A Quasi-Steady Evaluation of Submarine Rising Stability: The Stability Limit

When submarines blow ballast to surface from depth in an emergency, they can experience a roll instability if they ascend with large flow incidence angles. It is shown that an instability is caused by the destabilizing hydrodynamic rolling moment on the sail (which points upwards into the onset crossflow) overcoming the static righting moment (the center of gravity is below the center of buoyancy) as the boat is accelerated upwards by buoyancy. The former increases with velocity squared while the latter is constant. Conventional first order rolling moment models are shown to underpredict the nonlinear hydrodynamic rolling moment, especially at high incidence angles. However, properly modelling the quasi-steady hydrodynamics still does not fully explain the early onset of the roll instability.