Starting with bias ply tires: The old standard on cars was the four-ply bias ply tire. The tires were constructed using nylon or rayon cords in the tire plies. Using the four ply tire as an example, the carcass first ply is wrapped around one metal wire tire bead, then runs at about a 30 degree angle (diagonally) across one sidewall, then across the tread, then across the other sidewall, and wraps around the other bead. The second ply runs at a 30 degree angle, but in the opposite direction. The third runs as does the first, and the fourth runs as does the second. Each ply is at about a 60 degree angle to each other (from where the term “bias" comes from). The tread and sidewalls have the same number of plies. This results in a very strong sidewall and tread, but with very little flexibility. With the weight of a vehicle on the tire, the sidewall has very little flexibility, and as the vehicle rolls, its weight causes the tread to “squirm", or deform against the road surface. At proper inflation pressure, this is the only part if the tire that can flex, and is the main reason why treadwear is higher on bias tires than on radials. Also, on the road surface the circumferential sipes in the tire treads tend to close up or pinch together, which isn't beneficial in the rain. It also results in rather high rolling resistance. These tires tend to run warmer due to this friction with the road surface. Radial tires, to my knowledge, were first produced my Michelin in about 1947. Radials didn't make inroads in the US until the late 1960's. The radial tire construction varies from the bias tire in a number of ways. The carcass ply wraps around one tire bead as with the bias tire, but runs straight across the first sidewall, the tread, and the second sidewall to the other bead. It does not run at an angle, but runs radially from the theoretical center of the tire. This is where the term “radial" comes from. The carcass ply is generally rayon, or possibly an aramid fiber, and is generally a single ply (some radial tires a second ply runs over the first). This forms the tire carcass. Unlike the bias, the carcass is constructed with a single ply, or at most, two plies. The tread plies are separate from the carcass plies, and are placed on the carcass, running circumferentially around the tire. Tread plies are generally two, sometimes more. The tread plies can be rayon or aramid, and oftentimes are reinforced with a special steel wire mesh. This results in a very stiff tread. With the weight of a car on the radial tire, the sidewall is very flexible, due to its single ply. You'll probably notice the characteristic bulge in the sidewall at the bottom of the tire. When rolling, it is the sidewall that flexes, while the tread stays relatively rigid. The tread does not squirm on the road surface, and the tread sipes remain open. This is a major reason why radial tires do not wear as quickly as the bias. Also, rolling resistance is greatly reduced. One drawback to a radial tire is that during to its single ply sidewall, that sidewall can be easily damaged from rubbing against curbs. This dissertation isn't all-encompassing by any means. It is written at 3 AM because I couldn't sleep!
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