Linear Algebra Approach to Induced Drag Minimization of an Aircraft

초록

In general, induced drag of a single wing is minimized when the lift distribution is elliptic. However, most aircraft obtain longitudinal stability by using a horizontal tail. Even if the main wing has an elliptic lift distribution, the induced drag of the whole aircraft is not minimized at the trim condition. This paper presents a method to find the twist angle distribution that minimizes the induced drag of the whole aircraft using a vortex panel method combined with linear algebra techniques. With a given set of constraints such as fixed lifts at the main wing and the tail, induced drag is expressed as a quadratic form of the twist distribution. As the solution is not unique, an additional objective is proposed to find an optimal distribution. The proposed methodology is tested with three example designs and compared with AVL. Depending on the design, as much as five percent reduction in the induced drag is achieve while maintaining the given trim condition.