Lift and moment on thin arrowhead wings with supersonic edges oscillating in symmetric flapping and roll and application to the flutter of an all-movable control surface

H. J. Cunningham
naca-tn-4189
Jan 1958


A theoretical treatment is presented for determining lift and moment on thin arrowhead or pointed-tip wings of which the delta plan form is a special case with an unswept trailing edge. On the basis of linearized supersonic potential-flow theory for the symmetric flapping and rolling modes of harmonic oscillation, expressions have been developed for the section and total forces and moments to the third power of the reduced frequency. A limitation to the Mach number range is that the component of flow normal to all edges is supersonic or sonic. Sample results are given in the form of curves to show that retention of terms to the third power of the frequency gives good accuracy aver a range of frequency that covers many practical flutter applications. Plots are given of the spanwise distribution of section force and moment for symmetric flapping and rolling modes. Approximating the section force and moment by multiplying the section quantities of a rigid translating wing by the flapping and rolling mode shapes ()termed a 'finite-wing strip theory') is shown to result in an overestimation of forces and moments in comparison with the results of the present analysis. A modal type of flutter analysis for an all-movable control surface wherein all bending and twisting flexibilities are effectively concentrated in a supporting shaft is made by use of natural (coupled) modes. A sample flutter analysis using two coupled modes is given for a Mach number of 1.6 for an arrowhead wing with the leading edge swept back 45 degrees and the trailing edge swept forward 15 degrees. A near coincidence of the first two natural frequencies is found to be detrimental as regards stiffness required to prevent flutter.

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