Car Physics: Slip Angle and the Pacejka magic formula

Hi People, I was wondering if you could give me a hand with a couple of problems. How is lateral slip angle calculated? I have been trying to use this formula that I came across: slip_angle = sideslip_angle + omega * b / wheelbase + wheel_angle (where b is the longitudinal distance from the CG to the wheel position) Is this correct? Because it doesn't seem to be giving me the correct answers. My second question is what range of values does the pacejka magic formula take for slip angle (and camber angle)? is it in radians or degrees? Any help would be greatly appreciated. George.

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>Hi People, > >I was wondering if you could give me a hand with a couple of problems. >How is lateral slip angle calculated? >I have been trying to use this formula that I came across: > >slip_angle = sideslip_angle + omega * b / wheelbase + wheel_angle > >(where b is the longitudinal distance from the CG to the wheel position) > >Is this correct? Because it doesn't seem to be giving me the correct >answers. > >My second question is what range of values does the pacejka magic formula >take for slip angle (and camber angle)? is it in radians or degrees? > >Any help would be greatly appreciated. > >George.

That's not quite right because it doesn't take into account the true velocity at the tire. You need the rotational velocity of the car included in the calcs so rotational damping occurs. If the car was sitting in one spot and spinning around its center of mass, could you find the direction each tire is moving, along with how quickly they're moving? (Velocity vectors) Use 3-D vectors for this (if you're doing it in 3-D). Given the rotational velocity of the car, find the true velocity vector for the tire's contact patch. Add the car's translational velocity vector to this. Then, using the normal to the surface the tire is on, project the vector onto the plane (so you subtract the part of the velocity that is going directly towards or away from the plane, this component BTW, can get you the shock absorber/damper velocity. I define my tire orientation with one vector, and a rotation angle around it (sticking out one side of the wheel). Project this vector against the plane in the same manner (this eliminates the effect of camber angle for slip angle calculation.) Once you've got these two projected vectors, which are giving tire contact patch velocity relative to the surface it's rolling on, as well as the orientation of the wheel with camber not included, you DOT these two and subtract 90 degrees to get the slip angle. Slip angle is really the angle between the direction the tire is facing and moving, so the above stuff gets the solution in 3-D. I don't have an answer for your Pacejka question. Hope that helps, Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

[email hidden] (J. Todd Wasson) wrote in <[email hidden]>:

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>>Hi People, >> >>I was wondering if you could give me a hand with a couple of problems. >>How is lateral slip angle calculated? >>I have been trying to use this formula that I came across: >> >>slip_angle = sideslip_angle + omega * b / wheelbase + wheel_angle >> >>(where b is the longitudinal distance from the CG to the wheel >>position) >> >>Is this correct? Because it doesn't seem to be giving me the correct >>answers. >> >>My second question is what range of values does the pacejka magic >>formula take for slip angle (and camber angle)? is it in radians or >>degrees? >> >>Any help would be greatly appreciated. >> >>George. > > That's not quite right because it doesn't take into account the true > velocity >at the tire. You need the rotational velocity of the car included in >the calcs so rotational damping occurs. If the car was sitting in one >spot and spinning around its center of mass, could you find the >direction each tire is moving, along with how quickly they're moving? >(Velocity vectors) > > Use 3-D vectors for this (if you're doing it in 3-D). Given the > rotational >velocity of the car, find the true velocity vector for the tire's >contact patch. Add the car's translational velocity vector to this. >Then, using the normal to the surface the tire is on, project the vector >onto the plane (so you subtract the part of the velocity that is going >directly towards or away from the plane, this component BTW, can get you >the shock absorber/damper velocity. > > I define my tire orientation with one vector, and a rotation angle > around it >(sticking out one side of the wheel). Project this vector against the >plane in the same manner (this eliminates the effect of camber angle for >slip angle calculation.) Once you've got these two projected vectors, >which are giving tire contact patch velocity relative to the surface >it's rolling on, as well as the orientation of the wheel with camber not >included, you DOT these two and subtract 90 degrees to get the slip >angle. > > Slip angle is really the angle between the direction the tire is > facing and >moving, so the above stuff gets the solution in 3-D. > > I don't have an answer for your Pacejka question. > > Hope that helps, > >Todd Wasson >--- >Performance Simulations >Drag Racing and Top Speed Prediction >Software >http://PerformanceSimulations.Com

