General Longitudinal Stability Equations for Hydrofoil Systems with Specific Application to the Cape Cod Boat

A longitudinal stability analysis of hydrofoil systems has been made. The equations of motion include the terms corresponding to an automatic control with finite time lag. The methods used for solution of such equations have been discussed for the case when the critical time lag of an automatic control - hydrofoil craft combination is desired. The resulting equations have been applied to the Cape Cod Boat, a 14 ft tandem foil test craft, which used an automatic control sensitive to displacements from a preset depth. The critical time lag was obtained for this craft based upon an assumed two degrees of freedom and flight at an intermediate depth of approximately two and one half chords below the surface. Both the frequency response method and the transcendental characteristic stability equation solution were employed to determine the aforementioned critical time lag. Further examination was made of the Cape Cod craft's stability characteristics when control gearings are varied and zero time lag in control is assumed. (Author).