Car physics: instant centers = force application?

Hi all, I'm thinking about a bit more intelligent suspension setup. I currently just use a vertical motion of the wheel, with roll centers & CG. I've read about instant centers in side and front view, but I don't quite get it yet. Suppose you want to have anti-dive/lift; isn't the arm for pitch moments the difference in height of the IC (side) and CG? It looks as if with a side and front IC, there's no place for rollcenters anymore, as I would apply roll using the arm from IC(front) height - CG height. And as for determining camber change rates and IC/RC changes, most people (as seen from earlier discussions) seem to just 2D paths (rear views), instead of full 3D path calculations, right? That reminds me, I think the Olley book from Doug Milliken might have nice, crisp, directly implementable formulae for suspension motion, doesn't it? ;-) Thanks, Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

The way I like to think of that stuff is as a plane connecting the tire contact patch with the instant axis--at this point the tire will move along the plane normal, and the planar componant of the tire force will be applied through the suspension to the sprung mass, while the normal componant will apply to the unsprung mass of the tire. So for example for an anti-dive front suspension, this plane will slope down towards the front of the car... Of course, if you're simulating the suspension arms individually, it will all 'fall out', and the only time you'll have to even think about this stuff is when choosing your arm lengths and so on... -Dave P. "Ruud van Gaal" <[email hidden]> wrote in message news:[email hidden]...

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> Hi all, > > I'm thinking about a bit more intelligent suspension setup. I > currently just use a vertical motion of the wheel, with roll centers & > CG. > > I've read about instant centers in side and front view, but I don't > quite get it yet. Suppose you want to have anti-dive/lift; isn't the > arm for pitch moments the difference in height of the IC (side) and > CG? > It looks as if with a side and front IC, there's no place for > rollcenters anymore, as I would apply roll using the arm from > IC(front) height - CG height. > > And as for determining camber change rates and IC/RC changes, most > people (as seen from earlier discussions) seem to just 2D paths (rear > views), instead of full 3D path calculations, right? > > That reminds me, I think the Olley book from Doug Milliken might have > nice, crisp, directly implementable formulae for suspension motion, > doesn't it? ;-) > > Thanks, > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/

Hi Ruud! The instant centers are a nice tool to help with engineering aspects of the car mechanics, but to do simulations directly with them I would actually find them rather tedious to work with. What I find more natural from the simulation modelling point of view is to consider the suspension in geometrical terms as giving the position R(s) of the contact patch and the orientation matrix (or quaternion, depends on your preference) O(s) of the wheel in terms of a slightly abstract suspension travel variable s. If you know the functions R(s) and O(s) you know everything there is to know about suspension geometry (assuming the steering can be tacked on independently from suspension travel, which is not completely true, but very much so). You typically do not have this info, however, but you may try with a linear approximation along the lines R(s)~=R(0)+P*s O(s)~=T(A*s)*O(0) (for matrices, where T represents a rotation for the angle |A*s| about the axis A)) Then all the info about your suspensionis given by the initial position and orientation and the axis P (which should basically be a unit vector if s is supposed to give the length of suspension travel) along which the contact patch moves and the axis A around which the wheel is rotated and whose magnitude gives the speed of rotation with the travel. These can be translated into the language of instant centers as they basically describe the same thing (the linearization of suspension movements), but that would require a bit of work better left to the reader at this point ;). Of course, as Dave said, doing proper suspension eliminates most of these problems anyway :). But even that one can have a few catches to be wary about. -Gregor On Mon, 29 Apr 2002, Ruud van Gaal wrote:

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> Hi all, > > I'm thinking about a bit more intelligent suspension setup. I > currently just use a vertical motion of the wheel, with roll centers & > CG. > > I've read about instant centers in side and front view, but I don't > quite get it yet. Suppose you want to have anti-dive/lift; isn't the > arm for pitch moments the difference in height of the IC (side) and > CG? > It looks as if with a side and front IC, there's no place for > rollcenters anymore, as I would apply roll using the arm from > IC(front) height - CG height. > > And as for determining camber change rates and IC/RC changes, most > people (as seen from earlier discussions) seem to just 2D paths (rear > views), instead of full 3D path calculations, right? > > That reminds me, I think the Olley book from Doug Milliken might have > nice, crisp, directly implementable formulae for suspension motion, > doesn't it? ;-) > > Thanks, > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/ >

