Math for VSFX

Updated on Nov 25  2017

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copyright Deborah R. Fowler



Tire Rotation

Deborah R. Fowler



Tire Rotation

Posted on Nov 25  2017


   
Recall that the circumference of a circle is 2 * PI * radius


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.

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This is true for any radius.



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.

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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 units / sec *  1 / ( 2 * PI * r )    rev / units = rev / sec 
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 units / time step  *  rev / units * degrees / rev  = degrees / time step


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