the front tyres spend in the regime of increased lateral
force before reaching the normal regime can produce enough momenum
impulse and hence yaw rate that the recovery is impossible.
The second effect to consider is more complicated and may actually
contribute more. Let us assume that most of the cornering force comes
from the outside wheels (this is true for the cars in GPL which have a
relatively high ceter of gravity). In order to stop a spin we need to
produce a torque on the car that opposes the direction of the spin. Let
us also assume that the lateral force on the tyre does not depend too
much upon its orientation, which is also true at high slip (yaw) angles
for the tyres of the time. These are all plausible simplifications and
may be argued, but it is easiest to show the idea with them. Anyone who
has ever worked in science will know this kind of approach.
Let us assume a right hand turn. With no lock the situation looking from
above on the front wheels looks like this:
Picture 1:
_ _
| | F | |
| |----> | |
|_| |_| ^
\ / \
\ / \
\ / \
\ / \ velocity vector
O c.g.
Let us consider this a balanced situation, so that the torques produced
by all wheels (including rears) are 0 and the car maintains a slip
(towards the up-left direction) if no steering corrections are applied.
The force on the outside wheel is for the sake of simplicity considered
negligible. Consider now the case when the driver tries to recover by
dialing some opposite lock:
Picture 2 (okay, so the lines are not perpendicular, imagine them to be)
:
^
F /
/\ /
\ \/
\ \
\/
\
\
\
O c.g.
As the force becomes closer to perpendicular to the vector between the
center of gravity (c.g.) while the magnitude of the force stays roughly
the same, the torque actually increases so the net torque of all tyres
is not 0 anymore but actually contributes to the direction of the spin.
Only if the magnitude of the force diminishes enough to cancel this
effect (the tyre gets back into the normal slip angle regime) does the
opposite lock help, otherwise it can actually cause harm and you would
be better of dialing in some further lock INTO the spin.
> But I think alot of these parameters are indeed fudge factors, depending on
> the level that they have gone with their aero and tire model, specifically.
> Getting the basic rigid body physics right (so the car rotates if you blip
> the throttle in mid-air) is pretty easy. Making a decent aero and tire
> model is much more difficult, because these are non-linear phenomena, and
> there are no "perfect" mathematical relationships to govern them. Aero and
> tire behaviour will always contain a certain amount of empirical data, and
> the flow over a more modern car shape (especially F1) is much more complex
> to simulate than the flow over, say, a 1968 F1 car with rudimentary wings.
> Likewise, the transitional behaviour of a modern slick is a much more
> problem to model than the older tires. I equate the addition of empirical
> data with adding a fudge factor. As soon as you have to add some sort of
> rule based input, then you are "tuning" your simulation to produce something
> resembling the real bahaviour, rather than relying solely on well-defined
> mathematical relationships, such as the more basic rigid body motions of the
> chassis, suspension, engine rotating mass etc. The aero model, for example,
> might be defined by a set of drag and lift equations, but at the end of the
> day it will need a lookup table for lift and drag coefficients based on
> angle of attack and yaw at the least. Temperature? Humidity? Traffic?
> More "fudge factors".
A physics model by any other name would still be a physics model. When
doing physics you always have to have in mind that what you are doing is
just an approximation, it can never be totally exact. The boundary
between exact and approximation can be hard to determine sometimes.
But there is a difference between fudging it and approximating
something. Approximating means deviating from reality for the sake of
simplicity, but at the same time knowing in what ways you are deviating
and therefore when the deviations will be noticable. Fudging it means
making something work without knowing how. There is a huge difference in
both approaches.
Tyre and aero model always involve a bit of fudging, true. But there are
a few properites that these models have to obbey so that they still at
least do not contradict reality, the main one being that the energy can
only be lost by the forces produced if no power is applied.
-Gregor