Hey Gregor, Thanks for the info on the wheel travel representation; I guess matrix A (the rotation of the wheel as a function of wheel travel (generalized coordinate s)) can be calculated from the IC. When I look at the future, I might have people just enter the rods and out would come an IC and 'A'. For now though, I was wondering how to apply the forces & moments that result from the IC's not being exactly on the lines through the contact patches. It seems for acceleration, you have a different point of force application as compared to braking (since for braking you need to know whether you have inboard or outboard braking; this changes the attack point or contact point). I had read an old mail by Dave (thanks Dave for the explanation) stating indeed something about a plane through both IC's and the contact point (which, I believe, changes whether you're talking about braking or accelerating forces, or torques rather). I'm not simulating the actual rods, since I want to keep things a bit more simplistic and less CPU-costly. But I do want anti-* behavior, or at least be able to identify all the moments that result from the suspension geometry. I believe the IC's are then all I would really need (no need for rollcenters). I hope I understood Dave correctly, and drew a little picture of an anti-dive suspension at: http://www.racer.nl/temp/suspforce.jpg If I understand things correctly, I could do: - Let p=CP-IC (a line vector describe the plane in 2D from the side). CP=contact point btw. - Normalize p (for a dot product/projection later on) - Calculate Fx (longitudinal) - Calculate the force that causes/is anti-dive by v=Fx dot p. I'm not sure though how to exactly apply 'v' to the body or wheel: does it generate a moment around the IC or around the body's CG? In other words: I want to apply the anti-dive force (v) to the body. The body ofcourse revolves around its CG, but do I then apply v having an arm of CP.x-IC.x or CG.x-IC.x (SAE coordinates; x = longitudinal)? And yes, I know I should have taken a subclass in physics at University. ;-) Thanks, Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

Darn it, my newsreader didn't show the original post on this one either! Can someone repost it? Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

Try Google, Todd, it's quicker than waiting for somebody to repost. "J. Todd Wasson" <[email hidden]> wrote in message news:[email hidden]... > Darn it, my newsreader didn't show the original post on this oneeither! Can

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> someone repost it? > Todd Wasson > --- > Performance Simulations > Drag Racing and Top Speed Prediction > Software > http://PerformanceSimulations.Com > > My little car sim screenshots: > http://performancesimulations.com/scnshot4.htm >

On 01 May 2002 22:09:09 GMT, [email hidden] (J. Todd Wasson) wrote: >Darn it, my newsreader didn't show the original post on this one either! Can >someone repost it? Here it is. Your news feed isn't exactly helping there, is it? Must you wonder what else you've been missing. :) What I'm wondering about is what torques/forces I can derive knowing the instant center of a suspension (which arms; IC.height-CG.height or IC.height-ContactPoint.height?) and whether that does away with needing explicitly defined roll centers. Ruud --- Hi all, I'm thinking about a bit more intelligent suspension setup. I currently just use a vertical motion of the wheel, with roll centers & CG. I've read about instant centers in side and front view, but I don't quite get it yet. Suppose you want to have anti-dive/lift; isn't the arm for pitch moments the difference in height of the IC (side) and CG? It looks as if with a side and front IC, there's no place for rollcenters anymore, as I would apply roll using the arm from IC(front) height - CG height. And as for determining camber change rates and IC/RC changes, most people (as seen from earlier discussions) seem to just 2D paths (rear views), instead of full 3D path calculations, right? That reminds me, I think the Olley book from Doug Milliken might have nice, crisp, directly implementable formulae for suspension motion, doesn't it? ;-) Thanks, Ruud van Gaal Free car sim: http://www.racer.nl/ Pencil art : http://www.marketgraph.nl/gallery/

Hi Ruud! I see the stuff you are showing is already a part solution to the problem I gave in the other post for the reader ;). Indeed one car reproduce the axis A and the direction of travel of the contact patch (P, I believe I put it) from the instant axis. The only problem I see so far is that instant axis itself is defined by 5 parameters, while the vectors A and P share 6 components between them. As far as I can see the instant axis description cannot produce a component for the direction of travel that points in the direction of the axis of rotation (you cannot rotate the wheel around the direction of travel). What you basically need to do after you get the direction of travel of the contact patch is to find the componets of the force in the direction of the travel (just F_p=((F.P)/(P.P))*P even if P isn't normalized and . is a dot product) and perpendicular to it (F_r=F-F_p). You apply the perpendicular force directly to the car body (as it goes directly throu suspension linkage), while the other one you apply to the wheel to make it travel (but you can usually add it to the body with little ill effect directly, depends on how you are doing it so far). You bring a good point there about the point of application of the force; this is the pitfall I mentioned when talking about implementations of 'proper' suspensions. You must find the direction of travel (P only, as A remains the same) for all the points at whcih various forces operate, and add them together via procedure described before. If you know P(r) and A(r) at some point, then you get something like (signs not guaranteed) P(r')=P(r')+A(r)x(r'-r) Either that, or you may completely equivalently calculate the total force vector F and torque vector T acting on the wheel, and then the effective force which causes the suspension travel becomes something like (exercise again left to the reader, including discovering all mistakes in the formula ;) ) F_eff=F.P+M.A, where F_eff is of course a scalar. What is interesting to note is that even pure torques may cause suspension travel if the suspension rotates in the proper direction (the torque M and the axis A coincide). -Gregor On Wed, 1 May 2002, Ruud van Gaal wrote:

