rec.autos.simulators

Perhaps it's not so bad. If you multiply the inertia mentioned by the
appropriate gear ratios (depending on where the inertia 'are' in the
engine; in front of the transmission or behind it, and in front of or
behind the final drive ratio), then I'd say it's not that bad. If not
correct. ;-)

The are also some efficiencies associated with these numbers as well
in Gillespie's book. Which are in the range of 97%-99% mainly though.
But still, I've always found my Ferrari (virtual!) to spin up a bit
too quickly.
The quaternion code works btw. :) Cost me a whole day to find a bug
where I mixed up 1 line of world & body coordinates, sigh, but voila.
Now to throw the car into the air and see how it rotates with
precession. That shouldn't be hard, given my driving style. ;-)

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.racesimcentral.net/
Car simulation: http://www.racesimcentral.net/

My guess, however, is that your simulation already takes slip ratios
into account, and such losses are taken care of automatically if it's
done this way.

-Gregor

  I think it might be correct, as Gillespie's formulas are dealing with an
"effective mass increase", to simulate the rotational inertia effects, right?
If so, I think I might have it down ok.  In a creative flash, I got an idea how
to do it with all the sections operating at different speeds and input/output
torques and think it works fine.  I end up making a big term that is the
"equivalent polar moment of inertia", which changes with each gear.  When the
wheels spin up, they seem to do it appropriately.  With some setups, they'll
zip up until the engine speed is hovering around the torque peak at a rate that
seems right (from my Firebird burnin' days :0), then catch, rock the car back a
little, and take off.  The performance matches my SAS program really closely,
so I think it might be ok.  Obviously, if you discover something I may be
missing here, let me know :0)

  That's still a fuzzy area for me.  The debate will continue there.  The racer
and dyno folks insist driveline efficiencies are never anywhere near this high,
while engineers and students usually say they must be because of heat reasons,
but I haven't seen any real evidence on their behalf.  The racers and dyno
folks show example after example.  Heck, I've even got a tech book on automatic
transmissions that says the efficiencies are typically around 80%, so who
knows?  I know my SAS program works rather well with numbers on the low end,
but not at the high end.  

  1 line is all it takes.  Endlessly frustrating, isn't it!!?  lol   I still
haven't touched quaternions, so may come asking you for help when it's time.
When you toss the car, compare it to my vector3b.exe program and let me know of
any obvious differences, if you'd be so kind :0)  

  Thanks,

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

  Well, what I'm really referring to here is the ratio of torque output at the
flywheel to the rear wheels (or is it the other way around?? :0) )  SAS doesn't
use slip ratios because I didn't understand them when I wrote it.  It still
makes good predictions, but the final rpm will be off a few percent because the
slip ratio is locked to 0 (coulomb friction model.)   It calculates the
traction limit and doesn't allow the force to exceed it, kind of like traction
control.  It'll still tell you what speed range to expect wheelspin, but it
controls it.  

  When running my 3-D project, I get performance that matches up really closely
to SAS predictions, even with the slip ratio included, so it appears to not
really be a factor.  The losses I'm talking about are frictional through the
drivetrain.  In drag racing circles, folks are always talking about "rear wheel
vs. flywheel horsepower," and looking for quick answers to the percentage
difference.  Anyway, I could go on and on about this, but to make a long story
short, on one side I find engineering folks arguing that 70-90% efficiency
would cause far too much heat and is therefore impossible.  But on the other
side are the dyno test guys that seem to prove them wrong time and again.
Well, I've covered this in another post, so I won't go further :0)  

  It's still a bit of a mystery that I'd love to be able to prove one way or
the other, and finally dispel the myth that one side or the other believes once
and for all :0)  Geeze, I need a life.....  :-P

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

You need to be very careful about the radius also,
if you allow it to change. If you do, this can create
another high frequency dynamical "vibration" mode in
the overall system that can interact with the longitudinal
dynamics that interacts with the suspension dynamics that
upsets the ...;)

--
Matthew V. Jessick         Motorsims

Vehicle Dynamics Engineer  (972)910-8866 Ext.125, Fax: (972)910-8216

Hehe, that makes me all the more curious!

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Car simulation: http://www.marketgraph.nl/gallery/racer/

This is exactly what those equations do. They collect terms such that
you can divide one torque by that effective inertia  to find one
angular acceleration (for a chosen one of the rotating pieces that
are geared together.)   You can them find the other accelerations
using the gear ratios between the pieces.

