tjvirden wrote: ↑Thu Sep 23, 2021 12:39 pm
Yes, it does, almost perfectly. Your assumption is correct, for tires of the construction that are available to buy. The tread of course has variable thickness so the outer surface is not circular, but the casing (the fibres embedded in elastomer matrix) experiences high stress at normal pressures so the tread has virtually no impact on the casing shape, which is circular (constant radius) from the points of rim contact.
To be blunt: diagrams that "show" non-circular casings are purely imaginary for the sorts of tires used on road bikes. Even heavy-treaded gravel/MTB tires at low pressure have very little deviation from this. Except, of course, at the contact patch - the tire conforms to a hard surface and there's a mix of tire/surface deformation on soft surfaces. Even then, the casing will have near-constant radius between the rim and the contact patch.
I'll say, my drawing is bad. But your statement is kinda right and wrong at the same time. Tire form almost circular shape with nearly constant arc but how close it looks VS a circle depend on casing width VS rim width ratio.
Hypothetically, say you have 50mm wide rim, and only 63mm wide tire casing (about casing width of 23c tire). You can't do outward arc then inward arc to form a near complete circle. There is not enough tire casing for that. (try to draw it if you will). Tire will start upward arc first then inward arc almost right away creating a very short y axis height thus wide but short shape. It's like we slice a very small part of a circle and put it on top of straight rim wall.
In another extreme put 54mm mounted width tire (2.25" mtb) tire on 15mm id rim. This tire likely have >160mm casing width. It's plenty to form nearly a complete circle on top of the narrow base rim. So the tire likely arc outward aggressively first once it clear rim base to form a near complete circle. Look at this combo, it looks light a light bulb with narrow rim at the base of circular-ish tire on top.
First option is wide because of the rim, but with short casing thus low height. Second option is both wide and tall. Real world tire aren't this extremely different as this hypothetical combo but principle still there. They form consistent arc, but doesn't have to represent a complete circle, can be just smaller part of it in the case of wide rim narrow tire.