rec.autos.simulators

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.racesimcentral.net/
Pencil art  : http://www.racesimcentral.net/

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

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/

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. :)
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/

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

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

 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!

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 ;-)

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

 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

...

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!!)