Optimum Spanloads Incorporating Wing Structural Considerations And Formation Flying
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For single aircraft, a discrete vortex method which performs the calculations in the Trefftz plane has been used to calculate optimum spanloads for non-coplanar multi-surface configurations. The method includes constraints for lift coefficient, pitching moment coefficient and wing root bending moment. This wing structural constraint has been introduced such that wing geometry is not changed but the modified load distributions can be related to wing weight. Changes in wing induced drag and weight were converted to aircraft total gross weight and fuel weight benefits, so that optimum spanloads that give maximum take-off gross weight reductions can be found. Results show that a reduction in root bending moment from a lift distribution that gives minimum induced drag leads to more triangular spanloads, where the loads are shifted towards the root, reducing wing weight and increasing induced drag. A slight reduction in root bending moment is always beneficial, since the initial increase in induced drag is very small compared to the wing weight decrease. Total weight benefits were studied for a Boeing 777-200IGW type configuration, obtaining take-off gross weight improvements of about 1% for maximum range missions. When performing economical, reduced-range missions, improvements can almost double. A long range, more aerodynamically driven aircraft like the Boeing 777-200IGW will experience lower benefits as a result of increasing drag. Short to medium range aircraft will profit the most from more triangular lift distributions.
Formation flight configurations can also result in large induced drag reductions for load distributions that deviate from the elliptical one. Optimum spanloads for a group of aircraft flying in an arrow formation were studied using the same discrete vortex method, now under constraints in lift, pitching moment and rolling moment coefficients. It has been shown that large general improvements in induced drag can be obtained when the spanwise and vertical distances between aircraft are small. In certain cases, using our potential flow vortex model, this results in negative (thrust) induced drag on some airplanes in the configuration. The optimum load distributions necessary to achieve these benefits may, however, correspond to a geometry that will produce impractical lift distributions if the aircraft are flying alone. Optimum separation among airplanes in this type of formation is determined by such diverse factors as the ability to generate the required optimum load distributions or the need for collision avoidance.
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