The Circumferential Contact Problem for the Belted Radial Passenger Car Tire

The belted radial passenger car tire is idealized as a prestressed circular ring connected to a hub through a distribution of linear springs modeling the sidewall. A second distribution of such springs exterior to the ring represents the tread rubber. The tire is supposed to be at rest, loaded at its hub, and pressed onto a flat, rigid, frictiontess roadway. In this situation the linear differential equations of the model are solved using a singular perturbation technique. Given the load at the hub, the solutions furnish the length of tread in contact with the road, the radial and circumferential displacement of all points on the ring, and the distribution of pressure over the region of contact.