Car Physics: Suspension geometry

Well, it's been a while since a new physics thread has appeared so how's about this :- I've been thinking about suspension geometry lately and the path that it prescribes on the hub centre. Assuming that we don't want any forward / backward motion of the hub centre with up and down movements, the path of the hub centre with relation to the body is a 2d path. Assuming that this is correct, rather than waste all of that CPU power on constraining the links of the suspension in order to remove the 5 DOFs necessary, why not just move the wheel / hub through this path? Just food for thought, I know that Gregor is calculating all of the links realtime, and from the research that I have done into rigid body dynamics, closed-loop constraint systems are quite expensive CPU wise. Is there something that I am blatantely missing? Colin

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>Well, it's been a while since a new physics thread has appeared so >how's about this :- > >I've been thinking about suspension geometry lately and the path that >it prescribes on the hub centre. Assuming that we don't want any >forward / backward motion of the hub centre with up and down >movements, the path of the hub centre with relation to the body is a >2d path. Assuming that this is correct, rather than waste all of that >CPU power on constraining the links of the suspension in order to >remove the 5 DOFs necessary, why not just move the wheel / hub through >this path? > >Just food for thought, I know that Gregor is calculating all of the >links realtime, and from the research that I have done into rigid body >dynamics, closed-loop constraint systems are quite expensive CPU wise. > >Is there something that I am blatantely missing? >

Not missing anything at all as far as I can tell. I'm doing it just as you've described. The only possible drawback that I can see is that acceleration laterally of the wheel in relation to the body from lateral force at the contact patch (it can arc towards/away from the body since it's a 2-D path now) isn't accurately calculated as it would be with methods like Gregor uses. My method isn't as perfectly correct as it could be, but since compliance isn't modelled too often, even in really high end simulation, it's negligable enough to forget about in comparison imo. The only time I can see it making a difference is on suspension systems that are so wildly out of typical design that the wheels can travel further along the track width axis than they can vertically. Nobody does this in real cars anyway, so I plan to follow my current course. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

I think that for most all intents and purposes, this is the way to go, esp. if the forces in the links aren't directly relevant to you (and these can be tacked on independently afterwards). I did my system the way it is just to see if it works, but nothing special comes out of it (esp. as I currently waste in on a suspension as stiff as a Champ Car ;) ). -Gregor Colin Reed wrote:

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> > Well, it's been a while since a new physics thread has appeared so > how's about this :- > > I've been thinking about suspension geometry lately and the path that > it prescribes on the hub centre. Assuming that we don't want any > forward / backward motion of the hub centre with up and down > movements, the path of the hub centre with relation to the body is a > 2d path. Assuming that this is correct, rather than waste all of that > CPU power on constraining the links of the suspension in order to > remove the 5 DOFs necessary, why not just move the wheel / hub through > this path? > > Just food for thought, I know that Gregor is calculating all of the > links realtime, and from the research that I have done into rigid body > dynamics, closed-loop constraint systems are quite expensive CPU wise. > > Is there something that I am blatantely missing? > > Colin

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> Not missing anything at all as far as I can tell. I'm doing it just as > you've described. The only possible drawback that I can see is that > acceleration laterally of the wheel in relation to the body from lateral force > at the contact patch (it can arc towards/away from the body since it's a 2-D > path now) isn't accurately calculated as it would be with methods like Gregor > uses. My method isn't as perfectly correct as it could be, but since > compliance isn't modelled too often, even in really high end simulation, it's > negligable enough to forget about in comparison imo. The only time I can see > it making a difference is on suspension systems that are so wildly out of > typical design that the wheels can travel further along the track width axis > than they can vertically. Nobody does this in real cars anyway, so I plan to > follow my current course.

