Vortex-lattice treatment of rectangular wings with oscillating control surfaces

Abstract

The vortex-lattice method for simple harmonic motion of general frequency (R. & M. 2961) is used to calculate the derivatives for rectangular wings with oscillating constant-chord flaps. The discontinuous chordwise boundary condition associated with fullLspan flaps, is replaced by a continuous equivalent downwash which is determined on the basis of two-dimensional oscillatory theory. In the particular case when the frequency tends to zero, the equivalent downwash is obtained on a distinct quasi-steady basis ; stability derivatives are then evaluated by using an alternative form of the vortex-lattice method for low frequency (R. & M. 2922). To allow for the spanwise discontinuity due to outboard flaps, a further adjustment is made to the boundary condition by the use of partial-span downwash factors. Comparison of the stability derivatives with values obtained by the Multhopp-Garner method, indicates that the present treatment for low frequency is satisfactory for full-span and outboard flaps oil plan-forms of aspect ratio 2 and 4. For general frequencies, results for aspect ratio 2 with full-span flaps compare well with the values for lift and pitching-moment derivatives obtained by Lawrence and Gerber.