Pacejka longitudal force and road adhesion

Hi while reading Genta ( for the purpose of development of a vehicle sim) I got a bit confused let us consider Pacejka magic formula for longitudal force ( Genta p 64) the maximum value of longitudal force might be equal to D D = mu p *Fz mu p =b1*Fz+b2 Fz - load and b1 and b2 are respective coeffs. at pp 526 for large front wheel drive saloon car the following coeefs are given b1=-7.6118 b2=1122.6 we take at front wheels Fz =3381 H ( or 3.381 kN for Pacejka) so we have D = 3708.49 Now we have that road adhesion might not exceed (road friction coeff) * Fz even if I get road friction ==1 anyway seems that Pacejka max force is greater than road adhesion.... Does it mean I should limit output force if it exceeds adhesion or that the force is actually physically OK? the another question might be is there straight way to couple friction coefficient with Pacejka coeffs? or for each type of road/tire there is a need in separate Pacejka coeffs set? Regards Serge http://www.vrtainment.de

On 30 Mar 2003 09:11:34 -0800, [email hidden] (Serge Kourdakov) wrote: >while reading Genta ( for the purpose of development of a vehicle sim) >I got a bit confused > >let us consider Pacejka magic formula for longitudal force ( Genta p >64) What year is that book from anyway? Seems the Pacejka formula in that book is from about '91. There was a major update in '96, with I think combined long/lat forces. Also, probably at that time as well, a lot of the coefficients changed name. Anyway, I should read Pacejka's book. ;) ... >at pp 526 for large front wheel drive saloon car the following >coeefs are given >b1=-7.6118 b2=1122.6... >D = 3708.49 > >Now we have that road adhesion might not exceed (road friction >coeff) * Fz I'm not sure about the difference between road adhesion and friction. What b2 is doing is merely: mu=b2/1000+b1*Fz/1000, where Fz is in kN to make things fuzzy. :) So b2 is road friction coefficient, apart from the load sensitivity (b1, which is the b2 change per kN if I write that up quickly, so basically mu change per million Newton (that's an awkward way to say it)). >even if I get road friction ==1 >anyway seems that Pacejka max force is greater than road adhesion.... > >Does it mean I should limit output force if it exceeds adhesion or >that >the force is actually physically OK? No, the Pacejka result is quite ok as the road reaction force. Whereever it derives from (friction) doesn't really matter; at the given input variables (slip angles, slip ratio, camber) is gives you the resulting force that the road puts back onto the wheel. So there is no adhesion or friction difference here. >the another question might be is there straight way to couple friction >coefficient with Pacejka coeffs? D is the peak force, and is just about mu (D/Fz = mu). The current effective mu is just Fx/Fz longitudinally or Fy/Fz laterally. >or for each type of road/tire there is a need in separate Pacejka >coeffs set? Yes, unfortunately. Still, the Pacejka '96 variant has lamba coefficients, which enable you to tweak more physical aspects of the formula, instead of more mysterious and subtle coefficients. Some lamba's affect more than one Pacejka coefficient, that is. Those lamba's might be useful in simulating multiple road variants using a bit of lamba tweaking. Once you get on loose soil though, there are completely different theories. Although I like to think you can sum effects a bit. Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

On Sun, 30 Mar 2003, Ruud van Gaal wrote: > On 30 Mar 2003 09:11:34 -0800, [email hidden] (Serge Kourdakov) > wrote: > Anyway, I should read Pacejka's book. ;) Which leads me off on a tangent -- I often wonder why people use Pacejka instead of some other tire model...and then wonder what the Magic Formula coefficients "mean" physically. There is a nice picture in Pacejka "Tire and Vehicle Dynamics" (Figure 2.11) that attempts to place all the different types of tire models into one overall framework, and rank them on different aspects. On the left are pure curvefitting models like the Magic Formula scheme, next are what he calls "similarity method" which include some simple tire theory in addition to measurements on real tires. This is where our Radt-MRA Non-Dimensional approach fits in, see RCVD Chapter 14 and also a chapter in Pacejka. In this case, at least some of the numbers that describe the tire have some physical significance, for example the cornering stiffness and peak friction values (as functions of various operating variables). I know that some sims use the Non-Dimensional scheme but can't tell you off hand which ones (just that various people have contacted me over the years and mentioned that they were using it). We have a brief discussion here: http://www.millikenresearch.com/mrandim.html For unknown reasons, Pacejka doesn't reference the early paper by Radt and Milliken (my father), Motions of Skidding Automobiles, which also discusses this approach. -- Doug

