Physics and mathematics fails. To make the profile of a tyre, on the inside, anything other than a circular arc, you need circumferential bands as found in radial car tyres. The metal of the rim provides this below the edge of the bead hook, but above that the hoop stress and pressure are in equilibrium only for a circular cross section, if we ignore the different circumferential hoop stress between the periphery and bore of the toroid, which is a reasonable simplification when the cross section is very small compared with the radius of revolution.
The external profile of a bias ply bicycle tyre is, then, the interior circle + the casing and tread thickness profile, and this doesn't depend on whether it's a tubular or a clincher, although there are more clinchers with very non-uniform tread thickness (thick in centre, tapering significantly towards the side wall) which can give a somewhat elliptical profile.
Physics and mathematics fails. To make the profile of a tyre, on the inside, anything other than a circular arc, you need circumferential bands as found in radial car tyres. The metal of the rim provides this below the edge of the bead hook, but above that the hoop stress and pressure are in equilibrium only for a circular cross section, if we ignore the different circumferential hoop stress between the periphery and bore of the toroid, which is a reasonable simplification when the cross section is very small compared with the radius of revolution.
The external profile of a bias ply bicycle tyre is, then, the interior circle + the casing and tread thickness profile, and this doesn't depend on whether it's a tubular or a clincher, although there are more clinchers with very non-uniform tread thickness (thick in centre, tapering significantly towards the side wall) which can give a somewhat elliptical profile.