Further car simulator questions

Thanks to all the help I got in response to my earlier post "Basics of a
car simulator", I now have something quite similar to a drag racer close
to working in my code - i.e. I have most of the longitudinal forces
under control. I've adopted the model I was asking about before - a
central engine RPM is affected by torque coming from the engine, which
is a function of throttle and current RPM, and coming from the tyres,
which at each tyre is a function of engine RPM, contact patch velocity
and load that involves calculating the slip ratio and plugging that into
the Pacekja Magic Formula. Linear force also results from the
tyre/ground interaction, accelerating the car body.

My problem is that I can't find a thorough discussion of the inherent
opposing forces, so I've sort of made them up - and I want to find out
how well I've managed that.

Firstly there is the obvious air resistance on the car body, which can
be modelled as directly proportional to velocity and always acts in the
opposite direction. Of course I probably should worry about downforce
here as an effect on load, but for now I'm just simulating my cars as
bricks.

Then I assume there is an analogue to air resistance acting against the
engine RPM?

But it strikes me that there must also be an ordinary frictional force
acting against RPM since all the rotating elements have to be in contact
with something. If I apply the approximation for friction that doesn't
differentiate between static and moving objects, it seems to me that
must produce a reactionary force that simply has a known value and isn't
proportional to RPM in any way.

So am I right in concluding that the forces that prevent an engine at a
certain RPM with no throttle applied spinning forever comprise a part
proportional to RPM and a static part? If so, is it common to simulate
both of these?

-Thomas

Thomas Harte wrote:
> Thanks to all the help I got in response to my earlier post "Basics of a
> car simulator", I now have something quite similar to a drag racer close
> to working in my code - i.e. I have most of the longitudinal forces
> under control. I've adopted the model I was asking about before - a
> central engine RPM is affected by torque coming from the engine, which
> is a function of throttle and current RPM, and coming from the tyres,
> which at each tyre is a function of engine RPM, contact patch velocity
> and load that involves calculating the slip ratio and plugging that into
> the Pacekja Magic Formula. Linear force also results from the
> tyre/ground interaction, accelerating the car body.
>

Great! Sounds like you're moving right along :-)

Speaking of drag racing (shameless plug):

http://www.PerformanceSimulations.co.../ToddSim7a.wmv


> My problem is that I can't find a thorough discussion of the inherent
> opposing forces, so I've sort of made them up - and I want to find out
> how well I've managed that.
>
> Firstly there is the obvious air resistance on the car body, which can
> be modelled as directly proportional to velocity and always acts in the
> opposite direction. Of course I probably should worry about downforce
> here as an effect on load, but for now I'm just simulating my cars as
> bricks.
>

That works. Good to take things one at a time :-) You'll find
downforce to be an easy addition anyway, I'm sure. It works just like
your aero drag force does, with a coefficient of lift and being
dependent on velocity^2. Only difference is it acts in different
locations and directions.

> Then I assume there is an analogue to air resistance acting against the
> engine RPM?
>

Chances are your model already does this without your knowing it. Just
crank up the drag coefficient and/or frontal area. If the acceleration
and top speed drop, then you've got this one licked already.

> But it strikes me that there must also be an ordinary frictional force
> acting against RPM since all the rotating elements have to be in contact
> with something. If I apply the approximation for friction that doesn't
> differentiate between static and moving objects, it seems to me that
> must produce a reactionary force that simply has a known value and isn't
> proportional to RPM in any way.
>

I think you're talking about engine friction here? Anyway, the
difference between static/dynamic friction is not used anywhere in my
model at all, actually. In general, if you look at scientific studies
on friction of two materials pressed together, you'll find that they'll
frequently map friction coefficient as a function of sliding speed,
temperature, contact pressure, and so forth, so in reality the high
school taught notion of static/dynamic friction isn't always very
useful, especially under extreme conditions that are found in racing
cars.

Sounds to me like what you're wanting to do is apply a constant
friction torque (not a force of course, as this is a rotating object).
You could indeed try this and you'll be fairly close for most rotating
objects., i.e., a bearing system. If you used the assertion that
there's no difference between static/dynamic friction, then yes, to the
first order your assumption is correct. The friction torque would be
constant.