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> >> Anyway, I should read Pacejka's book. ;) > >Which leads me off on a tangent -- I often wonder why people use Pacejka >instead of some other tire model...and then wonder what the Magic Formula >coefficients "mean" physically. >

No Pacejka here. Just a work-in-progress Wasson model :-P I actually did try using springs in the contact patch a long time ago as people have talked about here often. Using about 20-50 springs per contact patch actually worked surprisingly well. Sort of a poor-man's FEM tire model. The new one's better though ;-) Todd Wasson Racing Software http://PerformanceSimulations.com My car sim http://performancesimulations.com/scnshot4.htm

On 31 Mar 2003 04:16:55 GMT, [email hidden] (J. Todd Wasson) wrote: >> >>> Anyway, I should read Pacejka's book. ;) >> >>Which leads me off on a tangent -- I often wonder why people use Pacejka >>instead of some other tire model...and then wonder what the Magic Formula >>coefficients "mean" physically. Couple of things here; the fact that it is used professionally (but I'm sure other models are). Second because I know people here that deal with Pacejka a lot (even are his students), and they have fitting programs and all that, so it's not really a dead end, but very interesting in fact. >No Pacejka here. Just a work-in-progress Wasson model :-P Where can I download the research papers? ;-) Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

Hi Doug and the gang! On Sun, 30 Mar 2003, Doug Milliken wrote: > > Which leads me off on a tangent -- I often wonder why people use Pacejka > instead of some other tire model...and then wonder what the Magic Formula > coefficients "mean" physically. > Been wondering that myself quite often... ;)

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> > There is a nice picture in Pacejka "Tire and Vehicle Dynamics" (Figure > 2.11) that attempts to place all the different types of tire models into > one overall framework, and rank them on different aspects. On the left > are pure curvefitting models like the Magic Formula scheme, next are what > he calls "similarity method" which include some simple tire theory in > addition to measurements on real tires. This is where our Radt-MRA > Non-Dimensional approach fits in, see RCVD Chapter 14 and also a chapter > in Pacejka. In this case, at least some of the numbers that describe the > tire have some physical significance, for example the cornering stiffness > and peak friction values (as functions of various operating variables). >

I believe the main problem with the Pacejka formula is that in trying to present a comprehensive tyre model it obscures the fact that the formula itself (once all the constants have been evaluated for a given load) probably represents the simplest mathematical expression having the property of being everywhere analytical and at the same time capturing the typical tyre features (linear at small slip, reaching a peak and then leveling off). Things then get nasty once you try to describe the full load dependent picture by introducing further constants, as some of the constants do have a direct physical meaning while for others it's very hard to distinguish between physics and simple fitting value. For a gaming racing simulation it then becomes hard to incorporate effects like tyre wear, pressure dependence etc. in a meaningful way by altering the coefficients directly. What I'd suggest would be to use the 'bare' Pacejka formula (which certainly has its merits) and link the few remaing parameters to physical quantities like maximum grip, sliding force, stiffness, peak slip etc., all of which may change with load, wear, etc., which would then bring it closer to the nondimensinal scheme (but not quite). -Gregor

Doug Milliken <[email hidden]> wrote in message news:<[email hidden]>... > Which leads me off on a tangent -- I often wonder why people use Pacejka > instead of some other tire model...and then wonder what the Magic Formula > coefficients "mean" physically. Well.. they do, after many readings throughout his book they sort of make sense to me. > I know that some sims use the Non-Dimensional scheme but can't tell you > off hand which ones (just that various people have contacted me over the > years and mentioned that they were using it). Here we go.. I'm one. :-D > We have a brief discussion here: > http://www.millikenresearch.com/mrandim.html > > For unknown reasons, Pacejka doesn't reference the early paper by Radt > and Milliken (my father), Motions of Skidding Automobiles, which also > discusses this approach. But he does reference you Doug.. he calls the RCVD tyre model the "similarity model" and there's a reference to you in the first paragraph. Anyway... I wonder.. one thing I had to "tweak" myself in the RCVD model is the stiffness value.. it is supposed to be function of Fz but I couldnt find a way to express this this in RCVD.. have I missed something? Stefano Casillo driving.multiplayer.it/netkar

On Sun, 30 Mar 2003 21:11:00 -0500, Doug Milliken <[email hidden]> wrote:

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> >On Sun, 30 Mar 2003, Ruud van Gaal wrote: > >> On 30 Mar 2003 09:11:34 -0800, [email hidden] (Serge Kourdakov) >> wrote: > >> Anyway, I should read Pacejka's book. ;) > > This is where our Radt-MRA >Non-Dimensional approach fits in, see RCVD Chapter 14 and also a chapter >in Pacejka. In this case, at least some of the numbers that describe the >tire have some physical significance, for example the cornering stiffness >and peak friction values (as functions of various operating variables).

