I mean the optimal taper ratio for an unswept trapezoidal wing for minimising induced drag.
I see a lot of places recommending a value of 0.45 to give as close to an elliptical distribution, therefore maximising Oswald efficiency (to 1). However, Hoerner (Fluid-Dynamic Drag, chapter 7-2) has this plot which suggests the optimal taper ratio is about 0.356 (graphical line fit).
Similar graphs are produced in this paper: Induced Drag of High-Aspect Ratio Wings Tommy M. Chen and Joseph Katz
This exact taper ratio is used by BAe regional jets also.
I haven't read about this thoroughly enough. Maybe this value considers root chord and wing area to be fixed, therefore as taper ratio is decreased the aspect ratio must increase to maintain a constant area. The increased AR (really the increased span) reduces the induced drag.
Does anyone know the answer? I'd really like to be able to justify my taper ratio for an aircraft design assignment.