Car physics; Pacejka and friction coefficients
Ruud van Gaal
I'm trying to deal with sliding in my sim at this moment.
For skid sounds, it seems looking at slip angles and slip ratios
getting large are a nice way to go.
For sliding, I'm not too sure. I use Pacejka to get long/lat forces
based on slipRatio/Angle/normal force and camber (camber is still 0 at
the moment).
So I get an Fx (longitudinal) and Fy. For sliding, I should check if
the resultant force (Fx+Fy) doesn't exceed the maximum force of the
tire. ( |Fx+Fy|<=maxForce )
However, how do I extract a friction coefficient (or similar, the
maximum total tire force) for a given situation? Could the Pacejka
constants help here? I think so, since the peak of the Fx force for a
given set of Pacejka input parameters will be the maximum force that
the tire can generate. However, this means I would have to search for
the optimal slipRatio (which delivers the highest Fx), which delivers
the highest output.
Or perhaps, it's just D+Sv, because the formula is like D*sin(...)+Sv
(or was it Sh, haven't got the book at hand right now).
Second, an effect that I'm still missing is the car switching ends
when flooring the throttle from a standstill. Given a large wheel spin
velocity, at the rear, the car won't move forward quickly, because of
the reduced Fx force. However, since slipAngle is calculated as the
ratio of longitudinal and lateral wheel speed (wrt the road), the
slipAngle builds up as the car wants to drift left or right, I just
get a Pacejka Fy which stabilizes the car in yaw.
So, where do I go wrong? It seems that because of the large spinning
velocity the lateral friction coefficient becomes almost 0 (like with
a motor where you can let the rear wheel drift along the track,
keeping the front wheel locked on the tarmac).
Thanks for any ideas,
Ruud van Gaal, GPL Rank +53.25
Pencil art : http://www.marketgraph.nl/gallery/
Free car sim : http://www.marketgraph.nl/gallery/racer/
Gregor Veble
I do skid sounds by checking for the size of the slip vector (ratio and
angle combined), and slightly below the optimal value I turn the volume
up to full when past the optimum, and then also change the pitch when
the value of the slip vector increases.
About Pacejka, I have absolutely no experience with that, but it seems
to be you are using the lateral and longitudinal forces separately based
on slip angle and ratio. For illustration, as an approximation (which I
still use :) ) you can combine them in a slip vector, calculate the
force that corespods to the magnitude of this slip vector, and point it
in the opposite direction to it.
The (complete, if such a thing exists) Pacejka formula should do
something similar and enable you to plug in both the ratio and angle
values simultaneously and getting both the lateral and longitudinal
forces from that. The calculations should not be done independently for
both axes. You really don't need to perform any special sliding checks
if this is done correctly. This will also take care of the twitching
problem, by the way.
-Gregor
Ruud van Gaal
<gregor...@uni-mb.si> wrote:
>I do skid sounds by checking for the size of the slip vector (ratio and
>angle combined), and slightly below the optimal value I turn the volume
>up to full when past the optimum, and then also change the pitch when
>the value of the slip vector increases.
I wondered about that, if pitch increases. It seems though you only do
it slightly, couldn't hear much variation from a testrun with your
SimEngine. I now use the slipvector for lateral skid sounds, and the
slip ratio to detected skidding in the long. direction. Somehow I
think the two sounds sound different (because of other spring rates
long vs lat), but it will do for now.
>About Pacejka, I have absolutely no experience with that, but it seems
>to be you are using the lateral and longitudinal forces separately based
>on slip angle and ratio. For illustration, as an approximation (which I
>still use :) ) you can combine them in a slip vector, calculate the
>force that corespods to the magnitude of this slip vector, and point it
>in the opposite direction to it.
I used the slipvector in v0.1 (not to be funny, lol), and it worked
great for lowspeed; no low-speed instability whatsoever. Perhaps it's
something useful after all when doing lowspeed. :) Got the idea from
RARS, which targets more to robot simulation actually.
I can't really point it in the opposite direction, because I take the
resultant force vector as the sum of the lateral and longitudinal
force. I will try capping it (am now only reducing the lateral force
if the longitudinal force gets large, so this changes the direction of
the force, which doesn't feel right intuitively).