Doug, is there any more info on the MRAND technique besides the chapters in RCVD and Pacejka's latest book? (I'll have to reread both though) Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

Hi Gregor, Good to see you joining in. :) On Mon, 31 Mar 2003 11:28:12 +0200, Gregor Veble <[email hidden]> wrote: .... >What I'd suggest would be to use the 'bare' Pacejka formula (which >certainly has its merits) and link the few remaing parameters to physical >quantities like maximum grip, sliding force, stiffness, peak slip etc., >all of which may change with load, wear, etc., which would then bring it >closer to the nondimensinal scheme (but not quite). The later Pacejka formulae (1996+) allow this with lamba values, that all have physical meaning. This is how I know some engineers tweak tire data. Each lamba can affect the formulae at more than one spot, leaving the base Pacejka coefficients (that Racer uses for example) as more of a fitting result. From there on, you only tweak the lamba values. Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

On 31 Mar 2003, Stefano Casillo wrote: > Doug Milliken <[email hidden]> wrote in message news:<[email hidden]>...... > > I know that some sims use the Non-Dimensional scheme but can't tell you > Here we go.. I'm one. :-D Cool! I should have mentioned that some sims that I know about also use the third type from Pacejka's figure 2.11 -- Simple Physical Model. It sounds like this might be what Todd W is doing??

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> > http://www.millikenresearch.com/mrandim.html > > > > For unknown reasons, Pacejka doesn't reference the early paper by Radt > > and Milliken (my father), Motions of Skidding Automobiles, which also > > discusses this approach. > > But he does reference you Doug.. he calls the RCVD tyre model the > "similarity model" and there's a reference to you in the first > paragraph.

Only a minor point --Pacejka missed that one early paper, but as you say he does reference two other papers. > Anyway... I wonder.. one thing I had to "tweak" myself in the RCVD > model is the stiffness value.. it is supposed to be function of Fz but > I couldnt find a way to express this this in RCVD.. have I missed > something? Our ref 124: Radt, H. S. and D. A. Glemming. "Normalization of Tire Force and Moment Data." Tire Science and Technology, TSTCA, Vol. 21, No. 2, pp. 91-119. April-June, 1993. is another place to look. Not sure how to order a copy of this paper. The description in RCVD is very brief (book is too long anyway...) -- Doug Milliken

>> > I know that some sims use the Non-Dimensional scheme but can't tell you >> Here we go.. I'm one. :-D > >Cool! I should have mentioned that some sims that I know about also use >the third type from Pacejka's figure 2.11 -- Simple Physical Model. It >sounds like this might be what Todd W is doing?? Can't comment because I don't have the book.. :-( Todd Wasson Racing Software http://PerformanceSimulations.com My car sim http://performancesimulations.com/scnshot4.htm

On 2 Apr 2003, J. Todd Wasson wrote:

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> >> > I know that some sims use the Non-Dimensional scheme but can't tell you > >> Here we go.. I'm one. :-D > > > >Cool! I should have mentioned that some sims that I know about also use > >the third type from Pacejka's figure 2.11 -- Simple Physical Model. It > >sounds like this might be what Todd W is doing?? > > Can't comment because I don't have the book.. :-( > > Todd Wasson

Simple Physical Model might be, for example, a "brush" model of the tire with stiffness to the "bristles". There are a number of these types of models in the literature with advantages and problems with each type. The 4th and last category in Fig 2.11 is detailed physical models (finite element) which calculate very slowly--it will be a few years<grin> before these models can be used for anything approaching realtime. Pacejka's new book is recommended to all you tire modelers out there.

