The lift on delta wings with leading edge separation in periodic flow

At present, a number of theories exist for the calculation of lift on delta wings with leading edge separation. Of the accepted theories, all but one are based upon the assumption of very small aspect ratio - the exception provides excellent agreement with experimental data for an aspect ratio range of practical interest. However, none of the theories account for the presence of unsteady disturbances in the mean flow. The situation in which a delta wing experiences leading edge separation in the presence of unsteady disturbances is of great practical interest. Such a situation is often encountered by a delta winged vehicle when landing and taking off. In this paper, a semi-empirical theory is developed which adequately predicts the lift on delta wings of practical aspect ratios (up to 2. 0) and angles of incidence (up to 15°) under the conditions described above. A small aspect ratio lifting line method is semi-empirically modified so as to predict accurately the lifts occurring at larger aspect ratios in the steady case. The semi-empirical parameters are determined with the aid of a high speed digital computer, the IBM 360/65. The modified steady flow results are then extended into the unsteady flow regime by assuming a suitable form for the disturbance and again using a lifting line approach. The most compelling feature of the lifting line analysis is the fact that it is far more conceptually straightforward than any of the previous methods. It is also an extremely versatile and powerful method of attacking three dimensional flow problems and is easily utilized in the unsteady regime; only with great difficulty would it be possible to adapt any of the previous methods to the unsteady flow problem considered in this paper. In fact, the most difficult part of the present analysis lies in the solution of the lifting line equation for the component of circulation induced by the leading edge separation rather than in the determination of the unsteady component of circulation.