A response surface equation for the drag polar for an airplane flying in the vicinity of wavy sea surface

The drag polar equation is the key issue to calculate the performance-based parameters during various flight phases and determine the optimum conditions. This is an essential feature to be included in airplane flight control system to manage the flight. The aircraft under certain emergency conditions are instructed to land on sea water. This underlines the combinational role of ground effect and the surface wave shape on airplane aerodynamic responses. Up to now, many investigations have described the airfoil and wing aerodynamic behaviors near the ground but none was devoted to an airplane flying near a wavy surface. In this paper, intensive numerical simulations have been carried out on a general aviation airplane flying near the water wavy surface. The effects of ground proximity as well as the wave amplitude have been investigated on airplane 2D longitudinal forces and moment. Some limited wind tunnel tests have also been performed on the same model, in the vicinity of water surface to validate the numerical calculations. A statistical quadratic equation based on Response Surface Model, RSM, has been proposed for the airplane flying in the vicinity of the wavy water in which, the wave shape deterioration due to both the airplane flowfield and the viscous dissipation has been taken into account. The statistical measures approve the model quality and accuracy in comparison to the numerical simulation data. The results show that the oscillations in aerodynamic forces are strong functions of the wave amplitude. The time variations of both C L and C D follow the shape of the surface wave while it does not have any remarkable effect on their mean values.