Prandtl's biplane theory applied to canard and tandem aircraft

Prandtl's biplane theory for elliptic loadings is generalized to apply to nonelliptic spanwise load distributions. The induced drag is calculated by assuming an infinite stagger distance so all of the mutually induced drag acts upon the rear surface which has no effect upon the front surface. Consequently, the mutually induced drag is calculated by integrating the Trefftz-plane downwash of the front surface over the independent load distribution on the rear surface. This procedure is verified by explicit solutions that give the same mutually induced drag irrespective of the fore and aft location of the larger span when carrying either an elliptic or a uniform load distribution. It was found that the mutually induced drag was less when the larger span had a uniform load distribution, but the total induced drag was not decreased because of the additional self-induced drag produced by the change from the ideal elliptic loading to a uniform loading. However, when the larger span carried a uniform loading it allowed the smaller span, when either fore or aft, to support more of the aircraft's weight at the minimum induced drag condition.