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>> >> > I know that some sims use the Non-Dimensional scheme but can't tell >you >> >> Here we go.. I'm one. :-D >> > >> >Cool! I should have mentioned that some sims that I know about also use >> >the third type from Pacejka's figure 2.11 -- Simple Physical Model. It >> >sounds like this might be what Todd W is doing?? >> >> Can't comment because I don't have the book.. :-( >> >> Todd Wasson > >Simple Physical Model might be, for example, a "brush" model of the tire >with stiffness to the "bristles". There are a number of these types of >models in the literature with advantages and problems with each type. The >4th and last category in Fig 2.11 is detailed physical models (finite >element) which calculate very slowly--it will be a few years<grin> before >these models can be used for anything approaching realtime. > >Pacejka's new book is recommended to all you tire modelers out there. > >

Sorry for the delay. I've been having a heck of a time getting online lately. Indeed, my tire model is a physical model somewhere between the first and last ones you described. I did try a very, very basic FEM model at one point, although it could be argued whether it was really an FEM model at all. This was just a bunch of springs in the contact patch (I think I mentioned it already). It worked surprisingly well, as you don't have to worry about combination slip effects; they work themselves out with no troubles. But the new approach is much faster, more precise, and more "accurate." It lets me put all sorts of dependencies with tire pressure, slip velocity, and so forth into it, but of course it's all just theoretical, so loads of fun to play with to see if my thinking of how tires work reflects reality :-) Still though, I think it will automatically take care of load sensitive effects to a large extent. We'll see if what I think is the chief cause of load sensitivity is really right after I can put that together and compare it with some real data <rolling eyes>. My gut tells me it'll be pretty good and let you take a physical approach to tire design in the sim in a way that would make sense to sim racers (not just programmers), and in a way not seen before. Of course, it could completely suck too :-D Todd Wasson Racing Software http://PerformanceSimulations.com My car sim http://performancesimulations.com/scnshot4.htm

On 10 Apr 2003, J. Todd Wasson wrote:

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> >> >> > I know that some sims use the Non-Dimensional scheme but can't tell > >you > >> >> Here we go.. I'm one. :-D > >> > > >> >Cool! I should have mentioned that some sims that I know about also use > >> >the third type from Pacejka's figure 2.11 -- Simple Physical Model. It > >> >sounds like this might be what Todd W is doing?? > >> > >> Can't comment because I don't have the book.. :-( > >> > >> Todd Wasson > > > >Simple Physical Model might be, for example, a "brush" model of the tire > >with stiffness to the "bristles". There are a number of these types of > >models in the literature with advantages and problems with each type. The > >4th and last category in Fig 2.11 is detailed physical models (finite > >element) which calculate very slowly--it will be a few years<grin> before > >these models can be used for anything approaching realtime. > > > >Pacejka's new book is recommended to all you tire modelers out there. > > > > > > Sorry for the delay. I've been having a heck of a time getting online lately. > > > Indeed, my tire model is a physical model somewhere between the first and last > ones you described. I did try a very, very basic FEM model at one point, > although it could be argued whether it was really an FEM model at all. > > This was just a bunch of springs in the contact patch (I think I mentioned it > already). It worked surprisingly well, as you don't have to worry about > combination slip effects; they work themselves out with no troubles. But the > new approach is much faster, more precise, and more "accurate." It lets me put > all sorts of dependencies with tire pressure, slip velocity, and so forth into > it, but of course it's all just theoretical, so loads of fun to play with to > see if my thinking of how tires work reflects reality :-) > > Still though, I think it will automatically take care of load sensitive effects > to a large extent. We'll see if what I think is the chief cause of load > sensitivity is really right after I can put that together and compare it with > some real data <rolling eyes>. My gut tells me it'll be pretty good and let > you take a physical approach to tire design in the sim in a way that would make > sense to sim racers (not just programmers), and in a way not seen before. > > Of course, it could completely suck too :-D

Todd, funny about getting online, I've had troubles lately too. When I get on, things are often very slow. Maybe all the people getting Iraq news? Or just surfing more because they are out of work<sigh>? Your spring model fits the simple physical model category, I'll bet that a little bit of searching will find something similar in the literature-- many of these have been proposed over the years and some of them work quite well. The way I heard it (at a tire company), to do finite element on a tire, takes thousands of elements, and with tires the elements deform and are nonlinear in load-deflection (unlike standard linear FEM on metal structures). It's still super-computer or cluster-computer stuff--if the answer is supposed to model some real tire. If your model works, you might consider publishing a paper on it (eventually).