Well, seeing as I'm going for a 'game' simulation I don't think I would really have to worry about the lateral forces mentioned above. But if I do it right, I'll be able to have realtime editable suspension geometry with camber / caster / WPI / toe etc all calculated automatically :-) Colin

Colin Reed <[email hidden]> wrote in message news:[email hidden]... > Just food for thought, I know that Gregor is calculating all of the > links realtime, and from the research that I have done into rigidbody > dynamics, closed-loop constraint systems are quite expensive CPUwise. > > Is there something that I am blatantely missing? Out of curiosity, since I'm not into coding stuff, how much are you guys worrying about roll centre location and movement? Though that too could be pre-mapped in 2D... Jonny

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>Well, seeing as I'm going for a 'game' simulation I don't think I >would really have to worry about the lateral forces mentioned above. >But if I do it right, I'll be able to have realtime editable >suspension geometry with camber / caster / WPI / toe etc all >calculated automatically :-) > >Colin

Yes, the force effect is negligable. Even the SAE stuff online rarely tries to take it into account, and this is stuffed aimed at real life vehicle design for the most part. To get caster changes, you'll need to do forward and rearward motion of the wheel too. I've got camber and track width change with wheel travel, but toe change (bump steer) will require tie rod ends to be calculated too. Not something I've done just yet. Be warned, allowing the players to set up the car gets much more complicated to deal with when you go this route. Also, a lot of what people have learned about front/rear roll stiffness can go out the window when dynamic camber starts changing. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

I haven't got around to implementing suspension yet, but when I do I intend to do a full constraint system. I don't expect to gain anything much over the 2D system that you suggest, but the way I'm doing my modelling it should just be something that drops out of my rigid body simulator. My reason is that I don't only want to use it for suspension, but if I just develop a method of generally linking and constraining rigid bodies together (either with rigid links or springs) then it can also be used for other things (eg towing a trailer, or towing another car using tow rope). It also means it's not just limited to vehicle simulation, but any physics system involving linked rigid bodies. Just thought I'd add another perspective onto things. Mike. "Colin Reed" <[email hidden]> wrote in message news:[email hidden]...

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> Well, it's been a while since a new physics thread has appeared so > how's about this :- > > I've been thinking about suspension geometry lately and the path that > it prescribes on the hub centre. Assuming that we don't want any > forward / backward motion of the hub centre with up and down > movements, the path of the hub centre with relation to the body is a > 2d path. Assuming that this is correct, rather than waste all of that > CPU power on constraining the links of the suspension in order to > remove the 5 DOFs necessary, why not just move the wheel / hub through > this path? > > Just food for thought, I know that Gregor is calculating all of the > links realtime, and from the research that I have done into rigid body > dynamics, closed-loop constraint systems are quite expensive CPU wise. > > Is there something that I am blatantely missing? > > Colin

On 7 Aug 2001 21:53:39 -0700, [email hidden] (Colin Reed) wrote: >I've been thinking about suspension geometry lately and the path that >it prescribes on the hub centre. Assuming that we don't want any >forward / backward motion of the hub centre with up and down >movements, the path of the hub centre with relation to the body is a >2d path. You can still have fore/aft movement of the hub due to bushing compliance under acceleration and deceleration. I wouldn't model it in a Formula Ford sim, because of the low power and spherical bearings in the suspension, but a Gran Turismoish game with hopped up street cars would be more realistic if it was included. Bushing compliance is why static toe-out is so great on the front end of FWD street cars - they toe-in under power and toe-out under braking. -Scott Johnson "There is nothing, I think, more unfortunate than to have soft, chubby, fat-looking children who go to watch their school play basketball every Saturday and regard that as their week's exercise." - John F. Kennedy, 1962

> I think that for most all intents and purposes, this is the way to go, > esp. if the forces in the links aren't directly relevant to you (and > these can be tacked on independently afterwards). I did my system the > way it is just to see if it works, but nothing special comes out of it > (esp. as I currently waste in on a suspension as stiff as a Champ Car ;) > ). If you don't mind me asking Gregor, what method do you use for the constraints, I've looked into generalized coords and constraint forces but neither handle closed systems very well (plus I'm not very good with large matrices :-(). I've read some stuff on Lagrangian multipliers but that went straight over my head :-} I think I'll stick with the 2d method for the while until I find a system that satisfies my requirements. The best 'feeling' suspension that I have done so far was a system of two REALLY stiff springs for the two lower links with a macpherson strut connecting the wheel and body. 'Twas absolutely lovely, until you hit a wall or steep slope and the wheels exploded because the springs became unstable. (:-( deep sigh) I also had a system using the Dynamo dynamics package which looked really realistic but for some reason when specifying the inertia tensor using the correct method it would blow up and bodies of about 1000kg would make it totally upset :-( Colin P.s. Todd, when are we gonna be seeing some graphical shots of your sim, I'm really interested :-)

