The main wings of most aircraft produce adverse yaw during roll. In order to control the lateral direction of the aircraft during the roll, the rudder is often mixed with the aileron. Lifting-line theory is used here to develop spanwise lift distributions that require the minimum number of terms in the Fourier-series solution for controlling the yawing moment during pure rolling motion using only the main wing. It is shown that the yawing moment can be controlled for arbitrary rolling moments and/or rolling rates by adding symmetric twist in the main wing. The induced-drag penalty for using this method to control the yawing moment is significant and discussed in detail. For example, it is shown that if zero yawing moment is prescribed, the induced drag can increase by 108% for a prescribed rolling moment or by 300% during a steady rolling rate relative to the induced drag in steady level flight. Because this is the minimum-series solution, it does not represent the solution for yaw control with minimum induced drag, since more terms could be used in the Fourier series describing the lift distribution to control yaw with less induced drag. However, the solutions presented here can be useful for aircraft with continuous trailing-edge technologies that are
Nomenclature:, Fourier coefficients in the lifting-line solution for the section-lift distribution, Eq. (1); , coefficients in the decomposed Fourier-series solution to the lifting-line equation related to planform, Eqs. (8) and ( 9); b, wingspan; , coefficients in the decomposed Fourier-series solution to the lifting-line equation related to symmetric baseline twist, Eqs. ( 8) and (10);, induced-drag coefficient; , induced-drag coefficient produced by the elliptic lift distribution for a given aspect ratio and lift coefficient, Eq. (21); , total lift coefficient;̃, section-lift coefficient;̃, , section-lift slope; , rolling-moment coefficient; , yawing-moment coefficient; , , change in yawing moment with rolling moment; ,̄, change in yawing moment with rolling rate; c, section chord length;̄, wing mean chord length; , coefficients in the decomposed Fourier-series solution to the lifting-line equation due to antisymmetric twist related to roll control, Eqs. ( 8) and (11); c root , chord length at wing root; , coefficients in the decomposed Fourier-series solution to the lifting-line equation related to rolling rate, Eqs. (8) and ( 12); , coefficients in the decomposed Fourier-series solution to the lifting-line equation due to symmetric twist related to yaw control, Eqs. (8) and (13); j, term in the infinite series;̃, section lift; N, number of terms retained when truncating the infinite Fourier series; , angular rigid-body rolling rate;̄, dimensionless angular rigid-body rolling rate [pb/(2V ∞ )]; , wing aspect ratio ( 2 ∕ ); , wing taper ratio; , wing planform area; ∞ , freestream airspeed; z, spanwise coordinate relative to the midspan, positive out left wing; , spanwise variation in local geometric angle of attack relative to the freestream; 0 , spanwise varia...