Longitudinal Stability of a Supercavitating Vehicle

At very high speeds, underwater bodies develop cavitation at the trailing edges of sharp corners or from contours where pressures are sufficiently low to allow the formation of cavities containing water vapor. At sufficiently high speeds, a properly designed cavitator at the nose of an underwater vehicle can induce the formation of a vaporous cavity that entirely envelops the vehicle. The injection of gas behind the cavitator can result in the creation of cavities of comparable size at lower vehicle velocity and drag than would be required for vapor cavities. The formation of the cavity results in a significant reduction in drag on the vehicle and so-called high-speed supercavitating vehicles (HSSVs) have been reported to operate at speeds in excess of 100 m/s. The first part of this paper presents a derivation of a model for the longitudinal or pitch-plane dynamics of an HSSV. The vehicle is characterized by its mass and moment of inertia relative to a reference frame fixed to the body. The cavitator is assumed to be a disk, with a scale parameter that can be adjusted to represent an acute cone having an opposite sign for its lift curve slope. The control surface lift curve is specified relative to the cavitator lift effectiveness. A force model for a planing afterbody is also presented. The planing force model is found to be a significant source of damping and depending on a number of vehicle characteristics, the longitudinal dynamics may be stable. This result is significantly different than the conclusions of a number of previously published works. The final section of the paper examines the longitudinal stability at equilibrium of a 170-mm diameter HSSV. Results of parametric studies show the variation of pole locations associated with the transfer function relating cavitator angle to body pitch rate. The varied parameters are length, speed, fin effectiveness, body density, and the load carried on the aft planing surface.