Truck width: wheel travel

In this, I explain why the wheels travel the same distance, regardless of truck width. If it seems obvious or tedious to you, dear reader, just skip this short post. It’s just that it came up on a skate forum and it was an uphill battle to convince some members about this. My argumentation is as follows:

Take a look at the picture on the right. Focus your attention on the top left wheel (chosen randomly, but I’ll be referring to just this wheel).
· In the first frame, at the bottom, the skateboard turns to our right. The wheel traces an arc from left to right.
· In the second frame, the skateboard turns left and the wheel traces a smaller arc than before, right to left.
· In the top frame, the skateboard turns right again and the wheel traces an arc, left to right, approximately equal to that in the first frame.

Now, using your imagination, picture that the axle of the same truck is longer, just a few centimeters. I am asking you now to imagine new frames on top of the existing ones.
· In the first frame, the wheel traces an arc, left to right. The arc is longer, but parallel (more accurately: it belongs to a larger but concentric circle) to the original one. It lies on the left side of the original arc.
· In the second frame, the wheel traces an arc, right to left, shorter but again parallel to the original one. Again, it lies on the left of the original arc.
· Third frame, same as first frame.

In the 2nd case, the imaginary one, when the skateboard turns right, the left wheel traces a longer arc than in the 1st case that is actually depicted on the diagram. When the skateboard turns left, the wheel traces a shorter arc than the one of the diagram.

We know that the circumference of a circle is directly proportional to its radius (=2πr, in case you forgot). So, a circle with a radius twice as long as another circle will also have double the circumference. Therefore, as long as the rider is not riding in a closed loop, only in the same direction, the wheels trace curves of equal length on different truck widths (all other things being equal, of course).

[Picture credit: kook55 and I guess Carver Skateboards]


Addendum:

I caught a forum gem on the topic and I though it might be good to show you how this kind of para-theory circulates (image right). Notice that the author, after his authoritative account, moderates his position (“at least this is how… from experience…”).

I believe this is exemplary of consumers trying to justify (on behalf and instead of companies who can’t) why trucks are offered in all sorts of different axle lengths. In reality, there’s no reason for all this variety in axle lengths except that it’s the only thing incompetent truck companies can vary with confidence.

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