<p>This work investigates the role of fiber orientation in the analysis and simulation of a helically reinforced, pressurized torus. Therefore, the concept of the neutral wrapping angle of a straight cylinder is extended to a torus. This specific angle establishes an isotensoidal load condition by balancing axial and circumferential stresses. It varies for a torus along the cross section due to fluctuating circumferential stresses. Because of the curvature of the torus, the geometrical wrapping angle is not constant. Bending a reinforced straight cylinder into a toroidal shape or winding fibers onto a toroidal part inherently creates a varying geometrical wrapping angle, which follows a similar pattern to the toroidal neutral wrapping angle, but differs quantitatively. Using the finite element method and suitable modeling approaches, we analyze this difference as well as the interplay between fiber orientation and curvature effects on toroidal deformations. Specifically, we examine how deviations from the neutral wrapping angle superpose with the Bourdon effect. These interactions emphasize the need for precise modeling of varying wrapping angles, especially in highly curved toroidal geometries.</p>