Car phyics; wheel angular acceleration

Hi all, Some time ago (11-8-00), Todd Wasson wrote something about wheel angular acceleration. The problem was: a torque is put on the wheel axle by the engine, what will the wheel angular acceleration be? (problem is that is pushes a body, and tries to linearly accelerate the wheel itself, and tries to rotate the wheel, which is affected by inertia). Quoting Todd: This isn't hard. Let the wheel accelerate according to torque and moment of inertia without worrying about "excess" torque. The longitudinal force (and torque transmitted from the road to the tire, which opposes the rotation), will be generated by the slip ratio. Slip ratio is the ratio between the actual rotation speed and the rotation speed the tire would have if it was free rolling. You can then enter a slip ratio curve for a real tire and the wheel will lock and spin when enough braking or driving torque is applied. End qoute. Now with my RCVD book and renewed looks at tire physics, I've created a curve editor and have a slipRatio vs. traction force curve in my wheel class (and another one for braking force). And ofcourse stumbled on the problem that was discussed at that time, namely how fast will the wheel accelerate. How nice, these archives (and the more I learn about tire physics, the more I understand precisely what was said at those times). I am unsure of where I should put in the rotational damping of the wheel. On page 37 of RCVD (Race Car Vehicle Dynamics), it says, "Prior to the peak [of longitudinal force], an increase in slip gives an increased force which tends to damp the rotational velocity." It does not state what 'tends' means in terms of numbers/equations. If I do the following for a wheel: - calculate inertia of wheel, for now I take this to be a constant, using mass*radius^2 (all mass at outside of wheel) - torque is generated at the engine - torque*gear_ratios = torque at wheel axle - force at the contact patch (Fcp) = torque/radius (where radius=loaded radius actually, or am I better off using the undeflected radius of the wheel?) - angular_acceleration = torque / inertia (because like F=m*a, torque=inerta*ang_acc) Now the longitudinal force is calc'd using slip ratio: SR=ang_acc*radius_loaded/V-1 where V=actual wheel velocity (in the forward direction, or V*cos(slipAngle) if not). (I use the Calspan TIRF slip ratio because of being able to use radius_loaded instead of radius_effective, which I don't know how to calculate) Resulting long. force (Ft) = curve->GetValue(SR) (where curve is different for tractive forces and braking forces, Ft=tractive force in this case) So far so good, but there is a feedback of Ft somewhere that slows the ang. acceleration of the wheel down (otherwise the wheel would spin very quickly). Am I right into assuming to do this: - torque is generated at the engine - torque*gear_ratios = torque at wheel axle - force at the contact patch (Fcp) = torque/radius - subtract the current Ft from Fcp to account for the rotational 'damping'. - calculate net torque for wheel as: netTorque=(Fcp-Ft)*radius_loaded - angular_acceleration = netTorque / inertia It's hard for me to visualize correctly that this will result in a gradual acceleration of the wheel. On the other hand, it seems the slipratio curve models quite a few parameters at the same time, so I might just need to trust the equations and go ahead (my guts say it might need a bit more simulation frequency though; I now use 100Hz). Which I probably will, but it is still difficult to 'feel' slipping behavior going on without sound. I've looked at DirectSound (3D), which looks very nice and reasonably CPU-friendly, so I'll go for that instead of cooking up my own (which has terrible aliasing right now on the SGI). Sound from the tires are an entirely different field, I realise, but probably I'm not far off if I do: - no squeaks until slipRatio gets near its force peak - sound gets louder with higher slipratios, until a maximum (for example, SAE's slipping definition, SR=1) where it doesn't get louder anymore. - sound pitch, hm, I'll start up GPL for some empirical tests. And I should visit www.openal.org one more time to see how they do things (OpenAL is ofcourse a bit more open, so I can get the 3D sound working on SGI's too, although now with my MSFF support on Win32, the SGI version is getting less and less interesting). Thanks for any ideas on the wheel ang.acc. force damping issue, in the mean time I'm reading on about aerodynamics, and have ordered "Fundamentals of vehicle dynamics" by Gillespie, I think. Should give even more (basic) information about tires and such. For example how to visualize low-speed wheel rotation correctly (where I should do a spring model most probably). Ruud van Gaal, GPL Rank +53.25 MarketGraph : http://www.marketgraph.nl Pencil art : http://www.marketgraph.nl/gallery/ Car simulation: http://www.marketgraph.nl/gallery/racer/

