Determination of optimum planforms for control surfaces

A theoretical analysis is made to determine the optimum chord distribution, location, and extent of control surfaces, with the ratio of hinge moment to effectiveness as the criterion. Expressions for the effectiveness - for ailerons, the rolling moment, and for tail surfaces, the change of lift on the tail due to deflection of the surface-were derived from lifting line theory. Solutions found for a range of airfoil planforms indicate that, regardless of the characteristics of the tail surface, the chord of the rudder or the elevator should be very nearly constant over its span. The optimum ailerons are also of a characteristics shape, varying little with the planform of the wing.