- Matt

Yes, probably for the best ;)

- Matt

  Ok, here goes:

  If we've got two rigid, spinning bodies (one axis only, please, no inertia
tensors, they make my head hurt with all that precession stuff :0)) connected
by a gear.  The first body has moment of inertia i1, and the second has i2.
Assume they're both equal and connected by a 1:1 gear, so they spin at the same
speed.  What we really want is the acceleration of one of the bodies (they'll
both be the same in this case, of course.)  Once we've got the acceleration of
one, we can multiply by the gear ratio(s) between the two bodies to get the
acceleration of the other.

  If we have an input torque of 1 on the first body, we can find the rotational
acceleration (ra) by dividing torque (T) by the moment of inertia (i1).  
  ra = T / i1

  If both bodies are connected, we can add the two inertias:

  ra = T / (i1 + i2)

  I'm know you know this already.  Now, if set the gear so that the second body
rotates at twice the speed, it'll have to accelerate twice as quickly.  The
torque isn't changing, but we could double the rotational inertia (i2) to get
the same effect.  So we could define an "effective moment of inertia" (Ei2)
that would take care of this.   In this case, with the gear ratio of .5, which
doubles the acceleration:
  Ei2 = (1/.5) * i2
  Ei2 = 2 * i2
  Ei2 = 1/GearRatio * i2

  The first body, where we are applying the torque, doesn't need an effective
inertia.  The total of both bodies now becomes:

  EiTotal = i1 + 1/GearRatio * i2

  Anyway, in our example, where the real moments of inertia of both bodies are
identical, our total effective inertia (EiTotal) becomes 3.  1 for the first
body, and 2 for the second body because it has to rotate twice as quickly under
the torque.  

  Now, if our gear ratio is .5, we are only getting 1/2 the torque accelerating
the second body to begin with.  On top of that, its effective rotational
inertia has been doubled because it needs to accelerate twice as quickly.  Half
the torque and twice the rotational acceleration is the same as only giving
1/4th the torque, which is the same as having 4 times the rotational inertia
instead of 2.  Following me?

  If the gear ratio was 1/3, the second body would have triple the acceleration
(effective inertia is tripled), and also only 1/3rd of the input torque.  This
is the same thing as multiplying the moment of inertia by 9.  See?  It's
squared because it's got to accelerate faster and it has less input torque at
the same time.  

  For two bodies, define an effective inertia for each one.  The first one,
where we're applying the torque, is just i1, the true moment of inertia value.
The second "effective inertia" becomes:

  Ei2 = 1/(GearRatio^2) * i2

  The total effective inertia becomes:

  EiTotal = i1 + 1/GearRatio^2 * i2

  Now the fun part.  What about a third body at the end of the line, with
another gear?  As before, we could set an effective moment of inertia for each
body, then add them up.  The third body would have GearRatio set according to
the joint between it and the second body.  However, it's input torque will be
drastically different because it's changed at the first and the second
(sequentially arranged) gears.  I'd set the input torque by multiplying by the
first gear ratio, then use the equation above in addition to it.  The third
body's effective inertia becomes:

  Ei3 = GearRatio1 * (1/GearRatio2^2) * i3

  The second body is:

  Ei2 = 1/(GearRatio^2) * i2

  The first body is just i1.  Total?

  EiTotal = i1 + Ei2 + Ei3

   or, in long terms:

  EiTotal = i1 + 1/(GearRatio1^2) * i2 + GearRatio1 * (1/GearRatio2^2) * i3

  For a fourth body and gear, Ei4 would be:
Ei4 = GearRatio1 * GearRatio2 * (1/GearRatio3^2) * i3

  Fifth body and gear would be:
Ei5 = GearRatio1 * GearRatio2 * GearRatio3 * (1/GearRatio4^2) * i4

  So, to be show off ;0),  I think a six body system joined by sequential gears
rotational acceleration could be calculated like this:
6
5
4
3
RotationalAcceleration = Torque / (i1 + 1/(GearRatio^2) * i2 + GearRatio1 *
(1/GearRatio2^2) * i3 + GearRatio1 * GearRatio2 * (1/GearRatio3^2) * i3 +
(GearRatio1 * GearRatio2 * GearRatio3 * (1/GearRatio4^2) * i4) + (GearRatio1 *
GearRatio2 * GearRatio3 * GearRatio4 * (1/GearRatio5^2) * i5))

  See a pattern?  I haven't tested this yet, but think it will work.  Perhaps
the loss that Gillespie mentioned was due to each extra gear in the system.  I
forget exactly what you were describing, but maybe that's it.  

