Comment on "Numerical Lifting Surface Theory-Problems and Progress"

Abstract

N a recent paper, Landahl and Stark1 present a progress report on the status of numerical approaches to nonsteady lifting-surface theory for planar and nonplanar configurations as applied to the linearized thin-wing problem, with particular stress on the subsonic case. Over the past few years, in the course of studies adapting unsteady lifting-surface theory to marine propellers,24 Davidson Laboratory has developed a new method for the solution of the downwash surface integral equation. By proper expansion of the kernel function and introduction of the so-called lift operator/7 the chordwise integration is performed analytically with the additional advantage that the numerical solution is greatly simplified. These studies indicate that use of the generalized lift operator, which is in fact dictated by the nature of the integral equation itself, is a more accurate and rapid procedure than the usual numerical approaches for evaluating the steady and unsteady pressure distributions on lifting surfaces and resultant hydrodynamic forces. This technique has been used in Ref. 5, where the lifting surfaces are the blades of a marine propeller operating in nonuniform inflow, and in Ref. 6 for the case of a deeply submerged, flat, rectangular hydrofoil in steady flow. In Ref. 7, this new approach has been applied to several two-dimensional, unsteady airfoil problems and has yielded results identical to the known explicit solutions.