Effect of the wing shape on the thrust of flapping wing

Simulations of harmonically oscillating wings were performed using two-dimensional and three-dimensional boundary element method computer programs: the corresponding hydrodynamic forces were obtained by assuming potential flow. The maximum thickness of symmetric 4-digit NACA airfoils was varied in order to assess the effect of changing the foil shape on the generated thrust. It was found that the thrust coefficient per unit of wing mass decreases in magnitude when the thickness increases. The result indicates that, if the wing mass is fixed, its thickness has to be minimised in order to maximise the generated thrust. Another important finding is the dependence on the motion frequency, i.e. for a fixed foil thickness the thrust coefficient per unit of wing mass increases with the motion frequency. However, when the foil thickness becomes larger, the motion frequency effect on the generated thrust becomes less pertinent, i.e. the thrust range for a slender foil is larger than that of a thicker one over the same motion frequency range. The three-dimensional effect due to the wing spanwise shape was also investigated by changing the wing sweep angle and the influence on the generated thrust was insignificant within the range of investigated parameters. The outcome reinforces the idea that the function of swept wings for low-speed flyers, such as birds, is mainly structural as the sweep angle can be related to a desired aeroelastic response of the oscillating wing. (C) 2011 Elsevier Inc. All rights reserved.