On the Minimum Induced Drag of Wings -or- Thinking Outside the Box

Of all the types of drag, induced drag is associated with the creation and generation of lift over wings. Induced drag is directly driven by the span load that the aircraft is flying at. The tools by which to calculate and predict induced drag we use were created by Ludwig Prandtl in 1903. Within a decade after Prandtl created a tool for calculating induced drag, Prandtl and his students had optimized the problem to solve the minimum induced drag for a wing of a given span, formalized and written about in 1920. This solution is quoted in textbooks extensively today. Prandtl did not stop with this first solution, and came to a dramatically different solution in 1932. Subsequent development of this 1932 solution solves several aeronautics design difficulties simultaneously, including maximum performance, minimum structure, minimum drag loss due to control input, and solution to adverse yaw without a vertical tail. This presentation lists that solution by Prandtl, and the refinements by Horten, Jones, Kline, Viswanathan, and Whitcomb.