rec.autos.simulators

I am having a bit of trouble with the pacejka tyre formula.  From the book I
am reading the value at which most Forward force is generated is around
0.25-0.5.  However when I run it through my formula I get the peak at a
value of 8.1 longitudnal slip (which is incredibly high I think).

The maximum value of the forward force is 7100N for a downward force (Fz) on
the wheel of 4.2kN.  This is a ratio of around 1.7, which according to the
book is reasonable.

Has anyone come across this before, perhaps Todd, Doug or Ruud?

Thanks for the help (I am tearing my hair out!)

Ashley

PS.  My email is spam-proofed, please remove ".THISREMOVE" to email me.

What are your pacejka constants?

Chris

The input value for peak force can be calculated
for this type of fit, but not in closed form (IIRC).
(This is one reason why my company doesn't use it.)

Once you know this value of the input, scale your
input to put the peak where you want it in your fit.

It sounds to me like you are attempting to adapt a
fit originally built for lateral data to a longitudinal use.
The lateral fit may have been in degrees rather than radians.
This is actually a good thing. because it made it obvious
that you have to rescale (renormalize) the data to your
new applications input range. If the lateral fit had been
in radians, the peak placement would have seemed
somewhat reasonable and you wouldn't have found
how to put it where you need/want it ;)

(One problem with using other peoples data is that
not everyone is careful enough to properly document
details such as the units of various coefficients in their fits.
This can make that work hard for other people to use.)

Happy New Year,
- Matt

--
Matthew V. Jessick      Motorsims, a division of Moto1

Vehicle Dynamics Engineer  (972)910-8866 Ext.125

Thanks for the reply.  Here are all the pacejka constants that I use: -

1.7990      \\a0
0.0         \\a1
1688.0      \\a2
4140.0      \\a3
6.026       \\a4
0.0         \\a5
-0.3589     \\a6
1.0         \\a7
0.0         \\a8
-0.006111   \\a9
-0.03224    \\a10
0.0         \\a111
0.0         \\a112
0.0         \\a12
0.0         \\a13

1.65        \\b0
0.0         \\b1
1688.0      \\b2
0.0         \\b3
229.0       \\b4
0.0         \\b5
0.0         \\b6
0.0         \\b7
-10.0       \\b8
0.0         \\b9
0.0         \\b10

2.0680      \\c0
-6.49       \\c1
-21.85      \\c2
0.416       \\c3
-21.31      \\c4
0.02942     \\c5
0.0         \\c6
-1.197      \\c7
5.228       \\c8
-14.84      \\c9
0.0         \\c10
0.0         \\c11
-0.0037360  \\c12
0.03891     \\c13
0.0         \\c14
0.0         \\c15
0.639       \\c16
1.693       \\c17

0.013     \\f0_for_rolling_resistance
0.0000065   \\K_for_rolling_resistance
0.315       \\Rolling_Radius
0.7     \\TyreInertia

These are from the high performance rear wheel drive car that is in the
appendix of G.Genta's book (Motor Vehicle Dynamics modelling and
simulation).

Thanks for the help
Ash

PS.  If you have a set of pacejka contants that you KNOW are right they
would be very appreciated :)

Thanks for the reply - my reply is below:-

It DOES form the right shape and it does have a reasonable maximum value
(7100N).  Unfortunately I dont have the RCVD book, although I do have
Giancarlo Gentas similar book (which is excellent btw).

I am not sure what "closed form" is, my maths is letting me down a bit :(

I have coefficients for both lateral and longitudnal pacejka formula - the
b0-bx set of coefficients (in my post above) are for longitudnal.  I dont
think its a case of trying to stick the lateral coefficents in a longitudnal
formula, UNLESS the data is wrong (which wouldnt be the first time!) :)

Yeah, its hard to test code when you dont know for sure that the data is
right :/

Thanks alot for the help, and Happy New Year

Ash

What I meant by "Closed Form" is that I don't believe you can develop
a straightforward equation for the slip ratio for the peak force as a
function of the coefficients. That is because of the inverse tangent
functions used in the magic tire formulas. You would need to plot the
functions (as you have done) or solve through iteration for the
coefficient values to generate a particular desired value for the slip ratio
to give the peak force.  (In other words, if you eventually want
your fits to have a particular peak position, it may be difficult to
figure out how to cause that to happen.)