Hush, I'll tell you a little secret, don't say this to anyone ;). As you correctly said, Lagrangian mechanics would be the way to go. On the other hand, as my sim currently specializes in hard suspensions, and I cannot run it at much more than about 100Hz general frequency (due to the complex part based approach that takes too many cycles), I must neglect the mass properties of the wheel. Therefore, the suspension only acts to directly absorb the road forces on the wheel, which are not 'buffered' by the mass properties of the wheel. I therefore do as if I were calculating static loads on the suspension (a matrix inversion), and after I get the load on each of the links, the load on the spring-damper link gives the rate of change of the length of that link. I also take into account the rate of change on the steering link, and then I need to (iteratively, three iterations suffice) solve a nonlinear set of equations to find the velocity and angular velocity of the wheel mount. After that, I update the position and orientation of the wheel mount based on these velocities, but again need to solve a nonlinear system of equations to take into account any errors due to initial linear movement of the wheel mount. I repeat the procedure then. By not taking into account the mass of the wheel I'm not actually loosing much, and certainly nothing about car response. The only thing I am missing here is the high-frequency wheel hopping mode, as this one is eliminated. I could introduce accelerations of the wheel along the instantaneous travel axis, and as such take wheel hopping into account, but that would be somewhat faking it as not all forces would be properly taken into account should the link forces interest you (but would be almost perfectly well for almost any other application). I'll probably do a full Lagrangian picture in the future, it is definitely on my to-do list, but not anytime soon. I need to learn how to program more efficiently first :). Cheers, -Gregor Colin Reed wrote:

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> > If you don't mind me asking Gregor, what method do you use for the > constraints, I've looked into generalized coords and constraint forces > but neither handle closed systems very well (plus I'm not very good > with large matrices :-(). I've read some stuff on Lagrangian > multipliers but that went straight over my head :-} >

>Colin > >P.s. Todd, when are we gonna be seeing some graphical shots of your >sim, I'm really interested :-) > > Funny you should ask. I just put this up in this thread. Don't get excited, it's pretty ugly :-) I'll put up a couple more from outside one of the cars sometime soon. http://performancesimulations.com/scnshots.htm Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

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>> Just food for thought, I know that Gregor is calculating all of the >> links realtime, and from the research that I have done into rigid >body >> dynamics, closed-loop constraint systems are quite expensive CPU >wise. >> >> Is there something that I am blatantely missing? > >Out of curiosity, since I'm not into coding stuff, how much are you >guys worrying about roll centre location and movement? Though that >too could be pre-mapped in 2D...

I'm very concerned with it. After I get a few bugs worked out with what I have here and get some other stuff done, roll centers are going to be calculated on the fly in real time. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

It is interesting that you are only running at 100hz, I have my simulator cranked up to 240hz at the moment, I have the quaternions for each of the bodies double buffered which I then interpolate for the current frame, (makes for some really pretty replays :-)) The other thing that I was thinking about last night is that because 5 dofs are removed from a wheel that means I can effectively model the wheels with weighted 'fat' particles taking into account only the vertical velocity of the wheel, once the position has been decided, calculate the orientation. I really wish I had more time to work on this stuff, I am in crunch mode right now to finish my 'other' game for the GameCube launch here in Japan. Still I manage to get about an hour a day (whilst eating lunch) so that's not so bad. Colin

