Originally Posted by
Kontact
Wider rims make bicycle tires taller, not shorter. Period. The cross section is a hoop, and a wider rim adds to that hoop's circumference. If the tire gets 2mm wider, it will get at least 1mm taller.
No, that's also inaccurate.
It's true that widening the rim will cause the circumference of the virtual "circle" to grow, but it also causes the center of that virtual circle to move downward. For example, here are two circular cross-sections with the same arc length, but different "rim widths":
In the blue case, representing a zero rim width ("tire bead pinched together"), the circle's center is halfway between the rim and the top of the tire. In the red case, where the rim has been made very wide so that the tire is a half-circle, the circle's center is at the same height as the virtual rim. So while the red virtual circle has double the circumference of the blue, the inflated height of the tire is the same in both cases.
Under this geometric model, the maximum inflated height actually happens when the internal rim width is around ~30% of the cross-sectional arc length. (Although, you shouldn't use this to predict actual tires on actual rims. It's a good model for understanding why tires act how they do, but there are other factors that fudge the results significantly when you're concerned about millimeters in the real world.)