Ruud van Gaal <[email hidden]> wrote: : If I do the following for a wheel: : - calculate inertia of wheel, for now I take this to be a constant, : using mass*radius^2 (all mass at outside of wheel) Um... all mass isn't at the outside of the wheel though. You're going to hugely overestimate the moment of inertia (MI) if you do that. In general, however, for a race vehicle I'd say you'd be not far off if you simply ignored the MI of the wheel. It's really quite minor compared with the force being used to accelerate the car. I spent ages looking at a mathsy problem involving squat in motorbikes and came to the conclusion that essentially, MI of the wheel can effectively be ignored. (Standard text books on the subject do this all the time but simply don't tell you that they're doing so). Think of your car up on jacks with the wheel off the ground and the car in neutral. You can quite simply rotate the wheel with your hand - it doesn't require that much force. The MI of the wheel is only going to be relevant when the wheel is off the ground and then, quite frankly, who really cares how fast it's going? Anyway, my conclusion is that you can make your maths a lot simpler by ignoring the moment of inertia of the wheel entirely and your errors will be down at the 0.1% level or less. -- Richard G. Clegg Only the mind is waving Networks and Non-Linear Dynamics Group Dept. of Mathematics, Uni. of York UPDATED WWW: http://manor.york.ac.uk/

On 19 Sep 2000 11:52:38 GMT, Richard G Clegg <[email hidden]> wrote:

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>Ruud van Gaal <[email hidden]> wrote: > >: If I do the following for a wheel: > >: - calculate inertia of wheel, for now I take this to be a constant, >: using mass*radius^2 (all mass at outside of wheel) > > Um... all mass isn't at the outside of the wheel though. You're going >to hugely overestimate the moment of inertia (MI) if you do that.

Perhaps I'll use a different inertia then. The 'filled cylinder' for example, where mass is present in all parts. > In general, >however, for a race vehicle I'd say you'd be not far off if you simply >ignored the MI of the wheel. It's really quite minor compared with the >force being used to accelerate the car. Hm, but when I'm floating in the air, I need *some* inertia to calculate the wheel acceleration. Otherwise acceleration will be infinite (dividing by 0). And when standing still, the first acceleration done will be with no longitudinal force holding the wheel back, so in that case too, inertia is the only thing keeping the wheel from accelerating infinitely.

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> I spent ages looking at a mathsy problem involving squat in motorbikes >and came to the conclusion that essentially, MI of the wheel can effectively >be ignored. (Standard text books on the subject do this all the time >but simply don't tell you that they're doing so). Think of your car up >on jacks with the wheel off the ground and the car in neutral. You can >quite simply rotate the wheel with your hand - it doesn't require that >much force. The MI of the wheel is only going to be relevant when the >wheel is off the ground and then, quite frankly, who really cares how >fast it's going?

I care once it touches the ground again. :) In GPL, the Ring, there a place, I believe it's called Flugplatz (well, I *would* have it called it that lol), where you temporarily leave the ground, and it is quite important to keep the tires rolling quite the same speed as when you left the ground, otherwise instability occurs when you land back on your feet. Making sure not too shoot your rear wheels out from under your car and sweep into the hill that follows closely. :) > Anyway, my conclusion is that you can make your maths a lot simpler by >ignoring the moment of inertia of the wheel entirely and your errors >will be down at the 0.1% level or less. I will remember that, but when weight transfer happens, the inner wheel inertia's will probably suddenly have much more of an impact on that percentage. (they get closer and closer to the situation where the wheel is in the air) Ruud van Gaal, GPL Rank +53.25 MarketGraph : http://www.marketgraph.nl Pencil art : http://www.marketgraph.nl/gallery/ Car simulation: http://www.marketgraph.nl/gallery/racer/

Ruud, Give me a shout when you are starting these Car Physics threads. Its hard for me to keep up :) I am listening with great interest as I too have starting researching car physics and I am hopefully about to start a model. Its great to see so much interest in R.A.S :) Ash "Ruud van Gaal" <[email hidden]> wrote in message news:[email hidden]...