Pacejka indeed inputs: SR, SA, camber and Fz. From that you get Fx,
and Fy (and Mz) from 3 separate formulae. I don't have the book from
Genta here, so I can't check whether the lateral force looks at the
slip ratio. In my carsim, it doesn't seem to do so though. I'll check
it out when I get home. (first have to get v0.4.1 going tonight)
>The (complete, if such a thing exists) Pacejka formula should do
>something similar and enable you to plug in both the ratio and angle
>values simultaneously and getting both the lateral and longitudinal
>forces from that. The calculations should not be done independently for
>both axes. You really don't need to perform any special sliding checks
>if this is done correctly. This will also take care of the twitching
>problem, by the way.
You would think so, yes, but it doesn't seem to. Likewise, for wheel
locking, I have to interpolate the total force vector to move to
-slipVector as the locking becomes greater (SR nearing -1 or worse).
The twitching is almost gone by the way, and thanks for your replies!
I got it working in the end because of a stupid bug where I used the
suspension force on the wheel as a normal force, instead of taking the
REAL road force up (which is tireRate*(ySurface-yContactPath) in my
sim). Having fixed that, suddenly it all started working, although
with a damping coefficient of ~30, really magical values here. ;-)
I suspect Pacejka doesn't handle fast-spinning wheels correctly for
calculating Fy (lateral force). The tire will go stiff and the lateral
spring effect would reduce greatly, if I picture it. Perhaps that
should be reflected in the Pacejka constants (where at a certain point
you have BCD which is the cornerning stiffness; I use that in the
SAE950311 damping method, just like BCD for longitudinal stiffness).
I'll go read some more RCVD 'Simultaneous longitudinal and lateral
forces' to see what it says.
v0.4.1 btw displays lateral and longitudinal forces (and SA/SR for
each wheel) so it might be interesting to watch. I'll tweak my force
capping algorithm just a little more now.
Thanks,
Neil Everett
What you ideally need is the 'combined slip' Pacejka formula. This deals
with the interactions between long and lat slip. It is based on the
seperate formulae for 'pure' lat and 'pure' long slip, but then applies a
new additional calculation to give the 'combined slip' Fx and Fy. This is
what I use in my simulation work within my PhD. I have the documentation if
you're desperate.
Cheers,
Neil
ernesto fina
I'm also interested in the documentation you're talking about. Most of
all I'm
interested in Pacejka Coefficients for different kind of tires if you
have some.
I hope you can help me.
Best regards,
Ernesto Fina
Ruud van Gaal
<neil.e...@ntlworld.com> wrote:
>Ruud,
>
>What you ideally need is the 'combined slip' Pacejka formula. This deals
>with the interactions between long and lat slip. It is based on the
>seperate formulae for 'pure' lat and 'pure' long slip, but then applies a
>new additional calculation to give the 'combined slip' Fx and Fy. This is
>what I use in my simulation work within my PhD. I have the documentation if
>you're desperate.
Believe it, I'm desperate! :)
But really, I've bought an entire book for the Pacejka formula (G.
Genta's Modeling and Simulation), and it only contains the separate
formulae and an approach to combine them, but I'm having trouble with
the lateral force being allowed to keep big when the rears are
spinning.
Example (going the Genta route):
- I calculate Fx and Fy separately
- I use the elliptical approach to hold down Fy, this is done by:
Fy=Fy0*sqrt(1-(Fx/Fx0)^2)
Where:
- Fy is the lateral force we want to know
- Fy0 is the lateral force as calculated by Pacejka Fy=...
- Fx is the calculated long. force (Pacejka separate)
- Fx0 is the MAXIMUM long force (calculated from the Pacejka
separate formula as D+Sv)
- I stamp on the throttle, slipRatio goes up to say 2 or 3
- Fx at the rear becomes 1400, from a maximum (at optimal slip) of
2700 (at say, slipRatio=0.3).
- Fy is about 2000 (Pacejka Fy)
- Fy is reduced to not exceed a total force length of 2700. As Fx is
about half of it's maximum peak, the lateral force is allowed to grow
a lot.
Here's what I don't believe; when spinning, the method above keeps the
friction circle (or ellipse height/width, but let's stick to circles
for now) constant (because it takes Fx0 as the maximum force the tire
could ever generate). However, I known from doing donuts with GPL for
example, that when spinning the wheels, the friction coefficient goes
down considerably. So a car with spinning rear wheels and braked
fronts can be pushed even by someone and it will start rotating.
