Deborah R. Fowler
Tire Rotation
Posted on Nov 25 2017
Recall that the circumference of a circle is 2 * PI * radius
![](TireRotation/CircleUnrollRoll.gif)
A tire on a car will travel 2 * PI * r units / revolution. The pillars in the video below were place this distance apart.
Watch the back tire and you will see it aligns with the pillars.
![MISSING IMAGE](TireRotation/TireRotation.gif)
This is true for any radius.
![](TireRotation/TireRotationMonsterWheels.gif)
Or any speed. So how does speed of the vehicle factor in? The two figures above are moving at $F/10. The one below is moving at $F.
![MISSING IMAGE](TireRotation/TireRotationMonsterFaster50percent.gif)
If a vehicle is traveling at say 10 units / sec if you need to know the revolutions (rev) / sec for the tire
Take 10 units / sec and divide by 2 * PI * r units / rev
This gives you 10 units / sec * 1 / ( 2 * PI * r ) rev / units
Thus 10
So now you have an equation to calculate rev per sec
However, our rotation values are in degrees and there are 360 degrees / rev
So to get the tire speed we multiply rev / sec * degrees / rev to give us degrees / sec
Since we are using $F for both, this is what it looks like in Houdini:
The distance traveled by the car is tx = ($F / 10) and in that distance the tire needs to rotate the following amount:
(car tx at a given time step) / (2 * PI * r) * 360
I find it helpful to think of the fractions ( units / time step ) / ( units / rev ) * ( degrees / rev )
which re-written is
![MISSING
IMAGE](TireRotation/TireRotationIllustrated.gif)