On the kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow /

The derivation of the integral equation which involves this kernel function, originally performed elsewhere (see, for example, NACA Technical Memorandum 979) is reproduced as an appendix. A second appendix gives the reduction of the form of the kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow.This paper treats the kernel function of an integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The kernel function is reduced to a from that can be accurately evaluated by separating the kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the kernel function for the sonic case (Mach number of 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady cases) are given.NACA TN No. 3131."January 1954."Includes bibliographical references.The derivation of the integral equation which involves this kernel function, originally performed elsewhere (see, for example, NACA Technical Memorandum 979) is reproduced as an appendix. A second appendix gives the reduction of the form of the kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow.This paper treats the kernel function of an integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The kernel function is reduced to a from that can be accurately evaluated by separating the kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the kernel function for the sonic case (Mach number of 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady cases) are given.Mode of access: Internet