Calculation of subsonic flutter derivatives for an arrowhead wing with control surfaces

Abstract

Summary. An oscillatory lifting-surface theory for subsonic flow (Ref. 1) is used to calculate the aerodynamic forces on an oscillating arrowhead wing of aspect ratio 2 with trailing-edge control surfaces of varying span. The collocation method is outlined for simple harmonic motion of arbitrary mode and frequency and is applied for modes of plunging, pitching and control rotation. The discontinuous upwash in the control-surface problem is replaced by a smooth equivalent function. An alternative treatment for total forces, such as lift and pitching moment, is provided by the reverse-flow theorem with collocation solutions calculated for the \\'reversed wing\\' in appropriate modes. Values of the aerodynamic derivative coefficients are presented for a range of frequency at the Mach numbers 0.781 and 0.927. The variation of the pitching derivatives with frequency, Mach number and pitching axis is illustrated and shows good agreement with the results obtained by other collocation theories and by low-frequency wind-tunnel measurements. For the control-rotation mode, the calculated values of the indirect control derivatives indicate the good comparisons between the various methods of constructing equivalent upwashes and also the satisfactory comparison with the other collocation theories. Values of the direct control derivatives appear more sensitive and large variations in magnitude are associated with the different collocation methods and equivalent upwash treatments.