Numerical appraisal of multhopp's low-frequency subsonic lifting-surface theory

Abstract

Summary. A brief review of oscillatory theories reveals that some of these suffer from a defect that has been corrected in the Algol programme now subject to critical examination. Its features in steady and low-frequency subsonic flow are outlined, and extensive tabulated results are presented for seventeen plan- forms. The accuracy and convergence of solutions are studied in relation to arbitrary parameters representing chordwise and spanwise collocation positions, spanwise integration points and the essential central rounding of sweptback wings. Rectangular and other wings with streamwise symmetry, untapered and tapered sweptback wings, slender and curved-tipped wings show progressively slower convergence, and they are examined in respect of overall forces, spanwise loading, local aerodynamic centres, central chordwise loading and oscillatory pitching derivatives. Some new general criteria are recommended for selecting the arbitrary parameters. Serious inaccuracy arising from the original defect is established, and hence the need to examine theories for general frequency. The residual errors in the Algol programme may stem from high or low aspect ratio demanding extra spanwise or chordwise terms, but the most elusive cause of collocation error in the standard solutions is found to be insufficient central rounding of highly sweptback wings. It is demonstrated, however, that the rounding itself often influences the aerodynamics as much as the standard collocation error and in the opposite sense, so that one correction is useless without the other. Approximate results with both effects taken into account provide a few examples of improved comparisons with exact theory and experiment.