Most times when I see a failed bicycle tyre (one where the threads are showing through) they look something like this, with diagonal threads clearly visible
So I'd reason that most/all bicycle tires are Cross Ply in build, and not Radial.
My google-fu does return these points:
- Radial tyres are cheaper to make than the equivalent cross ply
- Radial tyres are lighter and have better fuel economy than a cross ply
- Radial tyres track better, where cross ply tyres have been known to "tramline" vehicles.
- Cross ply tyres have a more rigid sidewall, radial tyres have a more supple sidewall.
- Suspension needs to be altered in a car to accommodate the differences between ride handling in the two styles.
- Automobiles tyres are almost exclusively radial.
- 4WD tyres are predominantly radial, but cross ply have much better sidewall strength and resist damage better.
- Motorcycle tyres may be either, where radials are preferred for speed and cross ply are preferred for load carrying (touring or cruising)
- Truck (ie load carrying vehicles) might use either, with cross ply for load carrying and radial for long distance.
Even wikipedia is ambiguous, saying
Radial tires have occasionally found application on bicycles, used on the 1980s Miyata touring bicycle; models 1000 and 610, and more recently in 2009 on the Maxxis Radiale. Panaracer radial tires were also standard on the Jamis Gentry model bicycle in 1985.
I would have expected that radial construction with "supple side walls" to help a lot in reducing rolling resistance, but its uncommon.
Why are Radial tyre constructions uncommon in bicycle tyres?