Generally however, the friction torque in a real rotating system is
some function of the loads involved, sliding speed, and material
temperatures as well. I.e., in general the friction torque rises
fairly noticably as rotational velocity is increased in a bearing
system. In general though it seems likely that in the case of a
clutch, friction coefficient decreases with increasing sliding speed.

The clutch model in Virtual RC Racing initially assumed the friction
coefficient in the clutch was constant, but then we went to the track
to watch the lead engineer for one of the RC companies and, listening
closely to the engine, it seemed this wasn't the case. The clutches in
these engines just begin to engage at about 22,000 rpm (the engines run
a mind boggling ~48,000 rpm at the top end). These are centrifugal
clutches that cause the "clutch plates" to be pressed together with
increasing force as rpm rises, so at full throttle the clutch will then
slip more with the engine howevering over 30,000 rpm.

The engine hovers there at 30,000 rpm for a brief moment, then
eventually the car's speed catches up to the engine and the clutch
locks. Then of course the rpm rises again. However, if the assumption
that the friction coefficient was not a function of sliding speed, the
friction torque would stay constant right up until the clutch finally
locked, just as you correctly asserted. However, right before the
clutch finally locked up, there is a slightly noticable bobble in the
engine rpm. It drops just for an instant before it locks. It's very
subtle, but it's clearly there if we listened for it.

I interpreted this to mean that right before the clutch locked, the
friction coefficient in the clutch climbed. I.e., as the relative
sliding speeds got smaller, the friction coefficient climbed, and most
of this change seemed to happen near 0 sliding speed. So I went back
into the model and made friction coefficient a function of sliding
speed and suddenly Virtual RC Racing sounded more like the real car
with that subtle bobble in the engine rpm right as the clutch engaged.


Anyway, that's not entirely off the subject. Engines however are more
complicated than this, so moving right along:

> So am I right in concluding that the forces that prevent an engine at a
> certain RPM with no throttle applied spinning forever comprise a part
> proportional to RPM and a static part? If so, is it common to simulate
> both of these?
>
> -Thomas

With engines this isn't quite right. There are several components to
friction in engines that vary with different things and I think perhaps
you're not looking for a full discussion of those at this point. If
you're interested, then I'll cover some of that.

You might be envisioning the "static part" of engine friction to be a
constant torque, which another torque that varies with rpm could then
be added to. That's an interesting way to look at it and is the first
time I've heard a developer put the question that way. We had a
discussion on basically this subject here at ras back in August of 2000
(wow, it's been a long time :-D ) I only know the date because the
picture I used to illustrate the point is still sitting on my web site
with the date attached!

The discussion we had was not on the causes of engine friction, but if
I recall correctly, was concerning the "engine braking" effect on
handling and how to model that, in addition to getting part throttle
torque out of a full throttle power curve like you now are undoubtedly
using.

The typical approach taken by most developers does not appear to have
changed in the past five years. Richard Burns Rally is the only one
that immediately comes to mind that I'd strongly suspect, because of
their engine simulation, is very likely using a more complete and
accurate approach to the problem.

Here's how most developers deal with this:

http://www.performancesimulations.co.../throttle2.gif

This is a graph of torque vs. rpm at several throttle positions. The
top curve and bottom curve are 100% and 0% throttle. I know you're not
specifically asking about throttling effects here, but bear with me for
a moment. The top and bottom curves are taken from an F1 racing game's
ini files from back in 2000. I don't recall the title, but I think it
was the big EA game. Maybe it was called "F1 2000" :-)

Anyway, take a look at that bottom curve. That is indeed the engine
friction with all components taken into account. I.e., it includes
throttling work, crankshaft bearing losses, valvetrain losses,
piston/wall friction, and so on, all of which are functions themselves
of rpm and so forth (yet different). The bottom curve is below 0
torque, so of course it's a negative torque that acts to slow down the
engine, and if a drivetrain is attached to that, will also act to brake
the rear wheels.