Thanks alot for the reply, it helped alot. One day I might buy myself "Race Car Vehicle Dynamics" for help with stuff like this - but at the moment I'm a poor student :(. Can anybody give me a hand with this Pacejka stuff? Thanks again, George

On Sun, 22 Jul 2001 11:02:27 GMT, [email hidden] (George) wrote: >My second question is what range of values does the pacejka magic formula >take for slip angle (and camber angle)? is it in radians or degrees? It's degrees. And oh my, it takes the normal force as kiloNewtons. And slipratio as a percentage. What WAS he thinking! ;-) Anything to give you a hard time getting it right. Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

As long as it's not slugs and feet ... <hiding from Doug ;)> -Gregor Ruud van Gaal wrote:

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> > It's degrees. And oh my, it takes the normal force as kiloNewtons. And > slipratio as a percentage. What WAS he thinking! ;-) > Anything to give you a hard time getting it right. > > Ruud van Gaal, GPL Rank +53.25 > Pencil art : http://www.marketgraph.nl/gallery/ > Free car sim : http://www.marketgraph.nl/gallery/racer/

On Mon, 23 Jul 2001 19:03:08 +0200, Gregor Veble <[email hidden]> wrote: >As long as it's not slugs and feet ... > ><hiding from Doug ;)> LOL! He'll probably give you air density in poundforces per pound. Slugs, aren't those the little creatures from OddWorld, Abe's Oddysey? :) Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

>Thanks alot for the reply, it helped alot. One day I might buy myself "Race >Car Vehicle Dynamics" for help with stuff like this - but at the moment I'm >a poor student :(. >Can anybody give me a hand with this Pacejka stuff? It's an awesome book, although it doesn't cover any of the vector stuff above. That's all 3-D graphics stuff, but works great for physics too. Can't help ya with Pacejka yet though :-) The book covers the Raadt non-dimensionalized technique. I've played with that a little, and it looks good. It can be used in combination with Pacejka if you want. There are others here a lot more knowledgeable on that, so I'll pass on trying to help on that one... :-) Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

J. Todd Wasson <[email hidden]> wrote in message news:[email hidden]... > >Thanks alot for the reply, it helped alot. One day I might buymyself "Race > >Car Vehicle Dynamics" for help with stuff like this - but at themoment I'm > >a poor student :(. > >Can anybody give me a hand with this Pacejka stuff? > > It's an awesome book, although it doesn't cover any of the vectorstuff > above. That's all 3-D graphics stuff, but works great for physicstoo. Can't > help ya with Pacejka yet though :-) The book covers the Raadt > non-dimensionalized technique. I've played with that a little, andit looks > good. It can be used in combination with Pacejka if you want.There are > others here a lot more knowledgeable on that, so I'll pass on tryingto help on > that one... :-) I got a basic combined-slip, load-dependent model with a non-dimensional Pacejka curve working okay in my final year project - and I can provide numbers for that based on some rough Dunlop tyre maps, although longitudinal stuff was all guessed. LMK if info's wanted - perhaps the easiest way would be to email my FYP, or maybe just the relevant chapter. Jonny

On 23 Jul 2001 21:31:37 GMT, [email hidden] (J. Todd Wasson) wrote:

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>>Thanks alot for the reply, it helped alot. One day I might buy myself "Race >>Car Vehicle Dynamics" for help with stuff like this - but at the moment I'm >>a poor student :(. >>Can anybody give me a hand with this Pacejka stuff? > > It's an awesome book, although it doesn't cover any of the vector stuff >above. That's all 3-D graphics stuff, but works great for physics too. Can't >help ya with Pacejka yet though :-)

I believe the formula is mentioned, although somewhat quick & rough. Still, IIRC there's a picture of a hand somewhere and that's the hand of Pacejka himself! Not that that will get you a great tiremodel. ;-) Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

