Forces on a Submarine Hull Induced by the Propeller

Abstract

The induced-flow field generated by a propeller operating in the wake of a submarine can exert forces on the submarine in some arbitrary mode of motion in two ways: Either by pressures applied to the propeller blades and resulting in the conventional propeller thrust or by pressures applied to the hull surface. The ratio of these forces is shown, by theoretical analysis, to depend most strongly on the flow velocity which the particular hull mode of motion would generate at the propeller, to be slightly dependent on the shape of the propeller, and to be negligibly dependent on the magnitude or distribution of the submarine wake. The derived relations are valid for both the inertial and quasi-steady components of the induced-pressure field. The predominant factor in the force ratio is evaluated by a numerical technique which is applicable to any surface of revolution moving in almost any pattern of motion. As one application, it is shown that the steady longitudinal force on the hull is 8 to 1 2 percent of the steady component of the propeller thrust, in good agreement with measurements of the thrust-deduction factor. As another application, it is shown that a particular vibratory component of the hull force, tending to vibrate the hull in the accordion-vibration mode, is 6 to 8 percent of the same component of the propeller thrust.