Re: Car Physics : The Pacekja "Magic" Tyre Formula

Seems a little high for plysteer and conicity, but not out of the question. Are you calculating aligning torque? If so, there should also be some offset in that (AT <> 0 when lateral force = 0). This is sometimes called residual self aligning torque (RSAT). No more email from me this week -- it's time for the SAE Motorsports Engineering Conference in Detroit, schedule of papers is somewhere on the SAE site <www.sae.org>. -- Doug Douglas Milliken <[email hidden]> Milliken Research Associates Inc. On Mon, 13 Nov 2000, Ashley McConnell wrote:

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> Hi Folks, > > Sorry this is a bit off-topic, but I know some Car Physics gurus dwell in > these parts :). I am having a bit of trouble with the Pacejka formula. I > am currently reading G.Genta's car dynamics book and I am trying to program > a "simple" function that takes the sideslipangle and returns the Lateral > force (Fy). > > The problem is that when the sideslipangle is zero it produces at lateral > force of -198N (ish). I have used the data (coefficients a0-a13) from the > appendix of the book. I have tried to calculate it manually and I still > get -198N. I am using an Fz of around 3.6kN (just the weight of the car > divided in 4 as a first approximation) and I am assuming a Zero Camber > angle. > > Could this be the force due to Ply Steer and Conicity? It seems rather > high. There is also a small -ve value of Mz (around -2 from memory). > > Does this ring a bell with anyone, have I overlooked something very > fundamental - I AM only learning please dont be too hard on me :) > > If anyone would like more information I would be only too willling to give > it. I have my code and the data file if needed (I didnt want to post an > attachment). > > Thanks for the help folks > Ashley > > PS. I have managed to get the Longitudnal Slip -> Fx formula working > properly (at least!) > > > >

Hi Folks, Sorry this is a bit off-topic, but I know some Car Physics gurus dwell in these parts :). I am having a bit of trouble with the Pacejka formula. I am currently reading G.Genta's car dynamics book and I am trying to program a "simple" function that takes the sideslipangle and returns the Lateral force (Fy). The problem is that when the sideslipangle is zero it produces at lateral force of -198N (ish). I have used the data (coefficients a0-a13) from the appendix of the book. I have tried to calculate it manually and I still get -198N. I am using an Fz of around 3.6kN (just the weight of the car divided in 4 as a first approximation) and I am assuming a Zero Camber angle. Could this be the force due to Ply Steer and Conicity? It seems rather high. There is also a small -ve value of Mz (around -2 from memory). Does this ring a bell with anyone, have I overlooked something very fundamental - I AM only learning please dont be too hard on me :) If anyone would like more information I would be only too willling to give it. I have my code and the data file if needed (I didnt want to post an attachment). Thanks for the help folks Ashley PS. I have managed to get the Longitudnal Slip -> Fx formula working properly (at least!)

Whoa! Nice to have you visit this newsgroup Mr. Milliken! When I saw your name in the posting, wasn't sure, but the SAE is a dead giveaway :) Playing any sims lately? Doug Milliken wrote:

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> > Seems a little high for plysteer and conicity, but not out of the question. > Are you calculating aligning torque? If so, there should also be some > offset in that (AT <> 0 when lateral force = 0). This is sometimes > called residual self aligning torque (RSAT). > > No more email from me this week -- it's time for the SAE Motorsports > Engineering Conference in Detroit, schedule of papers is somewhere on the > SAE site <www.sae.org>. > > -- Doug > Douglas Milliken <[email hidden]> > Milliken Research Associates Inc. > > On Mon, 13 Nov 2000, Ashley McConnell wrote: > > > Hi Folks, > > > > Sorry this is a bit off-topic, but I know some Car Physics gurus dwell in > > these parts :). I am having a bit of trouble with the Pacejka formula. I > > am currently reading G.Genta's car dynamics book and I am trying to program > > a "simple" function that takes the sideslipangle and returns the Lateral > > force (Fy). > > > > The problem is that when the sideslipangle is zero it produces at lateral > > force of -198N (ish). I have used the data (coefficients a0-a13) from the > > appendix of the book. I have tried to calculate it manually and I still > > get -198N. I am using an Fz of around 3.6kN (just the weight of the car > > divided in 4 as a first approximation) and I am assuming a Zero Camber > > angle. > > > > Could this be the force due to Ply Steer and Conicity? It seems rather > > high. There is also a small -ve value of Mz (around -2 from memory). > > > > Does this ring a bell with anyone, have I overlooked something very > > fundamental - I AM only learning please dont be too hard on me :) > > > > If anyone would like more information I would be only too willling to give > > it. I have my code and the data file if needed (I didnt want to post an > > attachment). > > > > Thanks for the help folks > > Ashley > > > > PS. I have managed to get the Longitudnal Slip -> Fx formula working > > properly (at least!) > > > > > > > >