You are using the Pacejka et.al. tire models in a much more developed
way than I ever have. I have only used single fits for particular conditions.
Presumably, all those coefficients of yours (as you know of course ;)
deal with how to systematically adjust the fits for various conditions
of load, etc.  I don't know how you can easily debug a problem with
either the coefficients or your implementation of the equations without
access to the experimental data the coefficient set is supposed to match.
Hopefully, the source which gave the coefficient set contains
sufficient plots to help you debug the system...

Now that I understand more of where you are, I don't have many
suggestions. You may be able to set several fixed values for normal
force, camber, etc., (whatever inputs the coefficients exist to vary
the curveswith) and then attempt to guess which of the coefficients
or equations have the bug.

Another idea is to plot the curves through the entire positive _and_
negative range of the slip ratio. That might indicate a sign problem.
(Should the positive plot properly but the negative doesn't, etc.
this might indicate a sign problem in a coefficient or equation.)

Given what you have said about the curves looking correct but
having a suspicious character for the longitudinal slip ratio
for peak force, perhaps the problem is in the coefficients/code
that handle the effect of normal force variations.
I've seen data that indicates that more normal force can tend to
stretch out the plots. (Move the peak toward higher slip ratios.)
A bug may be causing you to get too much effect from normal
force variations... or some other effect that tends to move the
peak toward higher slip ratios.

I'm doing some similar debugging with modelling that results in
a "friction circle" for combined slip cases this weekend ;),
so you have my sympathy!

Luck,
--
Matthew V. Jessick      Motorsims, a division of Moto1

Vehicle Dynamics Engineer  (972)910-8866 Ext.125

  I'll echo part of Matt Jessick's comment.  I've never seen the Pacejka's
magic formula with so many constants before.  Guess I've never seen the full
version.  Wish I could help you out on this one, but it sounds like you're
ahead of me in this area.  For the work I've been doing I'll probably be using
the nondimensional technique described in Milliken's & Milliken's "Race Car
Vehicle Dynamics", as it looks quite a bit simpler to work with.  For now, I've
been using simple approximations while developing my model.  Saving the tires
for last, I guess :0)

  BTW, how is that book you've got?  Is it worth the $98 on Amazon.Com?

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

Thanks for the detailed reply,

Now I see were you are coming from, more of a manufacturing angle than
simulation.  You were concerned that it wouldnt be possible to create new
tyres from results used in the pacejka formula.

I am not using ALL the coefficients (in my reply above) in ONE  pacejka
formula.  That list is the contents of my "tyre file".  It has coefficients
for the 3 different pacejka formulas for Longitudnal - Fx (all the b's),
Lateral - Fy (all the a's) and Alligning Moment -Mz (all the c's).

I am not concerned about combining the Fx and Fy values (as I know that a
value of Fx will reduce the maximum value of Fy (and vice-versa).  I will do
this once I get a reasonable slip->Force function working correctly.

I have tried what you suggested with -ve values of slip, but unfortunately
it is a fairly good shape and semetrical, I have posted to the
alt.binaries.simulators.autos newsgroup if you are interested, its only 5k.

I am using kN for the force i,e. its 4.2kN per tyre.  This is calculated
using the mass of the car and its centre of gravity, using a method in
G.Gentas book. (the mass of the car is 1480kg).

Good luck with the friction circle stuff, that will be my next task once I
get Fx and Fy working :)

Thanks again for the help - much appreciated!

Ash

Thanks for the reply :)

I am not using ALL the coefficients (in my reply above) in ONE  pacejka
formula.  That list is the contents of my "tyre file".  It has coefficients
for the 3 different pacejka formulas for Longitudnal - Fx (all the b's),
Lateral - Fy (all the a's) and Alligning Moment -Mz (all the c's).

It is only the set of "b" constants that I am concerned with in the current
longitudnal slip pacejka formula.  The rest were just added for completeness

The book is great, but I cannot compare to RCVD, because I didnt get it (Its
alot dearer over here than G.Genta's).  Chris recommended it to me, I think
because it is slightly more slanted towards simulation.  I would really like
to get RCVD aswell sometime, it is always nice to get 2 versions of the
story :)

My book has some non-dimensional stuff for combining Fx and Fy (i..e
acceleration is happening in both longitudnal and lateral directions at the
same time).  Not sure if it is the same as in RCVD.