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| Hi all, | | Some time ago (11-8-00), Todd Wasson wrote something about wheel | angular acceleration. The problem was: a torque is put on the wheel | axle by the engine, what will the wheel angular acceleration be? | (problem is that is pushes a body, and tries to linearly accelerate | the wheel itself, and tries to rotate the wheel, which is affected by | inertia). | | Quoting Todd: | | This isn't hard. Let the wheel accelerate according to torque and | moment of inertia without worrying about "excess" torque. The | longitudinal force (and torque transmitted from the road to the tire, | which opposes the rotation), will be generated by the slip ratio. | Slip ratio is the ratio between the actual rotation speed and the | rotation speed the tire would have if it was free rolling. | | You can then enter a slip ratio curve for a real tire and the wheel | will lock and spin when enough braking or driving torque is applied. | | End qoute. | | Now with my RCVD book and renewed looks at tire physics, I've created | a curve editor and have a slipRatio vs. traction force curve in my | wheel class (and another one for braking force). And ofcourse stumbled | on the problem that was discussed at that time, namely how fast will | the wheel accelerate. How nice, these archives (and the more I learn | about tire physics, the more I understand precisely what was said at | those times). | | I am unsure of where I should put in the rotational damping of the | wheel. On page 37 of RCVD (Race Car Vehicle Dynamics), it says, "Prior | to the peak [of longitudinal force], an increase in slip gives an | increased force which tends to damp the rotational velocity." | It does not state what 'tends' means in terms of numbers/equations. | | If I do the following for a wheel: | | - calculate inertia of wheel, for now I take this to be a constant, | using mass*radius^2 (all mass at outside of wheel) | | - torque is generated at the engine | - torque*gear_ratios = torque at wheel axle | - force at the contact patch (Fcp) = torque/radius | (where radius=loaded radius actually, or am I better off using the | undeflected radius of the wheel?) | - angular_acceleration = torque / inertia (because like F=m*a, | torque=inerta*ang_acc) | | Now the longitudinal force is calc'd using slip ratio: | SR=ang_acc*radius_loaded/V-1 | where V=actual wheel velocity (in the forward direction, or | V*cos(slipAngle) if not). | (I use the Calspan TIRF slip ratio because of being able to use | radius_loaded instead of radius_effective, which I don't know how to | calculate) | | Resulting long. force (Ft) = curve->GetValue(SR) | (where curve is different for tractive forces and braking forces, | Ft=tractive force in this case) | | So far so good, but there is a feedback of Ft somewhere that slows the | ang. acceleration of the wheel down (otherwise the wheel would spin | very quickly). Am I right into assuming to do this: | | - torque is generated at the engine | - torque*gear_ratios = torque at wheel axle | - force at the contact patch (Fcp) = torque/radius | - subtract the current Ft from Fcp to account for the rotational | 'damping'. | - calculate net torque for wheel as: | netTorque=(Fcp-Ft)*radius_loaded | - angular_acceleration = netTorque / inertia | | It's hard for me to visualize correctly that this will result in a | gradual acceleration of the wheel. On the other hand, it seems the | slipratio curve models quite a few parameters at the same time, so I | might just need to trust the equations and go ahead (my guts say it | might need a bit more simulation frequency though; I now use 100Hz). | Which I probably will, but it is still difficult to 'feel' slipping | behavior going on without sound. I've looked at DirectSound (3D), | which looks very nice and reasonably CPU-friendly, so I'll go for that | instead of cooking up my own (which has terrible aliasing right now on | the SGI). | Sound from the tires are an entirely different field, I realise, but | probably I'm not far off if I do: | - no squeaks until slipRatio gets near its force peak | - sound gets louder with higher slipratios, until a maximum (for | example, SAE's slipping definition, SR=1) where it doesn't get louder | anymore. | - sound pitch, hm, I'll start up GPL for some empirical tests. | And I should visit www.openal.org one more time to see how they do | things (OpenAL is ofcourse a bit more open, so I can get the 3D sound | working on SGI's too, although now with my MSFF support on Win32, the | SGI version is getting less and less interesting). | | Thanks for any ideas on the wheel ang.acc. force damping issue, in the | mean time I'm reading on about aerodynamics, and have ordered | "Fundamentals of vehicle dynamics" by Gillespie, I think. Should give | even more (basic) information about tires and such. For example how to | visualize low-speed wheel rotation correctly (where I should do a | spring model most probably). | | | Ruud van Gaal, GPL Rank +53.25 | MarketGraph : http://www.marketgraph.nl | Pencil art : http://www.marketgraph.nl/gallery/ | Car simulation: http://www.marketgraph.nl/gallery/racer/

On Wed, 20 Sep 2000 10:16:31 +0100, "Ashley McConnell" <[email hidden]> wrote: >Ruud, > >Give me a shout when you are starting these Car Physics threads. Its hard >for me to keep up :) Lol. For clarity, I prefix all posts with "Car physics", although this thread has a typo, but it would just complicate archiving to correct it! ;-) >I am listening with great interest as I too have starting researching car >physics and I am hopefully about to start a model. Its great to see so much >interest in R.A.S :) Yes, and very helpful too. :) Good luck on your model, and check deja for some long threads with 'car physics' in RAS from the last 2 months. A lot of people are simulating cars, though with differing goals. I still don't have a too-clear goal. Going for GPL is probably a waste of time (it's doing ok as it is), it must do things that GPL does not. Like a ghost car :) Fun and interest are my main keywords for now. Ruud van Gaal, GPL Rank +53.25 MarketGraph : http://www.marketgraph.nl Pencil art : http://www.marketgraph.nl/gallery/ Car simulation: http://www.marketgraph.nl/gallery/racer/