-- Philippe "Philster" Sergerie

Holy crap !!! My head hurts, I'm going to read "Brief history of time" to settle down a bit. Then I'm gonna watch some cartoons....... "Ashley McConnell" <[email hidden]> wrote in message news:8up0kf$f87$[email hidden]... > Hi Folks, > > Sorry this is a bit off-topic, but I know some Car Physics gurus dwell in > these parts :). I am having a bit of trouble with the Pacejka formula. I > am currently reading G.Genta's car dynamics book and I am trying toprogram

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> a "simple" function that takes the sideslipangle and returns the Lateral > force (Fy). > > The problem is that when the sideslipangle is zero it produces at lateral > force of -198N (ish). I have used the data (coefficients a0-a13) from the > appendix of the book. I have tried to calculate it manually and I still > get -198N. I am using an Fz of around 3.6kN (just the weight of the car > divided in 4 as a first approximation) and I am assuming a Zero Camber > angle. > > Could this be the force due to Ply Steer and Conicity? It seems rather > high. There is also a small -ve value of Mz (around -2 from memory). > > Does this ring a bell with anyone, have I overlooked something very > fundamental - I AM only learning please dont be too hard on me :) > > If anyone would like more information I would be only too willling to give > it. I have my code and the data file if needed (I didnt want to post an > attachment). > > Thanks for the help folks > Ashley > > PS. I have managed to get the Longitudnal Slip -> Fx formula working > properly (at least!) > >

Hi Doug, Its great to hear from someone who completely knows his stuff and is willing to help! I do indeed attempt to calculate the Aligning torque (Mz) - unfortunately (?) it also comes up with a negative value - around -2Nm if I recall correctly. The car that the data is associated with is a Ferrari 355 (well it doesnt say, but its obvious from its outline). Would this more powerful car tend to have any more ply steer? If this was ply steer (198N) would it be applied in opposite directions for the left and right wheels? I would have thought that -198N would be a 198N force to the RIGHT applied to both wheels (when there is no sideslip angle for either wheel). Does anyone have any example values for the Pacekja formula that definitely produce no ply steer (i.e. the values a0-a13, b0-bx and c0-cx)? Thanks for the help Ashley Here is the data I used: - 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 0.310 //Rolling_Radius "Doug Milliken" <[email hidden]> wrote in message news:[email hidden]... | | Seems a little high for plysteer and conicity, but not out of thequestion.

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| Are you calculating aligning torque? If so, there should also be some | offset in that (AT <> 0 when lateral force = 0). This is sometimes | called residual self aligning torque (RSAT). | | No more email from me this week -- it's time for the SAE Motorsports | Engineering Conference in Detroit, schedule of papers is somewhere on the | SAE site <www.sae.org>. | | -- Doug | Douglas Milliken <[email hidden]> | Milliken Research Associates Inc. | | | | On Mon, 13 Nov 2000, Ashley McConnell wrote: | | > Hi Folks, | > | > Sorry this is a bit off-topic, but I know some Car Physics gurus dwell

in | > these parts :). I am having a bit of trouble with the Pacejka formula.I | > am currently reading G.Genta's car dynamics book and I am trying toprogram | > a "simple" function that takes the sideslipangle and returns the Lateral | > force (Fy). | > | > The problem is that when the sideslipangle is zero it produces atlateral | > force of -198N (ish). I have used the data (coefficients a0-a13) fromthe

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| > appendix of the book. I have tried to calculate it manually and I still | > get -198N. I am using an Fz of around 3.6kN (just the weight of the car | > divided in 4 as a first approximation) and I am assuming a Zero Camber | > angle. | > | > Could this be the force due to Ply Steer and Conicity? It seems rather | > high. There is also a small -ve value of Mz (around -2 from memory). | > | > Does this ring a bell with anyone, have I overlooked something very | > fundamental - I AM only learning please dont be too hard on me :) | > | > If anyone would like more information I would be only too willling to

give

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| > it. I have my code and the data file if needed (I didnt want to post an | > attachment). | > | > Thanks for the help folks | > Ashley | > | > PS. I have managed to get the Longitudnal Slip -> Fx formula working | > properly (at least!) | > | > | > | > |

I know - scary stuff :) nice email address btw :) - indeed they do Ash "Incubus" <[email hidden]> wrote in message news:7b5Q5.31605$[email hidden]...