This is nowhere reflected in the calculations.
So the problem then becomes, how to calculate the maximum friction
coefficient, based not only on load and a generic track coefficient
(1.7 for example), but also on slip ratio? Or heat, although I don't
think that heat is the thing here that makes things slippery (at the
start).
Thanks for the help, Neil, I'd love to take a look at your simulation
work, and how you take on combined Pacejka.
Ruud van Gaal
wrote:
>Neil,
>
>I'm also interested in the documentation you're talking about. Most of
>all I'm
>interested in Pacejka Coefficients for different kind of tires if you
>have some.
It seems these coefficients are often copyrighted or something. Not
really good for what's called a standard. :)
But well, I'm have low-priority plans on a Pacejka editor where you
can tweak the constant and see what it does (and hopefully mimic known
curves).
Matthew V. Jessick
spins,
as is discussed in this thread. One source of a lateral dispersion
for some suspensions is asymetry in the rear tire normal forces
caused by the driving torque. The engine torque is converted to
driving torque (turned 90 degrees) at the wheels, and this
torque on the driveshaft is reacted laterally partly in the front
and part in the rear suspension.
To summarize: One rear tire sees a higher normal force than the other.
For a locked differential, with the tires both rotating at the same slip
ratio, it's easy to see that the tire with the larger normal force will
have a larger forward force and this difference in forward force
between the two rear tires creates a yaw torque. Combined with the
reduced lateral force capability of the spinning tires (that can make the
car unstable), this yaw torque can start the car around.
- Matt
Dave Pollatsek
data non-dimensionalization... this lists formulas for combining slip angle,
slip ratio, and camber into one unified slip variable, giving you all those
"friction circle" behaviors you're wanting... they've also go a number of
datasets for various types of tires scattered throughout the book. Make
sure you get the load sensitivity curves for your friction and
cornering/camber stiffness, otherwise your roll stiffness adjustments won't
produce the correct understeer/oversteer effects. (The formulas make "mu"
and "C" look like constants, when in fact they're functions of normal
force/load--this lead me astray the first time I tried to use them!)
If you've got the rotational inertia of the wheels/drivetrain modeled, once
you plug these guys in, you'll be able to replicate just about any vehicle
behavior you can think of (donuts, brake-lockup understeer, trailing
throttle oversteer, etc)
Once you get to this point, you can get pretty far in modeling different
types of tires just by tweaking the "C" and "mu" curves, without (at first)
having to mess with the "magic numbers".
"Ruud van Gaal" <ru...@marketgraph.nl> wrote in message
news:3ad16138...@news.xs4all.nl...
Doug Milliken
Thanks for the nice comments below. I think that they are all
correct, except the spelling of our name<grin> -- see below.
I'm very curious -- what program(s) or product(s) have you used the
non-dimensionalized tire data in?
On Sun, 8 Apr 2001, Dave Pollatsek wrote:
> Check out Millikin & Millikin's Race Car Vehicle Dynamics, chapter on tire
> data non-dimensionalization... this lists formulas for combining slip angle,
> slip ratio, and camber into one unified slip variable, giving you all those
> "friction circle" behaviors you're wanting... they've also go a number of
> datasets for various types of tires scattered throughout the book. Make
> sure you get the load sensitivity curves for your friction and
> cornering/camber stiffness, otherwise your roll stiffness adjustments won't
> produce the correct understeer/oversteer effects. (The formulas make "mu"
> and "C" look like constants, when in fact they're functions of normal
> force/load--this lead me astray the first time I tried to use them!)
> If you've got the rotational inertia of the wheels/drivetrain modeled, once
> you plug these guys in, you'll be able to replicate just about any vehicle
> behavior you can think of (donuts, brake-lockup understeer, trailing
> throttle oversteer, etc)
> Once you get to this point, you can get pretty far in modeling different
> types of tires just by tweaking the "C" and "mu" curves, without (at first)
> having to mess with the "magic numbers".
> "Ruud van Gaal" <ru...@marketgraph.nl> wrote in message
.......
