A braiding machine in which spools wound with tensile elements are mounted on carriages that are disposed on a rotor track around the perimeter of the braiding machine. The perimeter of the braiding machine is non-circular, such that the area enclosed by the perimeter of the non-circular braiding machine is substantially less than the area enclosed by a circular braiding machine having a perimeter of the same length as the perimeter of the non-circular braiding machine.