|M.Sc Thesis||Department of Aerospace Engineering|
|Supervisor:||Assoc. Prof. Iosilevskii Gil|
|Full Thesis text - in Hebrew|
The induced drag force is usually associated with the energy that is released into the flow field in the process of the development of lift. It appears as kinetic energy of the vortices that are left behind the airplane during its motion. When a continuous vertical gust acts on the airplane, the lift distribution on it changes, and so does the field of vortices behind it. In most cases this constitutes a small perturbation to the original flight condition, but the result can be an increase in the induced drag, and therefore in the fuel consumption.
The induced drag added to an airplane due to the gust can be found using energy approach. The main difficulty in practical implementation of this method lay in obtaining the intensity of the vortices with sufficient accuracy. It can be achieved with numerical methods, but requires extensive computing resources. In principle, it can be achieved analytically using the method of asymptotic expansions, with the reciprocal of the aspect ratio serving as a small parameter. However, formal asymptotic methods do not offer an adequate solution to the problem, since this solution is invariably compiled from several different solutions, each applicable for a different gust frequency range.
In this work, an informal asymptotic theory of a wing in unsteady motion is developed. The theory allows obtaining leading order approximations for the intensities of the vortices left behind the wing, and the aerodynamic loads acting on the wing, which are uniformly valid for all frequencies. The expressions obtained for the loads recover the results of a strip theory for high frequencies and those of the Prandtl’s lifting line for low frequencies. They can be easily incorporated in aeroelastic equations of motion to calculate the induced drag of an elastically responsive airplane.