> > It seems these coefficients are often copyrighted or something. Not
> > really good for what's called a standard. :)
> > But well, I'm have low-priority plans on a Pacejka editor where you
> > can tweak the constant and see what it does (and hopefully mimic known
In my experience this is not "copyright", it is "trade secret" material.
Laboratory tire tests can cost many thousands (or 10's of thousands) of US
dollars, so companies don't normally give it away. Then there is the extra
cost of reducing the data to some useful format like Pacejka or our
non-dimensional.
A Pacejka editor would be a very nice thing - if it was fairly complete,
I'd gladly pay a small (shareware) price for a copy. I think that
some of his papers list all the formula and give samples of the different
shape curves that can be generated. Check at U of Delft (Holland), and
also at TNO (Dutch National Labs?) -- there have been many versions
of the Magic Formula scheme and many papers over the years.
-- Doug
Douglas Milliken <bd...@freenet.buffalo.edu>
Milliken Research Associates Inc.
And the shameless plug...
Best place to order our book - good price, cheap shipping for card orders:
<http://www.sae.org/servlets/productDetail?PROD_TYP=BOOK&PROD_CD=R-146>
There is even a little bit of Pacejka in our book - in the picture on page
423, the hand holding the pencil is Pacejka! He worked at Cornell Aero Lab
for some time in the 1960's.
Ashley McConnell
Ash
Chris West
Have you seen TyreGene from Yearstretch.
http://www.yearstretch.com/yearstretch/Shop/product.asp?intProdID=1
Chris
Doug Milliken
Chris,
Thanks for the link. It is kind of surprising that there is no
reference for Pacejka-96 (paper title and publisher).
Are there plans to complete the job? To be useful to us, it needs aligning
torque, longitudinal force (and Fy-Fx roll-off), overturning moment, etc.
Chris West
Iam not envolved with Yearstretch :O) Its something Ive come across in my
searches of the internet. I have my own little proggy for my pacejka needs
:O)
Chris
Doug Milliken <bd...@freenet.buffalo.edu> wrote in message
news:GBJ8w...@freenet.buffalo.edu...
David
ARe you helping Ruud with the Racer Project? Just asking since I know the
level of respect your name garners in the circles I run around in and well
I am wondering if I need to start downloading the Racer game now.
Dave
Doug Milliken <bd...@freenet.buffalo.edu> wrote in article
<GBJ8w...@freenet.buffalo.edu>...
Ruud van Gaal
<phobN...@yaSPAMhoo.com> wrote:
>Check out Millikin & Millikin's Race Car Vehicle Dynamics, chapter on tire
>data non-dimensionalization... this lists formulas for combining slip angle,
>slip ratio, and camber into one unified slip variable, giving you all those
>"friction circle" behaviors you're wanting...
Thanks. This book gets more meaning as I understand more of it on the
way. :)
It seems though, after reading it yesterdaynight, the M&M brothers
have a combined (nondimensionalized) slipAngle+camber, and a
slipRatio+slipAngle method, but a fully combined
slipAngle+camber+slipRatio is missing. Or is this just
slipRatio+slipAngle, where you insert the combined slipAngle+camber
nondimensionalized slip as slipAngle in the former slip variable (from
the combined slipRatio+slipAngle)?
I've seen the car spin out with a different algorithm (from Gregor
Veble), which is ok, but I use SAE paper 950311 to do lateral/long.
force buildup (delay of slipAngle and slipRatio), and its damping is
causing me problems. The moment I play around with the forces, the
damping goes wrong and I end up with a car sliding from left to right
at about 0.5Hz (if not slower). I'll probably try a 3-dimension spring
model, since the damping from SAE950311 only works when I set the
coefficients at ~30, instead of the 0.7 (of critical damping) that is
required according to that paper. I may be doing something wrong but
haven't figured it out yet, and I know better how to damp springs, so
a 3D spring model would probably be better nevertheless (and hook back
to the SAE950311 model of delay slipRatio and tanSlipAngle once the
car starts moving at non-lowspeed).
...
>If you've got the rotational inertia of the wheels/drivetrain modeled, once
>you plug these guys in, you'll be able to replicate just about any vehicle
>behavior you can think of (donuts, brake-lockup understeer, trailing
>throttle oversteer, etc)
Sounds good. I have to get rid of the damping algorithm that doesn't
behave right (and that I don't understand completely, there's a lot of
forces with the body that's doing gyroscopic effects etc) and get a
model that works better, and then tweak the friction coefficients
based on nondimensionalize combined slip perhaps.