Hi Colin! Colin Reed wrote: > > It is interesting that you are only running at 100hz, I have my > simulator cranked up to 240hz at the moment, I have the quaternions > for each of the bodies double buffered which I then interpolate for > the current frame, (makes for some really pretty replays :-)) > I'm running at whatever is stable :). Seriously, I can run at 200Hz easily, but since I am optimizing stuff, sometimes it means that you are 'unoptimizing' it at times ;), it doesn't bring the game to a halt if that happens (I have my timing routines set so that they catch up with the system time, and if the calcs become too slow, this never happens and the program exits when the preset difference between real and simulation time is reached). Also, there is no diference in handling between the two, so I guess there is no need to waste more cycles on that. > The other thing that I was thinking about last night is that because 5 > dofs are removed from a wheel that means I can effectively model the > wheels with weighted 'fat' particles taking into account only the > vertical velocity of the wheel, once the position has been decided, > calculate the orientation. > Indeed. If you manage to find a path for the vehicle, and the orientation on the path, you solved the problem completely. The Lagrangian multilpliers are only used when you cannot solve for the explicit path and orientation, but if you can do that, you are set to rock :). It may be hard to do with the general suspensions, but with some compromises I'm sure it's possible. Be aware, though, that if you want to do things really properly, you must also take the changes of orientation and subsequent changes of dhe direction wheel angular momentum into account, and that is probably the hardest part (I do handle that in my sim, but I neglect the actuall mass of the wheels, which is indeed far less relevant). If you neglect this, though, things are much easier. > > I really wish I had more time to work on this stuff, I am in crunch > mode right now to finish my 'other' game for the GameCube launch here > in Japan. Still I manage to get about an hour a day (whilst eating > lunch) so that's not so bad. > Good luck with your game! Man, you've gone Japanese, haven't you, cramming all free time activities (such as eating etc. :) ) into one hour ;). Cheers, -Gregor

The roll centre description is a linear approximation to a full suspension system. If you build the latter properly, the roll centers etc. come automatically correct out of it. -Gregor Jonny Hodgson wrote: > > Out of curiosity, since I'm not into coding stuff, how much are you > guys worrying about roll centre location and movement? Though that > too could be pre-mapped in 2D... > > Jonny

On Fri, 10 Aug 2001 10:05:57 +0200, Gregor Veble <[email hidden]> wrote: >The roll centre description is a linear approximation to a full >suspension system. If you build the latter properly, the roll centers >etc. come automatically correct out of it. Yes well, they're static here. :) I was wondering, as a general rule, the front RC is lower than the rear (in racing), right? But is the rear RC generally lower or higher than the CG? Or are there indications of how much a RC generally is below the CG at the front or rear? This one is still an unknown one for me (as a lot of other parameters ;-)), and it seems like I could abuse the RC's height as a sort of anti-rollbar. Thanks, Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

On Fri, 10 Aug 2001 10:04:33 +0200, Gregor Veble <[email hidden]> wrote:

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>Hi Colin! > >Colin Reed wrote: >> >> It is interesting that you are only running at 100hz, I have my >> simulator cranked up to 240hz at the moment, I have the quaternions >> for each of the bodies double buffered which I then interpolate for >> the current frame, (makes for some really pretty replays :-)) >> > >I'm running at whatever is stable :). Seriously, I can run at 200Hz >easily,

Geez, the F1 cars and Kart cars people are making for Racer seem to need at least 1000Hz. I should really do something about that and have multiplying factors (or RK4 or midpoint things, see gdmag, april '99) in to get separate frequencies. Probably even dynamic ones depending on the spring constants (or when touching bumper stops). Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

Hi Ruud, that's because I don't take into account the mass of the wheels in suspension movement, that's all. Very stiff suspensions/tyres will move the wheel hopping mode to high frequencies, and if you want that in you'll need to run at approximately that frequency to keep it stable. No such problem when you neglect the mass and with it (only) this high frequency hopping mode. If you keep the wheels rigidly attached to the suspension (as in a Kart), the required frequency will be much less, as that eliminates the wheel hopping as well. -Gregor Ruud van Gaal wrote:

