A ote on the Dynamic Stability of Aircraft at High - Subsonic Speeds when Considering Unsteady Flow

The effect of an increase in speed relative to the speed of sound on the unsteady flow round a harmonically oscillating aerofoil, is to increase the lag of the aerodynamic forces and moments behind the deflection when the frequency is small. It is shown theoretically that this will result in a serious deterioration of the damping of both the lateral oscillation and the high frequency longitudinal oscillation with high Mach numbers. Use is made of derivatives calculated for flutter purposes to estimate the unsteady derivatives at aircraft oscillation frequencies. Illustrative examples are presented. 1. I ntroduction.-Calculations on the dynamic stability of aircraft are generally made with quasi-steady aerodynamic coefficients, i.e., the forces and moments acting on each aerofoil surface at any instant of an oscillatory motion are calculated on the assumption that the aerofoil is in steady motion under the conditions pertaining at that instant. In the past flight-test results have confirmed the quasi-steady theory within the accuracy possible in such tests. Recent flight tests with the 11Jeteor, however, showed a marked divergence between the measured damping in yaw with rudder fixed and theoretical estimations based on quasi-steady aerodynamic derivatives ; this divergence increased with Mach number. The difference between theory and experiment is shown in Fig. 1, where the logarithmic decrement <5 of the directional oscillation is plotted as obtained from flight tests; quasi-steady theory and unsteady theory. It is seen that the observed loss in damping with higher Mach numbers can satisfactorily be explained by the effects of unsteady flow. Recent flight tests on a tailless aircraft at high speeds have also tended to throw doubt on the quasi-steady theory and some experiments in the free-flight tunnel at Langley Field by W. E. Cotter" seem to confirm the results of theory considering the effect of unsteady flow on the damping in pitch of tailless models even with incompressible flow. The effect on the damping of aircraft of taking into account the unsteady flow conditions was first considered by Glauert'. In common with more recent publicationst'" this treatment dealt only with incompressible flow. Under these conditions the effect of allowing for unsteady flow does not appear to be large for aerofoils oscillating about a point forward of the quarter-chord, at any rate for the range of frequencies likely to occur in flight. In this report an attempt has been made to take into account the unsteady conditions in compressible …