>Once you get to this point, you can get pretty far in modeling different
>types of tires just by tweaking the "C" and "mu" curves, without (at first)
>having to mess with the "magic numbers".
Good to hear; those magic numbers are a bit predictable to what they
do, but certainly not how to modify them with load!
Thanks,
Ruud van Gaal
<ash...@breathemail.net> wrote:
>You go away for a few days and miss a whole physics thread on R.A.S. :)
Thankfully you have deja.com! And I keep these threads in my archives,
intending to put summary version up on the Racer site. Some of them
are already up there.
Just so many things to do, and so little time...
Doug Milliken
On 9 Apr 2001, David wrote:
> Doug,
> ARe you helping Ruud with the Racer Project? Just asking since I know the
> level of respect your name garners in the circles I run around in and well
> I am wondering if I need to start downloading the Racer game now.
> Dave
No. I just lurk here and cause trouble<vbg>. Go and find an old
Atari Hard Drivin' or Race Drivin' (arcade games) or go to Silicon
Motor Speedway - I've been involved in those.
Separate note to Ruud: At the time that Chapter 14 on non-dimensional tire
data was written, it was a reasonable introduction to the concept. It's
not the final word - a lot has happened in the last ~7 years (book was
finished in mid-1994), and we have not published the new stuff.
Btw, Bill (co-author) is my father. Funny that someone called us
brothers...a good friend (engineer in Detroit) also calls us the
Milliken brothers!
Ruud van Gaal
<robinsons...@spamprodigy.net> wrote:
>Doug,
>
>
>ARe you helping Ruud with the Racer Project?
Haha, he's only doing that indirectly, Dave.
> Just asking since I know the
>level of respect your name garners in the circles I run around in and well
>I am wondering if I need to start downloading the Racer game now.
Well, people like Doug have been helping here more than once, and I've
gotten help from Chris West (from WSC, probably the most anticipated
sim yet) too, if that helps you to convince a download, lol. Not that
it all matters really, ofcourse, I'm doing the code by myself. It's
just ideas about simulations can grow to heights when people work
together with experiences and ideas. There are things to gain for
everyone by working together. Well, that's the philosophy behind Racer
in any case, and in a large part behind WSC too.
Look at Quake and its addons, it's a good way to improve the lifespan
of a product (and the quality as well!).
Racer is only a 3Mb download, so not too much if you want to check it
out sometime. It still has a big problem with lateral friction (power
oversteer), but that's being worked (mostly read) on. Differentials
are on its way (on paper) and that will result in a physics model that
already creeps up on some, if not a lot, of the commercial games. Oh,
how arrogant of me! ;-) But really, it's slowly beginning to feel ok,
and the formula's used are definitely not trivial anymore like in the
beginning.
Ruud van Gaal
<bd...@freenet.buffalo.edu> wrote:
...
>Separate note to Ruud: At the time that Chapter 14 on non-dimensional tire
>data was written, it was a reasonable introduction to the concept. It's
>not the final word - a lot has happened in the last ~7 years (book was
>finished in mid-1994), and we have not published the new stuff.
Are you working on publishing it then? Sounds interesting,
one-curve-fits-all is a nice one. Even though I'm picking up the idea
to have several tiremodels included, and use a model where appropriate
(which does seem to go and work best). Low-speed is a pain.
>Btw, Bill (co-author) is my father. Funny that someone called us
>brothers...a good friend (engineer in Detroit) also calls us the
>Milliken brothers!
Ah yes! Forgot about that. Now I will have to remember the spelling of
your name AND the family tree as well. ;-)
Doug Milliken
On Tue, 10 Apr 2001, Ruud van Gaal wrote:
> On Mon, 9 Apr 2001 23:15:42 GMT, Doug Milliken <bd...@freenet.buffalo.edu> wrote:
> >Separate note to Ruud: At the time that Chapter 14 on non-dimensional tire
> >data was written, it was a reasonable introduction to the concept. It's
> Are you working on publishing it then? Sounds interesting,
> one-curve-fits-all is a nice one. Even though I'm picking up the idea
> to have several tiremodels included, and use a model where appropriate
> (which does seem to go and work best). Low-speed is a pain.