> > >Todd, funny about getting online, I've had troubles lately too. When I >get on, things are often very slow. Maybe all the people getting Iraq >news? Or just surfing more because they are out of work<sigh>? Hehe :-) Fortunately today I haven't had any problems. >Your spring model fits the simple physical model category, I'll bet that a >little bit of searching will find something similar in the literature-- >many of these have been proposed over the years and some of them work >quite well. > The one I'm doing now was inspired by brush models, but goes futher into things in some areas (and probably not as far into other things). >The way I heard it (at a tire company), to do finite element on a tire, >takes thousands of elements, and with tires the elements deform and >are nonlinear in load-deflection (unlike standard linear FEM on metal >structures). It's still super-computer or cluster-computer stuff--if the >answer is supposed to model some real tire. Yes, it's certainly not something that you could do in real time on your home PC (or any computer, probably). I've got some basic FEM code, but haven't looked at it much. It's not well documented so it looks a bit too cryptic for me to probably do much with. It's still interesting stuff though. Quite some time back, I took a stab at making something like an FEM model. It's quite hysterical :-) This doesn't use any shearing action, which might work fine if I remade it to do so. For now it's just an interesting screen saver ;-) http://performancesimulations.com/files/funnytire.exe Good for a nice laugh. Actually, it's a completely accurate simulation of an exploding tire ;-) >If your model works, you might consider publishing a paper on it >(eventually). > Interesting. How would I go about doing that? Todd Wasson Racing Software http://PerformanceSimulations.com My car sim http://performancesimulations.com/scnshot4.htm

On 13 Apr 2003, J. Todd Wasson wrote:

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> >Your spring model fits the simple physical model category, I'll bet that a > >little bit of searching will find something similar in the literature-- > >many of these have been proposed over the years and some of them work > >quite well. > > The one I'm doing now was inspired by brush models, but goes futher into things > in some areas (and probably not as far into other things). > > >The way I heard it (at a tire company), to do finite element on a tire, > >takes thousands of elements, and with tires the elements deform and > >are nonlinear in load-deflection (unlike standard linear FEM on metal > >structures). It's still super-computer or cluster-computer stuff--if the > >answer is supposed to model some real tire. > > Yes, it's certainly not something that you could do in real time on your home > PC (or any computer, probably). I've got some basic FEM code, but haven't > looked at it much. It's not well documented so it looks a bit too cryptic for > me to probably do much with. It's still interesting stuff though. > > Quite some time back, I took a stab at making something like an FEM model. > It's quite hysterical :-) This doesn't use any shearing action, which might > work fine if I remade it to do so. For now it's just an interesting screen > saver ;-) > > http://performancesimulations.com/files/funnytire.exe > > Good for a nice laugh. Actually, it's a completely accurate simulation of an > exploding tire ;-)

W'all now y'all, lissen up--that there tire come apart and beat that ol' fender right off'n that car... > >If your model works, you might consider publishing a paper on it > >(eventually). > > Interesting. How would I go about doing that? The SAE Motor Sports Engineering conference accepts all kinds of race car simulation papers. Next conference will be Fall 2004 (happens every 2 years), in Indy, just before the big PRI racing trade show: http://www.sae.org/calendar/gvmtgs.htm#2004 (down toward the bottom of the list) No cash, but exposure to race engineers and once your paper is accepted it will be published (glory) in a book of collected papers. Author instructions here: http://www.sae.org/products/papers/paprinfo/present.htm

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>http://performancesimulations.com/files/funnytire.exe >> >> Good for a nice laugh. Actually, it's a completely accurate simulation of >an >> exploding tire ;-) > >W'all now y'all, lissen up--that there tire come apart and beat that ol' >fender right off'n that car... >

Hehe.. The funny thing is I'm 95% sure you've actually had someone say that to you exactly that way :-)

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>> >If your model works, you might consider publishing a paper on it >> >(eventually). >> >> Interesting. How would I go about doing that? > >The SAE Motor Sports Engineering conference accepts all kinds of >race car simulation papers. Next conference will be Fall 2004 (happens >every 2 years), in Indy, just before the big PRI racing trade >show: http://www.sae.org/calendar/gvmtgs.htm#2004 > (down toward the bottom of the list) > >No cash, but exposure to race engineers and once your paper >is accepted it will be published (glory) in a book of collected papers. >Author instructions here: > http://www.sae.org/products/papers/paprinfo/present.htm > > >

Excellent! Thanks, Doug. Todd Wasson Racing Software http://PerformanceSimulations.com My car sim http://performancesimulations.com/scnshot4.htm