Numerical solutions of induced velocities by semi-infinite tip vortex lines

The method of Rand and Rosen⁹ (for improving convergence on computed axial induced velocity for a helical wake) is extended to include all velocity components, all points in the wake, and nonhelical vortex lines (contraction). The method is based on finding upper and lower bounds on the truncated integral. Comparisons with other methods show that the present approach is efficient and accurate. Further, it avoids the errors associated with discretization of the vortex lines. Convergence occurs in only three to five revolutions, about 10% of the normal requirement.