Interference of Wing and Multipropellers

A systematic procedure is presented for the analysis of the interference of a wing with multipropellers. The assumptions are made that the radius of the propeller and the chord are of the same order and both are much smaller than the span. Using the chord to span ratio as the small expansion parameter, the local two-dimensional solution for the sectional lift to angle-of-attack relationship is uncoupled from the outer three-dimensional solution in the spirit of Prandtl's lifting line theory. Details of the nonuniform stream behind the propellers enter into the local sectional analysis. For the outer solution, the planform of the wing reduces to the lifting line and the stream behind the propellers reduces to a thin sheet of a jet carrying the sectional momentum gained across the propellers and supporting a pressure difference across the sheet. By representing the thin sheet of a jet as a vortex sheet, an integral equation is obtained. When the momentum gain across the propellers is not too large, the integral equation can be further simplified. Several numerical examples are presented to demonstrate the versatility of the analysis.