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> > Geez, the F1 cars and Kart cars people are making for Racer seem to > need at least 1000Hz. I should really do something about that and have > multiplying factors (or RK4 or midpoint things, see gdmag, april '99) > in to get separate frequencies. Probably even dynamic ones depending > on the spring constants (or when touching bumper stops). > > Ruud van Gaal, GPL Rank +53.25 > Pencil art : http://www.marketgraph.nl/gallery/ > Free car sim : http://www.marketgraph.nl/gallery/racer/

Ruud van Gaal <[email hidden]> wrote in message news:[email hidden]... > On Fri, 10 Aug 2001 10:05:57 +0200, Gregor Veble > <[email hidden]> wrote: > > >The roll centre description is a linear approximation to a full > >suspension system. If you build the latter properly, the rollcenters > >etc. come automatically correct out of it. Yup, I know this; I was wondering how much processing power you were throwing at doing this as opposed to hard-coding a suitable approximation ;-) > Yes well, they're static here. :) > I was wondering, as a general rule, the front RC is lower than the > rear (in racing), right? But is the rear RC generally lower orhigher > than the CG? Lower, I'm pretty sure. IIRC a modern slick-and-wings car tends to run front RC at ground level, rear maybe 50mm up; my 1/10th scale off-road buggy runs (very approximately) 3mm front, 7mm rear (this is a carpet setup; off-road uses a slightly higher rear I /think/). > Or are there indications of how much a RC generally is below the CGat > the front or rear? This one is still an unknown one for me (as a lot > of other parameters ;-)), and it seems like I could abuse the RC's > height as a sort of anti-rollbar. Yes you can, but this has at least two downsides. One, it can eliminate body roll in transients to the point where the driver has too little feedback; and two (which is more serious) it introduces large jacking effects. I suspect that the camber curves would also end up being far from optimal. HTH, Jonny

On Fri, 10 Aug 2001 21:50:42 +0100, "Jonny Hodgson" <[email hidden]> wrote:

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>> I was wondering, as a general rule, the front RC is lower than the >> rear (in racing), right? But is the rear RC generally lower or >higher >> than the CG? > >Lower, I'm pretty sure. IIRC a modern slick-and-wings car tends to >run front RC at ground level, rear maybe 50mm up; my 1/10th scale >off-road buggy runs (very approximately) 3mm front, 7mm rear (this is >a carpet setup; off-road uses a slightly higher rear I /think/).

Thanks, I'll try that in some F1 car I have here. >Yes you can, but this has at least two downsides. One, it can >eliminate body roll in transients to the point where the driver has >too little feedback; Not that in simming this is too much of an issue. :) > and two (which is more serious) it introduces >large jacking effects. I suspect that the camber curves would also >end up being far from optimal. That may be more severe, although jacking effects are still a bit implicit in my sim. Thanks for the info, Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

Here's a little RC info for F-1 cars: "This information was provided by M. Mazumdar from the USA. Regarding your discussion of roll centers and how much movement is permissible, I can tell you that current F-1 ,Indy and IRL cars tend to limit the movement of RC in the lateral & vert. directions to about 10 thousandths of an inch or less. Of course, the roll center moves vertically with the chassis. For one F-1 car from last year, the front RC was 6mm BELOW ground level and the rear about an inch ABOVE with a pitch sensitivity of 1:2 front to rear. Typical damper movements are 7mm or less for a F-1 car. Generally speaking, in F-1 front susp. rising rate is NOT used. Motion ratios tend to be 1 or greater. I can't recall exactly what the wheelrates are as of now but I will find out but they are pretty high. Indy cars tend to have different RC configurations as they run on 4 different courses. They generally run much stiffer at the front than at the rear. Wheelrates vary widely according to the type of course being run." Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com