>I am unsure of where I should put in the rotational damping of the >wheel. On page 37 of RCVD (Race Car Vehicle Dynamics), it says, "Prior >to the peak [of longitudinal force], an increase in slip gives an >increased force which tends to damp the rotational velocity." >It does not state what 'tends' means in terms of numbers/equations. > Remember the discussion on torque **from the road to the tire**? This torque FIGHTS the driving torque at the wheel. Prior to the peak, if the actual tire/belt velocity is constant and you attempt to speed up the wheel, this torque that FIGHTS the driving torque keeps increasing until the maximum torque/force the tire can make is reached. After this point, the torque that FIGHTS the driving torque decreases as the tire spins faster. (From the graph on page 38, look at Figure 2.16) Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

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> If I do the following for a wheel: > >: - calculate inertia of wheel, for now I take this to be a constant, >: using mass*radius^2 (all mass at outside of wheel) > > Um... all mass isn't at the outside of the wheel though. You're going >to hugely overestimate the moment of inertia (MI) if you do that. In general, >however, for a race vehicle I'd say you'd be not far off if you simply >ignored the MI of the wheel. It's really quite minor compared with the >force being used to accelerate the car. > > I spent ages looking at a mathsy problem involving squat in motorbikes >and came to the conclusion that essentially, MI of the wheel can effectively >be ignored. (Standard text books on the subject do this all the time >but simply don't tell you that they're doing so). Think of your car up >on jacks with the wheel off the ground and the car in neutral. You can >quite simply rotate the wheel with your hand - it doesn't require that >much force. The MI of the wheel is only going to be relevant when the >wheel is off the ground and then, quite frankly, who really cares how >fast it's going? > > Anyway, my conclusion is that you can make your maths a lot simpler by >ignoring the moment of inertia of the wheel entirely and your errors >will be down at the 0.1% level or less.

May I jump in here? I agree with you Richard by the effect being very small on overall acceleration. In addition to what Ruud said about his airborne wheels, I'd like to point out that if someone wishes to model wheelspin, it's important to have a polar moment of inertia present or the acceleration will be infinite. Again, I'd like to agree with you in that if you are NOT concerned with wheelspin, the actual effect of the polar moment of inertia of the wheels on total vehicle acceleration is very small. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

On 21 Sep 2000 05:02:15 GMT, [email hidden] (J. Todd Wasson) wrote: ...

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>> Anyway, my conclusion is that you can make your maths a lot simpler by >>ignoring the moment of inertia of the wheel entirely and your errors >>will be down at the 0.1% level or less. > > May I jump in here? I agree with you Richard by the effect being very small >on overall acceleration. In addition to what Ruud said about his airborne >wheels, I'd like to point out that if someone wishes to model wheelspin, it's >important to have a polar moment of inertia present or the acceleration will be >infinite.

Yup, I thought I pointed that out in my post. Even more so, my wheels are now moving detached from the car (adding the same rotation/translation as the car, as long as they're attached; still I might go back to putting the wheels in the car hierarchy, because this takes calculations and I could also just decouple the wheel from the car in rotational/translational sense when the wheel actually comes loose, thus saving precious transformation time in the usual case where the wheel is attached), so I can more easily unhook them if you bump them too hard (oh no, collision detection, another infinite area). In that case, a loose running wheel will have LOTS to do with its inertia. Ruud van Gaal, GPL Rank +53.25 MarketGraph : http://www.marketgraph.nl Pencil art : http://www.marketgraph.nl/gallery/ Car simulation: http://www.marketgraph.nl/gallery/racer/

On 21 Sep 2000 04:53:53 GMT, [email hidden] (J. Todd Wasson) wrote:

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>>I am unsure of where I should put in the rotational damping of the >>wheel. On page 37 of RCVD (Race Car Vehicle Dynamics), it says, "Prior >>to the peak [of longitudinal force], an increase in slip gives an >>increased force which tends to damp the rotational velocity." >>It does not state what 'tends' means in terms of numbers/equations. > > Remember the discussion on torque **from the road to the tire**? This torque >FIGHTS the driving torque at the wheel.

Yup, after your verbose explanation, I now have it working in software. :) Thanks! Ruud van Gaal, GPL Rank +53.25 MarketGraph : http://www.marketgraph.nl Pencil art : http://www.marketgraph.nl/gallery/ Car simulation: http://www.marketgraph.nl/gallery/racer/