Aircraft tire and method of manufacture

A pneumatic tire comprises a belt structure (350) and a torus shaped carcass (340) having a first inner radius and an outer radius. The carcass (340) comprises three or more layers of ply. At least one of these layers of ply is formed from a rubberized strip of one or more cords (25), the strip being wound in an geodesic pattern having the cords (25) extend across the carcass (340) from a first shoulder to a second shoulder in a path that has at least one point tangent to the first inner radius located in the bead area (312) of the tire (100).