On 13 Aug 2001 22:18:56 GMT, [email hidden] (J. Todd Wasson) wrote: >Regarding your discussion of roll centers and how much movement is permissible, >I can tell you that current F-1 ,Indy and IRL cars tend to limit the movement >of RC in the lateral & vert. directions to about 10 thousandths of an inch or >less. Of course, the roll center moves vertically with the chassis. For one F-1 >car from last year, the front RC was 6mm BELOW ground level and the rear about >an inch ABOVE with a pitch sensitivity of 1:2 front to rear. Thanks for the info! :) Seems dynamic rollcenters don't do too much here. Ruud van Gaal, GPL Rank +53.25 Pencil art : http://www.marketgraph.nl/gallery/ Free car sim : http://www.marketgraph.nl/gallery/racer/

Hi Todd, wow, good info, thanks for sharing it! It appears that the reports of understeer of modern F1 cars from certain F1 drivers are indeed true, considering how the roll centers need to pe positioned to cure that. Also, could you please explain the following statement, as I don't think I get it: "Generally speaking, in F-1 front susp. rising rate is NOT used." Does that mean that dampers are extremely soft on bump? -Gregor "J. Todd Wasson" wrote:

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> > Here's a little RC info for F-1 cars: > > "This information was provided by M. Mazumdar from the USA. > > Regarding your discussion of roll centers and how much movement is permissible, > I can tell you that current F-1 ,Indy and IRL cars tend to limit the movement > of RC in the lateral & vert. directions to about 10 thousandths of an inch or > less. Of course, the roll center moves vertically with the chassis. For one F-1 > car from last year, the front RC was 6mm BELOW ground level and the rear about > an inch ABOVE with a pitch sensitivity of 1:2 front to rear. Typical damper > movements are 7mm or less for a F-1 car. Generally speaking, in F-1 front susp. > rising rate is NOT used. Motion ratios tend to be 1 or greater. I can't recall > exactly what the wheelrates are as of now but I will find out but they are > pretty high. Indy cars tend to have different RC configurations as they run on > 4 different courses. They generally run much stiffer at the front than at the > rear. Wheelrates vary widely according to the type of course being run." > > > Todd Wasson > --- > Performance Simulations > Drag Racing and Top Speed Prediction > Software > http://PerformanceSimulations.Com

On Tue, 14 Aug 2001 09:41:23 GMT, [email hidden] (Ruud van Gaal) wrote:

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>On 13 Aug 2001 22:18:56 GMT, [email hidden] (J. Todd Wasson) wrote: > >>Regarding your discussion of roll centers and how much movement is permissible, >>I can tell you that current F-1 ,Indy and IRL cars tend to limit the movement >>of RC in the lateral & vert. directions to about 10 thousandths of an inch or >>less. Of course, the roll center moves vertically with the chassis. For one F-1 >>car from last year, the front RC was 6mm BELOW ground level and the rear about >>an inch ABOVE with a pitch sensitivity of 1:2 front to rear. > >Thanks for the info! :) >Seems dynamic rollcenters don't do too much here.

BTW More info on this at: http://www.presspley.com/racecarresearc/roll.htm Quite a coincidence, I just had some talks with Mark, who runs the site, if I estimate correctly. 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 <[email hidden]> wrote in message news:[email hidden]... > Also, could you please explain the following statement, as I don'tthink > I get it: > > "Generally speaking, in F-1 front susp. rising rate is NOT used." > > Does that mean that dampers are extremely soft on bump? Rising rate: motion ratio (between wheel movement and shock movement) varies with suspension travel, such that the effective spring rate at the wheel increases as the suspension moves into bump. Is that what you were unclear on? HTH, Jonny

Oh yes. :) Thanks! -Gregor Jonny Hodgson wrote:

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> > Rising rate: motion ratio (between wheel movement and shock movement) > varies with suspension travel, such that the effective spring rate at > the wheel increases as the suspension moves into bump. > > Is that what you were unclear on? > > HTH, > Jonny

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>BTW More info on this at: > >http://www.presspley.com/racecarresearc/roll.htm > >Quite a coincidence, I just had some talks with Mark, who runs the >site, if I estimate correctly. > >

Yes, someone from there contacted me yesterday, that's where I got the info. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com