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| Holy crap !!! | | My head hurts, I'm going to read "Brief history of time" to settle down a | bit. | | Then I'm gonna watch some cartoons....... | |

SAE Motor Sports conference (just got home) was great. Look in various racing magazines for coverage in a month or three... I never knew that David Hobbs was so funny -- he was the speaker after the banquet dinner and everyone in the place was rotf. ---- Plysteer works like a screw thread -- doesn't matter which way the tire is mounted, it always pulls left (or maybe right), depending on which way the cords are wound in the belt (and probably some other details of the tire construction). Same as if you rotate a nut around and then thread it on the bolt -- still turns the same way to tighten it. Conicity will change from + to - when the tire is rotated the other way. It can be pretty large, especially with wide tires (like these). It's rare to find a tire that has no plysteer or conicity. Sight along the side of cars that you follow on the highway, you will see that most of them "crab track" a little bit, this is usually due to tire asymmetry. Usually the rear axle is to the right of the front axle (at least in USA). Often easy to see on pick-up trucks, where there is more of the tire visible from the rears. Thanks for posting that data, I checked it against my copy of the book and didn't see any typos. Of course there could be an error in the book, so maybe someone can find an email for Genta and ask? Why not try with some of the other tire data he offers?, and please report your findings to ras. -- Doug Douglas Milliken <[email hidden]> Milliken Research Associates Inc. On Tue, 14 Nov 2000, Ashley McConnell wrote:

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> Hi Doug, > > Its great to hear from someone who completely knows his stuff and is willing > to help! > > I do indeed attempt to calculate the Aligning torque (Mz) - unfortunately > (?) it also comes up with a negative value - around -2Nm if I recall > correctly. The car that the data is associated with is a Ferrari 355 (well > it doesnt say, but its obvious from its outline). Would this more powerful > car tend to have any more ply steer? > > If this was ply steer (198N) would it be applied in opposite directions for > the left and right wheels? I would have thought that -198N would be a 198N > force to the RIGHT applied to both wheels (when there is no sideslip angle > for either wheel). > > Does anyone have any example values for the Pacekja formula that definitely > produce no ply steer (i.e. the values a0-a13, b0-bx and c0-cx)? > > Thanks for the help > Ashley > > Here is the data I used: - > > 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 > 0.310 //Rolling_Radius > > > "Doug Milliken" <[email hidden]> wrote in message > news:[email hidden]... > | > | Seems a little high for plysteer and conicity, but not out of the > question. > | Are you calculating aligning torque? If so, there should also be some > | offset in that (AT <> 0 when lateral force = 0). This is sometimes > | called residual self aligning torque (RSAT). > | > | No more email from me this week -- it's time for the SAE Motorsports > | Engineering Conference in Detroit, schedule of papers is somewhere on the > | SAE site <www.sae.org>. > | > | -- Doug > | Douglas Milliken <[email hidden]> > | Milliken Research Associates Inc. > | > | > | > | On Mon, 13 Nov 2000, Ashley McConnell wrote: > | > | > Hi Folks, > | > > | > Sorry this is a bit off-topic, but I know some Car Physics gurus dwell > in > | > these parts :). I am having a bit of trouble with the Pacejka formula. > I > | > am currently reading G.Genta's car dynamics book and I am trying to > program > | > a "simple" function that takes the sideslipangle and returns the Lateral > | > force (Fy). > | > > | > The problem is that when the sideslipangle is zero it produces at > lateral > | > force of -198N (ish). I have used the data (coefficients a0-a13) from > the > | > appendix of the book. I have tried to calculate it manually and I still > | > get -198N. I am using an Fz of around 3.6kN (just the weight of the car > | > divided in 4 as a first approximation) and I am assuming a Zero Camber > | > angle. > | > > | > Could this be the force due to Ply Steer and Conicity? It seems rather > | > high. There is also a small -ve value of Mz (around -2 from memory). > | > > | > Does this ring a bell with anyone, have I overlooked something very > | > fundamental - I AM only learning please dont be too hard on me :) > | > > | > If anyone would like more information I would be only too willling to > give > | > it. I have my code and the data file if needed (I didnt want to post an > | > attachment). > | > > | > Thanks for the help folks > | > Ashley > | > > | > PS. I have managed to get the Longitudnal Slip -> Fx formula working > | > properly (at least!) > | > > | > > | > > | > > | > > > >

Doug Milliken wrote:

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> > It's rare to find a tire that has no plysteer or conicity. Sight along the > side of cars that you follow on the highway, you will see that most of them > "crab track" a little bit, this is usually due to tire asymmetry. Usually > the rear axle is to the right of the front axle (at least in USA). Often > easy to see on pick-up trucks, where there is more of the tire visible from > the rears.

