Some people have some strange ways of measuring wheels. I like the closing door analogy. When measuring (forward) wheels, one front corner remains stationery (the hinge) while the other corner swings round.
The usual and most practical way of measuring that move in the absence of a turning circle is in a straight line, but that is actually a short-cut across the turning circle rather than the long way around following the circumference. How significant is the difference?
I wanted to make some wheeling templates for playing Irregular Wars: Conflict at the World's End. Base widths are only 30mm so micro-movements can be quite significant in determining whether, for example, chargers can actually contact.
So the radius of the turning circle is 30mm. This gives a diameter of 60mm, obviously, and a circumference of about 188mm. In the old days I would have had to work out the circumference using a formula but I cheated and used an online calculator. As the unit of measurement in this game for 15mm figures on 30mm bases is inches, there are about 188/25 move units around the circumference = 7.5 units. A 1 inch 'slow' wheel should therefore involve a turn through 360/7.5 degrees = 48 degrees.
The 'fast' wheel forms an isosceles triangle with two sides of 30mm (the base width in its start and finish positions) and one side of 25mm (the move measured by a straight line). I've long forgotten how to calculate the angles of a triangle from the length of its sides, but turning to another online calculator the outer angles are about 65 degrees and the inner angle about 49 degrees.
So, there is only 1 degree difference between the 'slow' and 'fast' wheels. Having made the template based on the true 48 degrees, it seems to reduce the move to 24mm rather than 25mm. It hardly matters and I think we can all sleep soundly again with our straight-line measurement of wheels.
Irregular Wars players may like to download the template here.