No current plans to publish. We use a more complete version in some of our
analysis software, and we aren't ready to give away all of our hard won
techniques, at least not just yet.
Low speed and stopping/reversing _is_ a pain. I've not heard of many
"clean" solutions for this problem, it's always "messy" in some fashion.
How come tires are so smart? They know how to work smoothly at low speed,
and have been doing it for years, even before computers existed<grin>.
Ruud van Gaal
<bd...@freenet.buffalo.edu> wrote:
...
>No current plans to publish. We use a more complete version in some of our
>analysis software, and we aren't ready to give away all of our hard won
>techniques, at least not just yet.
Too bad, we'll just have to wait then. :)
(or do our own derivations)
>Low speed and stopping/reversing _is_ a pain. I've not heard of many
>"clean" solutions for this problem, it's always "messy" in some fashion.
Sure is. I'm going to do multiple tire models and interpolate I guess.
Even then...
> How come tires are so smart? They know how to work smoothly at low speed,
>and have been doing it for years, even before computers existed<grin>.
Perhaps we could use a TireStick, where a small tire is run next to
your computer, and forces are measured and passed back to the
computer, where the sim reads it in. The 'perfect' tire model. Hehe.
With addon packs with tiny versions of different tires. You could
perhaps even plug in your favorite Mattell car! ;-)
Ashley McConnell
3d space, perhaps some kind of cage that fits over my head ;)
Ash
Ruud van Gaal
<ash...@breathemail.net> wrote:
>I think I am going to have to produce something similar for me to understand
>3d space, perhaps some kind of cage that fits over my head ;)
Keeping a 3D axis system built from pencils perhaps helps. :)
With a tiny car where you stick out the Y, oh sorry, Z in SAE terms
through the roof. Or copy and print out a big version of the SAE
vehicle axis system.
I often use my right hand and see if I can go from X to Y when my
thumb is pointing in Z, to determine righthandedness.
If we all looked like ET we couldn't do these things, you know, with
only 2 fingers. (oh my, he probably has 25 or something as it will
turn out) Makes it hard to believe he travelled through space. Ah, no
more beer for me!
Doug Milliken
On Wed, 11 Apr 2001, Ruud van Gaal wrote:
> > How come tires are so smart? They know how to work smoothly at low speed,
> >and have been doing it for years, even before computers existed<grin>.
>
> Perhaps we could use a TireStick, where a small tire is run next to
> your computer, and forces are measured and passed back to the
> computer, where the sim reads it in. The 'perfect' tire model. Hehe.
> With addon packs with tiny versions of different tires. You could
> perhaps even plug in your favorite Mattell car! ;-)
Or, in real life, just buy one of these Flat-Trac Roadway Simulators,
cheap at ~$10M!
<http://www.mts.com/menusystem.asp?DataSource=0&NodeID=1141>
Use the real physics with any car to drive your graphics display.
-- Doug
Douglas Milliken <bd...@bfn.org>
Milliken Research Associates Inc.
Ruud van Gaal
Cool! I'll order two just in case one breaks up during debugging. ;-)
Doug Milliken
On Fri, 13 Apr 2001, Ruud van Gaal wrote:
> On Fri, 13 Apr 2001 18:44:21 GMT, Doug Milliken
> <bd...@freenet.buffalo.edu> wrote:
>
> >
> >On Wed, 11 Apr 2001, Ruud van Gaal wrote:
> >> > How come tires are so smart? They know how to work smoothly at low speed,
> >> >and have been doing it for years, even before computers existed<grin>.
> >>
> >> Perhaps we could use a TireStick, where a small tire is run next to
> >> your computer, and forces are measured and passed back to the
> >> computer, where the sim reads it in. The 'perfect' tire model. Hehe.
> >> With addon packs with tiny versions of different tires. You could
> >> perhaps even plug in your favorite Mattell car! ;-)
> >
> >Or, in real life, just buy one of these Flat-Trac Roadway Simulators,
> >cheap at ~$10M!
> > <http://www.mts.com/menusystem.asp?DataSource=0&NodeID=1141>
> >Use the real physics with any car to drive your graphics display.
>
> Cool! I'll order two just in case one breaks up during debugging. ;-)
Don't forget to stock up on different kinds of cars too!