# [ODE] Simulating Wheels

Steve Baker sjbaker1 at airmail.net
Tue Nov 4 22:36:35 MST 2003

```Michael Lacher wrote:

> a) when a cylindrical wheel would be going through a curve, the force
> would work outward along the axis, eventually (as the cylinder begins to
> tip over) reducing the contact to a point. so in the extreme case they
> behave alike.

Real tyres deform quite a bit too - that's why we have rubber tyres
filled with air.  The deformation of the tyres acts like lateral springs.

Cars with cute-looking skinny tyres and larger wheels don't hold the road
as well as cars with thicker tyres and smaller wheels.

> b) real cars do not have parallel wheels, and the wheel setup is
> actually quite complex.

Indeed.  It'a a very subtle business.

> a) lower friction. Infinite or very high friction will make you car flip
> over more easily.
> b) lower the center of mass for the buggy. In a real world car most of
> the mass is very low (chassis, engine), testbuggys often have a very
> high center of gravity.

Sure - if you try to throw a car into a turn too hard, most likely the
tyres will squeal as they slide sideways - and if you persist, you'll
learn that static friction is MUCH higher than dynamic friction - so
once your tyres start to slide - the frictional coefficient will plummet
and you'll lose grip.  At this point the car is essentially uncontrollable
and you'll spin out.  On pretty much any *car*, this will happen long before
you risk rolling over - unless you are unfortunate enough to slide with enough
speed into something immovable like the kerb of the road.

Of course if you try the same trick with an SUV, an 18 wheel truck, BigFoot
- or anything with a high center of gravity and a relatively narrow wheelbase
- it'll roll over because the tyres continue to grip beyond the point where the
lateral forces are enough to roll the vehicle.  This is VERY dangerous!

Another thing that makes a huge difference in a car is the suspension.
When a stiff 'buggy' would roll over - a real car will simply have it's
body roll sideways whilst the wheels remain stuck to the road - perhaps
being pressed down by one or more anti-sway bars which transfer the compression
of the springs on the outside wheels into a somewhat matching compression of
the inside wheels.

Then there is the issue of 'sprung mass' versus 'unsprung mass'.  The
mass of the parts of the car that are below the springs (ie the wheels,
axles, etc) act to increase the inertia of the wheels - so when you hit
a bump, they accellerate upwards (because they can't keep on going straight),
but once they are accellerated upwards, a large 'unsprung mass' will make it
harder for the springs to push them back down onto the road.

On the other hand, the 'sprung mass' (the body of the car basically) doesn't
have to accellerate upwards when a wheel hits a bump - because it's cushioned
by the springs.  Having a higher sprung mass increases the inertia of the
body - which gives the springs something to press against when they are
pushing the wheel back onto the road.

Car enthusiasts are fanatical about reducing the unsprung weight - even if
it increases the weight of the car overall.

The 'laws' of friction are not proper physical laws at all - they are an
approximation of reality.  That approximation is very far from the truth
for car tyres.  The law we all learned in school says that the force due
to friction is independent of the area of contact between the two bodies.
However, we all know that wide tyres are used on race-cars precisely in
order to increase the area in contact with the road.

The physics of the friction of tyres against the road appears to be a complete
black art.  No two web sites or books I've read have explained it the same
way!

Think also about 'torque steer' on front wheel drive cars. In some cars, there is
a difference in the length (and mass) of the two drive axles (caused by the
difficulty of mounting the differential exactly in the center of the car because
that's where the engine is).

When you accellerate, the extra rotational inertia in the heavier axle causes
the differential to feed more power to one wheel than the other - resulting
in a sometimes vicious tendancy for the car to pull to one side when you
floor it.

Making a fully realistic car is DIFFICULT...probably more than most of us
could do single-handedly.

This is why I'd like to see a cooperative project to do it right.

> c) implement ackerman steering. This means that the steering wheels do
> not stay parallel, but the inner wheel turns a little more (because the
> radius of its curve is smaller). If using front or four wheel drive,
> also try to reduce speed for the inner wheel (like a differential
> would). This should also help with bendy wheels problems.

Right - and the wheels may not be vertical either.  Having the tops
of the wheels lean inwards towards the center of the car tends to
improve cornering because when the wheel is a few degrees away from
vertical, the contact patch of the tyres on the outside of the turn
becomes larger as the car leans and the rubber in the tyres deforms
rather than smaller (as it would if the wheel was vertical).  The
size of the contact patch on the wheels on the inside of the turn
reduces - but since the outside wheels are being pressed against
the road harder by the roll of the body - this is a net gain in
traction.

I suspect that using a spherical wheel in ODE somewhat simulates that.

But the cost of leaning the wheels in like that is more tyre wear - so
there is a compromise between cornering ability and replacement tyre
costs.  My tricked out MINI Cooper corners almost as well as a Formula 1
race car (1g lateral!) but I spend more on tyres than I do on gasoline!

> d) you can try to change friciton values for different directions
> (perpendicular to the wheel and in rolling direction) to simulate an
> oval shaped contact instead of a circular one.

The shape of that patch changes with speed too.  At higher speeds the
centrifugal force on the tyre tends to make the wheel more circular -
reducing the area of the contact patch.

---------------------------- Steve Baker -------------------------
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