Thanks for the help - much appreciated.

Ash

Yep, F1 tires seem to have values like that, but I guess the 1.7 drops
down quickly when not in optimal conditions though. (F1-2000 starts at
2.4 for some, but before the loading factor is included probably, see
a former thread some time ago).

Haven't been near too much physics lately, sorry, been putting most
energy into graphics, culling, ray-triangle intersection, sphere
visibilities and such. Very interesting. When I get a track working
(and rather, when I get a track that I can distribute), I'll probably
move back to car physics, since I find the Ferrari P4 I've put up now
doesn't act too real.

Seems like the formula you use takes so many coefficients that it's a
pain to debug. A little bit TOO much magic. But as the values seem
quite ok, you must be very near. It's just that one '-' instead of a
'+' can mean so much here.

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Car simulation: http://www.marketgraph.nl/gallery/racer/

...

Looks ok on sight, although in real life the negative side would be a
braking curve, right?

What force would that be?
Note that F1 cars are more in the range of 700-800kg. Also, not many
tires will reach a friction coefficient of 1.7 probably outside of F1
(and cart) racing. Or perhaps drag racers do.

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Car simulation: http://www.marketgraph.nl/gallery/racer/

  Ah!!  That makes much more sense now!  I wrote a curve editor that lets you
hit buttons to change some of the constants, but if I recall correctly, it only
had four or five in the equation.  Since most of the "b"s are 0, maybe the
leftovers are the same thing I was toying with.  It seems that one of the
constants was for maximum grip/friction coefficient (the 1.65 you listed?), one
defined the steepness of the initial slope (longitudinal stiffness, probably
the 1688 number?  I don't know!  lol)  While the other two controlled the
curvature between the initial upwards slope and the final low value, after the
peak.  The -10 sounds familiar here.  Actually, I think one of those two
numbers controlled the value it dropped to after the peak, the other ends up
working in conjunction with it to control how quickly it curves through the
peak and drops down.   If so, the 1688 or the 229 number might be screwy if
you're getting wierd results that don't match up right.  Could you post the
equation your book shows for the longitudinal "b" section?  Perhaps I can take
a look through my little editor and see if we can discover something.  If not,
maybe we'll all learn something about Pacejka's brilliant formula anyway :0)

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

Thanks everyone who helped!

The problem was that the longitudnal slipratio needs to be in percentage
(rather than a simple ratio).  Thanks Chris!

Now to solve the rest of the 132131919 problems :)

Thanks again folks
Ash

There are several papers (SAE and others) on the Pacejka curve fitting
techinque, but I don't have the references handy.  It has always required
large numbers of coefficients to describe a tire "completely" (over a range
of loads, etc), and this work continues, I believe mostly at Delft
University, Netherlands.  I've not tested the data-set in Genta's book,
but he has a web site at his university that you could check to see if
there have been any corrections.

The MRA-Radt Nondimensional technique only uses the Magic Formula curve fit
because it produces a good fit to the normalized test data.  The technique
could use a different formula if it was desired -- see Chap 14 in RCVD for
an introduction.

If you are referring to the Genta book, it's a lot cheaper in the USA
if you order it from your local book store, I got it from Barnes & Noble;
imo Amazon.com is often not the place to buy low-volume technical books.
At B & N you can order it in and look at it, before you buy.

While this may sound like a broken record (anyone remember what that
means?<grin>), our book is available direct from the publisher, and they
have a very reasonable shipping price for overseas if you pay by credit
card.  Last time I looked the link was:
 <http://www.sae.org/servlets/productDetail?PROD_TYP=BOOK&PROD_CD=R-146>

Happy New Year,

-- Doug

                Milliken Research Associates Inc.

  Great, thanks.  I'll try to find this site.

  I've looked at this and made a small program that lets you play with these
variables and see the results graphed at different loads and slip angles.
However, I can't seem to get these to match any of the other real tire data
shown in your book.  I can get any particular curve to match well, but the
resulting data for load variations on the same tire never matches up correctly.
 No load sensitivity in the equations?  However, I was pleased to see the peaks
of the force curves move along the slip angle direction with load changes,
along with seeing some change in cornering stiffness as load changes.
  Perhaps I am doing something wrong here, but I haven't been able to figure
out what it is yet.  

Thanks,

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