Originally Posted by
Atlas Shrugged
I am still curious at what point when a rim gets wider, does the diameter or height start to drop? When taken to an extreme width, the tire will get smaller in diameter. My gravel wheels are 25mm internal width; what would that do? It would be very interesting to have the actual dimensions over a large range of rim widths and a very supple tire. The graphic presented is laughable in its obvious errors.
I just realized that this could be solved mathematically writing an equation the gives tire height (h) for a given chord length and variable rim width (R). Solve for delta h vs delta R. Where delta h goes to zero, there's the rim width. Good college problem. Sadly, my head injury erased that math. Maybe I'll take it on for brain stimulus but I may well fire up Acad and get there faster by trial and error. (Not as exact but doable, not "can I?") (Say we mount a tire on a rim width that the tire comes off vertically and forms a semi-circle. Height = rim width/2, ie tire radius. Now pinch those rim sides together. Tire a full circle now. Height = full diameter but the diameter had been halved and height is the same. I'll place my first bet on the rim giving the maximum height being half way between.
So (pure fantasy, not drawn or anything - say we have an "25C" tire. Find that if we put if on a 32mm inside width rim the sidewalls come off it vertical. Then, if I placed the winning bet, the highest possible this tire can go will be on a 32/2 = 16mm rim. 1st bet 0.5. Any others? (Don't go measuring your tires and come back and tell me my 32mm for the vertical sidewall is wrong. I just pulled that out of a hat.)
Now, once this rim and maximum height is established, we can make a relationship between tire width and required rim to get maximum height. Then any tire can be simply laid out, width measured and height predicted. (But - a molded thread that holds its shape need not apply. This is just for tires that behave like balloons or flexible pressure vessels.)