Non-elliptic lift distribution wings to decrease vertical tailplane size in commercial aircraft

Aircraft performance can be assessed and improved by considering the key variables linked toweight and aerodynamics in the Breguet range equation. In this paper, the authors present a methodfor wing design that allows a reduction in induced drag and minimization of the weight associated withthe aircraft’s vertical tailplane, whilst ensuring desirable lateral-directional flight dynamics. The usecase is a general aviation aircraft for which the wing has been modified using Prandtl’s 1933 approachwhere the span constraint is removed to yield a non-elliptic lift distribution. It is shown that such a liftdistribution also contributes to the aircraft’s lateral-directional stability and as a result, the size andweight of the vertical tail can be reduced. This study was carried out using an analytical frameworkthat combines early design tools such as XFOIL and AVL deemed to be adequate for subsonic flight.Both cruise and approach configurations are considered. Wing twist distribution and span extensionhave been calculated using lifting line theory. The study demonstrates the design trade-off neededbetween flight dynamic modes, such as the Dutch roll mode, and vertical tailplane size when theaircraft is equipped with a wing designed to generate a non-elliptic lift distribution. It is shown thatthis approach allows a 14% improvement in the lift to drag ratio with 44.34% reduction in V-tailweight. These yield a total of 17% improvement in aircraft range. As for the approach phase it shareall the characteristics observed in cruise with the difference that Dutch roll mode is stable for almostall the smaller size of V-tail. Further work requires to focus on the placement of ailerons to removeadverse yaw tendencies.