**  Now, I've put Straightline Acceleration Simulator on sale (at the link in
my sig) for two weeks at only $10 a copy.  Go there and look at it, and tell
your friends please :0)  **

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

  Perhaps.  I'll try the equations from my other post in the 3-D model, since
it gets the same results as SAS, and see what happens.  This just might be
where folks are getting confused.  If so, the issue of "correct efficiencies"
can be put to rest in the drag racing community once and for all :0)  Won't
that be fun to debate with people?  

  You're telling me???  lol  I feel ya on this one!

  When you switched to quarternions, right?

  It's a huge relief when you fix something like that.  Makes you want to break
stuff, doesn't it?  :0)

  Yes, I've been thinking about that using the 3x3 matrix and inertia tensor.
It'll be a relief for sure, and will probably make the rest of everything much
simpler.

  This one I haven't figured out yet.  If you've got a spinning wheel attached
to the car and you turn it, how do you calculate the torques sent to the car?
Do you find the 3 axis (world) angular momentum change and apply that to the
body?  If so, that'd be pretty cool.  Just like GPL :0)  

  Yes.  Z is about the axis pointing into the screen, x is left/right and y is
up/down.  The matrix doesn't reorthagonalize itself, so if you spin it fast,
it'll go crazy and squash itself.  Just try slow rotation and let me know how
it compares.  

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

  I sure do like that word, don't I?  :0)

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com

  Hmm...  Maybe we shouldn't be talking about this stuff in a widely read
newsgroup ?  :-)  

  This has got me e***d.  It ought to be not too terribly difficult to do a
four wheel drive system that actually works the way it should.  Too bad I don't
know much about differentials yet :0P

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://www.racesimcentral.net/

Ok, anyway, I did a derivation yesterday night which I'll put up more
expandedly on my site this weekend probably (I have to run now to get
some deadlines done!), based on Gillespie's equations, but working out
all accelerations, since I want to know about torque, and derive
accelerations from that.
In the end, I get:
Tw=(C2*Iw)/(C1+Iw)

Where Tw is torque at the wheels/rear axle, Iw is the combined inertia
of rear axles and (connected) wheels. You start out with Te (engine
torque, from a curve). C2 and C1 are constants where:
C1=Ie*Ntf**2-ItNtf**2-IdNf**2
C2=TeNtf

Where:
Ie=engine inertia
Nt=transmission ratio (gear ratio)
Nf=final gear ratio
Ntf=Nt*Nf
Id=inertia of driveshaft
It=inertia of transmission

After moving down all equations tucked into eachother. It's without
the FxR term, because I just go from:
Te=engine torque
Tw=.... (see above)
Then apply the torque at the wheels, minus the road reaction force,
minus the braking force.

As for efficiencies; it's strange, I reread a part where he stated
80%-90% efficiencies, but then in an example continues to use 97%+.
Incorporating efficiences in the above? Hm, might be done as
Ie=.97*Ie, something like that (C1=eff_Ie*Ie*Ntf**2...)

Ok, have to hurry now, talk to you guys later,

Ruud van Gaal, GPL Rank +53.25
Pencil art    : http://www.marketgraph.nl/gallery/
Car simulation: http://www.marketgraph.nl/gallery/racer/

  Don't anybody use this!  I made a mistake!  I'm not 100% sure here because I
haven't tested it yet, but I suspect the equations really should be:

EiTotal = i1 + 1/GearRatio1^2) * i2 + 1/(GearRatio1^2 * GearRatio2^2) * i3

  This is a huge difference, so take note :0)  To simplify, this would be:

EiTotal = i1 + i2/GearRatio1^2 + i3/(GearRatio1^2 * GearRatio2^2)

For a powertrain:
i1 = polar moment of inertia of engine
i2 = " " " " " driveshaft
i3 = " " " " " wheels, diff, and axle(s)

Engine acceleration would then equal:

Ea = (EngineTorque + ((LeftTireTorque + RightTireTorque) / (GearRatio1 *
GearRatio2))) / EiTotal

   If I'm wrong, somebody correct me please :0)

Todd Wasson
---
Performance Simulations
Drag Racing and Top Speed Prediction
Software
http://PerformanceSimulations.Com