Wheelbase and front and rear truck angles are directly related1. In the following illustration, if the turning radius KO (red and yellow points) is to remain constant (for a specific lean of the deck) regardless of how long the deck is, then the pivot axes’ angles have to change accordingly2. Visualize this yourself: imagine the deck (purple ellipsis) being longer, along the dashed purple line, and notice that a way to keep KO constant is wider concentric circles, which would intersect the purple line at steeper angles (i.e, higher pivot angles).
An animated example might help. Take a skateboard with a front truck (any single pivot truck) with a pivot axis angle of 60°, on which the rider leans 20°. The front axle then turns close to 31° (31,64° to be precise, but I won’t demonstrate this in such precision). If the rear truck’s angle is 20° then the rear axle will turn approx. 7°. If we could on the fly change our wheelbase (distance between trucks) we get different turning radii:
The same rider, tilting a skateboard 20°, using the same 60° front truck, with a fixed wheelbase of 100cm, but a variable rear truck pivot axis angle would look like this:
Or, let’s just keep: front truck angle (60°), tilt angle (20°) and turning radius (101,28cm) constant and change rear angle and wheelbase at the same time appropriately (notice that we could, of course, use a negative rear truck angle):
What I wish was shown with some clarity, is that these three variables (front and rear angles and wheelbase) are sufficient and necessary to determine the turning radius of a skateboard, when tilted a given amount.
1. If needed, a more technical version of this article, incl. formal proof and formulas, is here.
2. In the examples that follow this note, the front pivot axis angle never changes. Keeping the front angle constant was an arbitrary choice. Indeed, it’s arbitrary to label either truck as “front” or “rear.” In the text, I kept the front constant for two reasons. 1) I wanted to keep the text’s focus only on one truck, to help the reader understand more easily the thought experiment with the wheelbase and the turning radius. It could get convoluted, with everything changing at once. 2) I kept the front (and not the rear) angle constant, because most, if not all, riders use the front part of the deck as reference for placing their feet and driving the board. Theoretically, if you changed only the rear angle and the wheelbase to get the same turning radius from a board, the rider would not realize she’s riding a different setup. Handling would feel the same. If you changed the front instead, riding would be radically different, even if the radius were the same.