A parabolic trailing-edge flap is defined as a parabolic deflection of the airfoil geometry aft of a hinge point. Whereas a traditional flap deflection causes a discontinuous camber-line slope at the hinge point, a parabolic deflection produces a camber line that is first-order continuous at the hinge point. The geometry manipulation of a parabolic flap is mathematically defined such that it can be applied to any airfoil with a known camber line and thickness distribution. Small-angle and small-camber approximations are used to find analytical predictions for the ideal section flap effectiveness as well as the section pitching moment in comparison to a traditional flap. Results of the parabolic flap are compared to those of a traditional flap producing equivalent lift using thin airfoil theory and the vortex-panel method. It is shown that the ideal section flap effectiveness for a parabolic flap can be 33-50% higher than that of a traditional flap, depending on the flap-chord fraction. Additionally, a parabolic flap will produce a change in pitching moment 5-50% greater than that of a traditional flap for a given change in lift. Results may be applied in the design of modern morphing wings, for which complex flap deflections can be produced.
CITATION STYLE
Douglas F, H., Jackson T, R., & James J, J. (2019). Geometric Definition and Ideal Aerodynamic Performance of Parabolic Trailing-Edge Flaps. International Journal of Astronautics and Aeronautical Engineering, 4(1). https://doi.org/10.35840/2631-5009/7526
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