That is the most common and easy way to deal with the question, "what
happens when you close the throttle?" I.e., make two primary torque
curves, one at full throttle (from a dyno test), and another one at
zero throttle. Unfortunately there are not very many dyno tests
published outside of scientific literature that were produced at zero
throttle with the engine running. There are some tests for what's
called "motored torque" so you might try Googling that and seeing if
you come up with something. Motored torque is, however, measured with
the engine turned off and generally with the throttles fully open as
it's an attempt to measure engine friction directly. So if you find
any data, make sure it was taken with the throttles closed (foot off
the gas pedal)! Using that would probably be closer than just guessing
at what the closed throttle torque curve would look like, so it's
better than nothing.

The rest of the curves are what you'd get with a simple linear
interpolation between the top and bottom curves based on throttle
position. Real, part throttle engine curves do not really look like
that though, far from it, actually

To get some indication of what the part throttle curves might look
like, keep in mind that with a car sitting in neutral and the
accelerator slightly pressed down, the engine rpm will stabilize at
some point. This point is precisely where the part throttle torque
curve at that throttle opening percentage or angle crosses 0 torque on
the graph. So the torque will rise to some point and drop back to 0 at
that rpm. Just something to keep in mind if later you want to get a
bit nastier on part-throttle torque stuff.

Anyway, taking this approach bypasses the need to try to analyze or
break down engine friction into more than one component. I've never
heard mass complaints about part-throttle engine behavior in sims.
Generally if someone's gas pedal doesn't feel right, they'll just
adjust the progressiveness of it in the game's controller setup area
and be done with it.

Getting much more involved than this requires some serious look into
engine operation. If you're interested really in the frictional
components, they are sort of all over the place in how they work. For
instance:

Piston/cylinder wall friction has one component that depends on the
mass of the pistons and scales with engine rpm (perhaps ^2, I don't
recall off the top of my head). This component isn't effected by
what's happening in the cylinder. I.e., it's independent of throttle
position or cylinder filling. The second component of this same
piston/cylinder wall friction, really the primary contributor usually,
is very highly dependent on cylinder pressure. As such, it's highly
dependant on throttle position. Cylinder filling/pressure is a
function of engine rpm too, so this friction component is a function of
throttle position and engine rpm.

Valve train friction: This varies considerably with engine rpm.

Crankshaft bearing friction: This is a spinning bearing like you'd get
with your front wheels. It just sits there and spins. At first glance
this might be one of those constant torque things, but measurements
show that it also increases with engine rpm almost linearly at some
rate.

Fan: That big fan on the front of your engine is an enormous power
sucker at high rpm. This increases at an ever increasing rate as
engine rpm rises.

So anyway, the point is, in reality there is not really a "constant
torque part" and a separate part that increases with engine rpm that
could be added together. You'd most likely be better off with the
example covered earlier.

Hope that helps and didn't stray too far off your question!

Todd Wasson
Racing and Engine Simulation Software
http://www.PerformanceSimulations.com
http://www.VirtualRC.com

Something just dawned on me. Going back to the graph that showed the
torque curves at different throttle positions. I said that zero
throttle tests with the engine running were rare. Not so! In fact
they're really quite common.

Chassis dynos are contraptions that you park a car on. They have a set
of rollers under the driven wheels. When you hit the gas, the
engine/drivetrain accelerates the rollers. Since the roller system's
moment of inertia and rotational velocity are known, the torque
produced at the wheels can be calculated fairly accurately. Granted,
the inertial losses from accelerating the drivetrain are undoubtedly
never included in this, but it's good enough for many purposes.

A fairly common thing that chassis dyno operators will do is perform
what's called a "coast down test." After the engine has reached peak
rpm, if I recall correctly, the driver will take his foot off the gas.
The whole system slows down and now you have a fairly good idea of what
the zero throttle torque curve looks like. I believe generally what
these guys will do during a coast down test is shift into neutral to
disengage the engine, then let the drivetrain slow down under it's own
inertia in an attempt to measure roughly what the drivetrain losses
are. This is somewhat silly in a way because the losses are completely
different when an engine load is applied, but anyway, that's not the
point...

Anyway, if you can find some "coast down" tests with the engine still
engaged to the drivetrain (not done in neutral or with the clutch
pressed in) you'll indeed have a fairly good picture of what the torque
curve as measured at the rear wheels looks like. This will be
different from what you get at the flywheel, but something is better
than nothing.

Todd Wasson
Racing and Engine Simulation Software
http://www.PerformanceSimulations.com
http://www.VirtualRC.com