On Mon, 23 Jul 2001 23:28:49 +0100, "Jonny Hodgson" <[email hidden]> wrote: >I got a basic combined-slip, load-dependent model with a >non-dimensional Pacejka curve working okay in my final year project - >and I can provide numbers for that based on some rough Dunlop tyre >maps, although longitudinal stuff was all guessed. Pacejka numbers are always wanted. So few of them around the net... Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

[email hidden] (Ruud van Gaal) wrote in <[email hidden]>:

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>On Sun, 22 Jul 2001 11:02:27 GMT, [email hidden] (George) >wrote: > >>My second question is what range of values does the pacejka magic >>formula take for slip angle (and camber angle)? is it in radians or >>degrees? > >It's degrees. And oh my, it takes the normal force as kiloNewtons. And >slipratio as a percentage. What WAS he thinking! ;-) >Anything to give you a hard time getting it right. > > >Ruud van Gaal, GPL Rank +53.25 >Pencil art : http://www.marketgraph.nl/gallery/ >Free car sim : http://www.marketgraph.nl/gallery/racer/

Hmmm, that may explain some of my problems - as i was feeding it the normal force in ordinary Newtons. P.S. there's a program I found to help generate Pacejka Constants, you can find it at http://www.YEARSTRETCH.com . I'm haven't had a close look at it so i can't tell you what it's like (not that i'd really know if it was any good ;) ). Thanks for the help, George

Ruud van Gaal <[email hidden]> wrote in message news:[email hidden]... > On Mon, 23 Jul 2001 23:28:49 +0100, "Jonny Hodgson" > <[email hidden]> wrote: > > >I got a basic combined-slip, load-dependent model with a > >non-dimensional Pacejka curve working okay in my final yearproject - > >and I can provide numbers for that based on some rough Dunlop tyre > >maps, although longitudinal stuff was all guessed. > > Pacejka numbers are always wanted. So few of them around the net... Thinking about it, the actual Pacejka curve is probably the one proposed in RCVD - if you were to implement the combined-slip model as desctibed there (around p480 I think) I could then provide some rough numbers for the other eight (!) parameters. I'm a little hesitant about supplying too much information since technically the University owns the copyright on my project, but I'm assured that the report itself is public domain so this should be okay... Jonny

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>> It's an awesome book, although it doesn't cover any of the vector stuff >>above. That's all 3-D graphics stuff, but works great for physics too. >Can't >>help ya with Pacejka yet though :-) > >I believe the formula is mentioned, although somewhat quick & rough. >Still, IIRC there's a picture of a hand somewhere and that's the hand >of Pacejka himself! Not that that will get you a great tiremodel. ;-) > >

Yes, it's the shorter version with (I think) four constants instead of 200,000 or so ;-) Pacejka is holding the pencil on page..... well, I'd know it if I saw it. Doug pointed that out for us all one day. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

On 24 Jul 2001 21:40:33 GMT, [email hidden] (J. Todd Wasson) wrote:

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>>> It's an awesome book, although it doesn't cover any of the vector stuff >>>above. That's all 3-D graphics stuff, but works great for physics too. >>Can't >>>help ya with Pacejka yet though :-) >> >>I believe the formula is mentioned, although somewhat quick & rough. >>Still, IIRC there's a picture of a hand somewhere and that's the hand >>of Pacejka himself! Not that that will get you a great tiremodel. ;-) >> >> > > Yes, it's the shorter version with (I think) four constants instead of >200,000 or so ;-) Pacejka is holding the pencil on page..... well, I'd know >it if I saw it. Doug pointed that out for us all one day.

