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The new requirement to test wind tunnel models of combat aircraft at high angles of incidence and high kinetic pressures has led to a review of the factors controlling the model stability. The review suggested that dangerous motions might occur (possibly without prior warning) on models at high angles of incidence unless special preventive measures were taken. An internal tuned damper and balance bump stops were recommended to limit the responses. The bump stops would also prevent the moment limits of the strain gauge balance from being exceeded. The effectiveness of both devices was confirmed by tests on a swept wing model which experienced dangerous bending oscillations in a vertical plane at a Mach number of 0.50 in the incidence range from about 27–29° together with dangerous yawing oscillations in a horizontal plane above an incidence of about 35°. Further research is recommended to ensure the safety of other models. For sting supported models in a conventional wind tunnel, it is shown by analysis that the structural damping in the sting bending mode needs to be about 4 to 6% critical damping. In a cryogenic wind tunnel corresponding levels would need to be 7 to 10% critical damping because of the possibility of increased negative aerodynamic damping relative to ambient conditions.