Here's my attempt to estimate mathematically how tire width varies with rim width...
T is the distance along the tire from bead to bead.
r is the radius of the circular shape the tire cross-section assumes when the tire gets inflated on a rim of width
w - width being the internal well width where the tire bead fits. The width of the tire is then 2
r.
Here I plot
r versus
w for several different tires:
