An asymptotic theory for the interference of large aspect ratio swept wings and multiple propeller slipstreams

This paper presents an asymptotic method for the analysis of the interference of multiple tractor propeller slipstream with large aspect ratio swept wings. It is assumed that the height of the slipstream is of the order of the wing chord and its spanwise extent is of the order of the wing span. Three different flow regions are identified by employing different stretching transformations. Asymptotic expansions are made in each of the three regions, using the chord to span ratio as the small expansion parameter. The details of the nonuniform flow in the slipstream enter into the wing sectional analysis. In the outer limit, the wing shrinks to a swept lifting line, and the slipstream reduces to a thin sheet of jet carrying the momentum gain from the propeller. The curvature of this jet sheet results in a pressure difference which is represented by a vortex sheet. The governing equations are solved by discretization. Several examples are considered for which experimental data are available. Comparison of the present results with the experimental data as well as other numerical solutions showed generally good agreement.