Just read about Pacejka '97 yesterday, hm. I use Pacejka 96, with some 30 or so constants. Still, every constant has its direct influence on the curve, which I intend to explain (as far as possible) on my site. It's not really such rocket science after all it seems, with often good physical backgrounds. Anyway, the Pacejka '97 methods seem to define combined slip operations. Need to check that out later. Another 10 constants or so. ;-) Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

| >>> It's an awesome book, although it doesn't cover any of the vectorstuff

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| >>>above. That's all 3-D graphics stuff, but works great for physics too. | >>Can't | >>>help ya with Pacejka yet though :-) | >> | >>I believe the formula is mentioned, although somewhat quick & rough. | >>Still, IIRC there's a picture of a hand somewhere and that's the hand | >>of Pacejka himself! Not that that will get you a great tiremodel. ;-) | >> | >> | > | > Yes, it's the shorter version with (I think) four constants instead of | >200,000 or so ;-) Pacejka is holding the pencil on page..... well, I'd

know

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| >it if I saw it. Doug pointed that out for us all one day. | | Just read about Pacejka '97 yesterday, hm. I use Pacejka 96, with some | 30 or so constants. Still, every constant has its direct influence on | the curve, which I intend to explain (as far as possible) on my site. | It's not really such rocket science after all it seems, with often | good physical backgrounds. | Anyway, the Pacejka '97 methods seem to define combined slip | operations. Need to check that out later. Another 10 constants or so. | ;-) | | | Ruud van Gaal, GPL Rank +53.25 | Pencil art : http://www.marketgraph.nl/gallery/ | Free car sim : http://www.marketgraph.nl/gallery/racer/

Ruud, Is Pacekja '97 available anywhere on the web? (In English <g>) Thanks Ash

On Wed, 25 Jul 2001 12:08:53 +0100, "Ashley McConnell" <[email hidden]> wrote: >Ruud, > >Is Pacekja '97 available anywhere on the web? (In English <g>) Couldn't find any. But here's the link (got it from the Racer forum) from the thesis which talks about it and has some constant (with completely different names): http://www.lib.ncsu.edu/etd/public/etd-373202299842941/etd.pdf Also contains a little note on combined slip with some constants, but I don't think it explains HOW! Anyone know this Pacejka method is in a book? These things should be published I guess. Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

Thanks Ruud, I have printed it out, but havent got to reading it yet, glad it turns out to be worth the read! Can you speed read or something! I dont know how you find the time to do all this stuff, I am starting to feel inadaquate ! :) Ash "Ruud van Gaal" <[email hidden]> wrote in message news:[email hidden]...

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| On Wed, 25 Jul 2001 12:08:53 +0100, "Ashley McConnell" | <[email hidden]> wrote: | | >Ruud, | > | >Is Pacekja '97 available anywhere on the web? (In English <g>) | | Couldn't find any. | | But here's the link (got it from the Racer forum) from the thesis | which talks about it and has some constant (with completely different | names): | http://www.lib.ncsu.edu/etd/public/etd-373202299842941/etd.pdf | | Also contains a little note on combined slip with some constants, but | I don't think it explains HOW! | Anyone know this Pacejka method is in a book? These things should be | published I guess. | | | Ruud van Gaal, GPL Rank +53.25 | Pencil art : http://www.marketgraph.nl/gallery/ | Free car sim : http://www.marketgraph.nl/gallery/racer/

On Wed, 25 Jul 2001 14:01:14 +0100, "Ashley McConnell" <[email hidden]> wrote: >Thanks Ruud, > >I have printed it out, but havent got to reading it yet, glad it turns out >to be worth the read! Can you speed read or something! I dont know how you >find the time to do all this stuff, I am starting to feel inadaquate ! :) Uhm, as I have little experience in Lagrangian stuff, I quickly skipped all the equations that are defined for all the body parts. And suddenly you end up in chapter 8 or so, the tire model. Skimming for familiar images works well btw. ;-) Skipping things you're bound not to understand really works. :) Then for subjects you want to learn about, read a bit of it. Then proceed to do things you do understand. Then later, get back to the original 'new' text, and it will begin to make a little more sense. As you peddle along, all things will begin to get clearer in time. But I don't stop when I don't understand some things, I just proceed with things I do understand. The gaps will fill them in by themselves, when you at least glance at papers you have lying around every now & then. I hate diving to deep into stuff. Let the right side of the mind have some time, it will deal with it when you're least aware of it. Hope this doesn't drive you insane, :) Ruud Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/