Method of fabricating a tire having a geodesic ply

A method of making a geodesic tubeless tire (10) comprising the steps of:

• forming a liner layer (35) into a cylindrical shape on a rotatable tire building drum (5),
• applying a single bias ply (30) reinforced with cords, the cords being oriented parallel at a constant bias angle .theta. to the tire building drum thereby forming the ply into a cylindrical shape overlying the liner;
• positioning a pair of bead cores (26) spaced at a fixed axial distance (l) over the ply establishing the cord length (L) of the ply (30);
• each bead core (26) having an axis coincident with the axis of the building drum (5) thus forming a cylindrical carcass subassembly, the cylindrical carcass subassembly having a pair of bead portions and a pair of turnup ends extending axially outwardly from the bead cores;
• inflating the carcass subassembly while allowing one bead portion of the tire to rotate relative to the opposite bead portion thereby reducing the shear tension in each ply cord, the resultant cord path between bead cores being substantially geodesic;
• stitching the ply turn-up ends (33) to the inflated carcass (20) at a radially outer location;
• applying two or more belt reinforcing layers (50,51) over the carcass (20) at least partially covering the ply turn-up ends (33), wherein the combination of the ply turnup ends (33) and the belt structure (50,51) fix the ply cord path of the ply (30).