Originally Posted by
FBinNY
Yes, but the except is a big exception. We don't have an expression for radial tire section or height, so we let the context guide us. When speaking of trail, tire width is a proxy for tire height, and/or overall change in wheel radius.
BTW - tire width and height are not the same, but for most purposes, especially when dealing only with a change we can use the width as a proxy for the height. However, we need to be careful when dealing with close vertical clearance because tread thickness can make a critical difference.
I mainly mess around with road bikes, so for most of my tires there isn't a lot of center-tread build up, at least not so my clearances are challenged. When I calculate trail I have both measured tire diamter and estimated it with a simple equation. Like all models the equation is not perfect, but it is useful:
diameter = bead seat diameter + 2 * measured tire width.
Sometimes it matches reality and sometimes it doesn't.
For the head of a cycle engineering department, it makes sense to need to understand the loss of trail with tire lean. It also makes sense to study a Vehicle Dynamics text book, most of which analyze tire contact patch issues for single-track vehicles, and how the tire interacts with the road under vehicle and dynamic loading.