Wow. I've noticed this before, but thought I must be seeing things! :) -- PD

On Sat, 18 Nov 2000, Grant Reeve wrote:

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> Pat Dotson wrote: > > > > Doug Milliken wrote: > > > > > > It's rare to find a tire that has no plysteer or conicity. Sight along the > > > side of cars that you follow on the highway, you will see that most of them > > > "crab track" a little bit, this is usually due to tire asymmetry. Usually > > > the rear axle is to the right of the front axle (at least in USA). Often > > > easy to see on pick-up trucks, where there is more of the tire visible from > > > the rears. > > > > Wow. I've noticed this before, but thought I > > must be seeing things! :) > > > I imagined this effect was just due to bad alignments with uneven toe settings > more than tire asymmetry. After all, how many people out there on the roads > bother checking their alignments more than once per forever?

Two reasons I think this is mostly due to tire effects: - I'm pretty sure that just about all tires have belts 'wound' in the same direction (plysteer the same way for nearly all) - At least in the USA, nearly all the crabbing is the same direction. Seems to me that if it was alignment, then it would be more random? I've not seen any studies on this, so it's all "educated speculation",

From Google with: +genta +"vehicle dynamics" Try this link, which includes an email address... <http://www.interdip.polito.it/meccanica/English/staff/pers_hmpg_en/genta_en.htm> On Fri, 17 Nov 2000, Doug Milliken wrote: > > Thanks for posting that data, I checked it against my copy of the book > and didn't see any typos. Of course there could be an error in the book, > so maybe someone can find an email for Genta and ask?

Pat Dotson wrote:

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> > Doug Milliken wrote: > > > > It's rare to find a tire that has no plysteer or conicity. Sight along the > > side of cars that you follow on the highway, you will see that most of them > > "crab track" a little bit, this is usually due to tire asymmetry. Usually > > the rear axle is to the right of the front axle (at least in USA). Often > > easy to see on pick-up trucks, where there is more of the tire visible from > > the rears. > > Wow. I've noticed this before, but thought I > must be seeing things! :) >

I imagined this effect was just due to bad alignments with uneven toe settings more than tire asymmetry. After all, how many people out there on the roads bother checking their alignments more than once per forever?

Doug Milliken wrote:

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> > Two reasons I think this is mostly due to tire effects: > - I'm pretty sure that just about all tires have belts 'wound' in the > same direction (plysteer the same way for nearly all) > - At least in the USA, nearly all the crabbing is the same direction. > > Seems to me that if it was alignment, then it would be more random? > I've not seen any studies on this, so it's all "educated speculation",

Good point about the consistency of the crabbing direction. But I was also just thinking, since you mentioned that the rear tires seem to crab a little to the right of the front tires, that perhaps it's just an effect of the camber of the roads. Since American's drive on the right and the roads will be cambered to the right, to keep a car driving straight the driver would have to maintain a very slight slip angle to the left to prevent the car falling off the road? Next time I'm driving on some of the 4 lane highways around here the left lanes are often cambered to the left, so I'll check if cars are crabbing in the other direction.

Doug, Thanks very much for your help and your explanations, its great we have a community like "this", that people are willing to lend a hand. I hope I can do the same for someone else some day when I become a bit more knowledgeable. I'll get an email off to him, I hope he doesnt mind. BTW, I tried one other set of data from the book (I think it was the "Small FWD Car"), but it yielded similar (-ve Fy) results. Thanks again Ashley "Doug Milliken" <[email hidden]> wrote in message news:[email hidden]... | | From Google with: +genta +"vehicle dynamics" | | Try this link, which includes an email address... |<http://www.interdip.polito.it/meccanica/English/staff/pers_hmpg_en/genta_en .htm>

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| | | On Fri, 17 Nov 2000, Doug Milliken wrote: | | > | > Thanks for posting that data, I checked it against my copy of the book | > and didn't see any typos. Of course there could be an error in the

book, | > so maybe someone can find an email for Genta and ask? |