A hydromechanical theory is developed for cycloidal propellersfor two limiting modes of operation wherein U » ΩR andU « ΩR, with U the rectilinear propeller speed (speed of advance)and ΩR the rotational blade speed. A first order theory is developedfrom the basic principles of the kinematics and dynamics of fluidmotion and proceeds from the point of view of unsteady hydrofoiltheory.
Explicit expressions for the instantaneous forces and momentsproduced by blade motions are presented. On the basis of theseresults an optimization procedure is carried out which minimizesthe energy loss under the constraint of specified mean thrust. Underoptimal conditions the propeller is found to possess high Froude efficienciesin both the high and low speed modes of propulsion. Thisefficiency is defined as the ratio of the average useful work obtainedduring one cycle of propeller operation to the average power inputrequired to sustain the motion of the propeller during the cycle.