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> Hey Gregor, > > Thanks for the info on the wheel travel representation; I guess matrix > A (the rotation of the wheel as a function of wheel travel > (generalized coordinate s)) can be calculated from the IC. > When I look at the future, I might have people just enter the rods and > out would come an IC and 'A'. > > For now though, I was wondering how to apply the forces & moments that > result from the IC's not being exactly on the lines through the > contact patches. It seems for acceleration, you have a different point > of force application as compared to braking (since for braking you > need to know whether you have inboard or outboard braking; this > changes the attack point or contact point). > > I had read an old mail by Dave (thanks Dave for the explanation) > stating indeed something about a plane through both IC's and the > contact point (which, I believe, changes whether you're talking about > braking or accelerating forces, or torques rather). > > I'm not simulating the actual rods, since I want to keep things a bit > more simplistic and less CPU-costly. But I do want anti-* behavior, or > at least be able to identify all the moments that result from the > suspension geometry. I believe the IC's are then all I would really > need (no need for rollcenters). > > I hope I understood Dave correctly, and drew a little picture of an > anti-dive suspension at: > > http://www.racer.nl/temp/suspforce.jpg > > If I understand things correctly, I could do: > - Let p=CP-IC (a line vector describe the plane in 2D from the side). > CP=contact point btw. > - Normalize p (for a dot product/projection later on) > - Calculate Fx (longitudinal) > - Calculate the force that causes/is anti-dive by v=Fx dot p. > > I'm not sure though how to exactly apply 'v' to the body or wheel: > does it generate a moment around the IC or around the body's CG? In > other words: I want to apply the anti-dive force (v) to the body. The > body ofcourse revolves around its CG, but do I then apply v having an > arm of CP.x-IC.x or CG.x-IC.x (SAE coordinates; x = longitudinal)? > > And yes, I know I should have taken a subclass in physics at > University. ;-) > > Thanks, > > > Ruud van Gaal > Free car sim: http://www.racer.nl/ > Pencil art : http://www.marketgraph.nl/gallery/ >

>Try Google, Todd, it's quicker than waiting for somebody to repost. > Ah yeah, good idea, thanks. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

>Here it is. Your news feed isn't exactly helping there, is it? Must >you wonder what else you've been missing. :) Hehe, I seem to catch most of the replies, but Gregor's didn't show up either. I checked Google as Hacsau said and viola, there it all is.. Duh!

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>I've read about instant centers in side and front view, but I don't >quite get it yet. Suppose you want to have anti-dive/lift; isn't the >arm for pitch moments the difference in height of the IC (side) and >CG? >It looks as if with a side and front IC, there's no place for >rollcenters anymore, as I would apply roll using the arm from >IC(front) height - CG height.

No, it's not the height difference. 100% anti dive/squat only happens when the line of action travels from the patch through the CG. The IC could be at any height as long as it's on that line, and you'll have 100% anti behavior. It's the angle that you want. I won't comment on the roll centers yet though because you'll figure it out on your own soon enough ;-) >And as for determining camber change rates and IC/RC changes, most >people (as seen from earlier discussions) seem to just 2D paths (rear >views), instead of full 3D path calculations, right? I'm doing 2-D paths. I think I figured out how to do it in full 3-D, but haven't had time to try it yet. That would give a way to get bump-caster too, which would be cool for force feedback wheels :-P Thanks for reposting :-) Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

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>>I've read about instant centers in side and front view, but I don't >>quite get it yet. Suppose you want to have anti-dive/lift; isn't the >>arm for pitch moments the difference in height of the IC (side) and >>CG? >No, it's not the height difference. 100% anti dive/squat only happens when >the >line of action travels from the patch through the CG. The IC could be at any >height as long as it's on that line, and you'll have 100% anti behavior.

Small correction. You're probably imagining the IC being exactly on the vertical line going through the CG, which in that case, you're right. That limits what you can do though with the suspension design. A simpler approach might be to allow a variable for anti dive and anti squat directly, allowing a user to simply specify 100N vertical force per 1000N longitudinal force, for instance. Sort of an anti-dive "rate" so to speak. Then just apply that force upwards to the body vertically above the wheel and downwards to the sprung mass at the same spot and you should be good to go. Expect really bad wheel hop once folks dial in much of either type of anti though. It's basically the same thing as stiffening the springs only when the throttle/brakes are applied. Todd Wasson --- Performance Simulations Drag Racing and Top Speed Prediction Software http://PerformanceSimulations.Com My little car sim screenshots: http://performancesimulations.com/scnshot4.htm

On Thu, 2 May 2002, Ruud van Gaal wrote: ... > What I'm wondering about is what torques/forces I can derive knowing > the instant center of a suspension (which arms; IC.height-CG.height or > IC.height-ContactPoint.height?) and whether that does away with > needing explicitly defined roll centers. There are lots of ways to define (model) suspensions... Fixed roll centers are a nice concept for visualization (they were probably invented by designer-draftsmen), but in most cars the roll centers really move around too much to be useful for detailed/precise calculations. The IC or Instant Axis approximation is a "next step" toward reality, each wheel gets treated separately. This replaces the roll center concept (which treats two wheels at a time). In Olley (our new book) he works the actual "4-bar" linkage problems (including steering) but with simplifying assumptions that should(?) make them calculate faster than the full nonlinear solutions. He also works them in several stages of complexity, so the derivations should be pretty easy to follow. -- Doug Milliken http://www.millikenresearch.com/olley.html (in case you forgot my earlier sales pitch!!)