The Equilibrium Configuration of a Towed Hydrofoil-Cable System in Two-Dimensional Steady Turns

摘要

This report describes a method for calculating the equilibrium configuration of a cable-towed hydrofoil system when the entire system rotates (as a rigid body) with constant angular velocity in the plane of the towpoint motion, the bulk of the analysis applying to the case of massless elements (cable and hydrofoil). This is done by obtaining an explicit solution (first integral) for the differential equation for the cable curve, from which the cable arc length and polar angle can be obtained by quadratures relative to the radius vector. Owing to the indirect nature of this problem, i. e., the requirement of satisfying two boundary conditions at an initially unknown boundary point, solution of any given problem involves certain numerical calculations. The latter have been considerably facilitated by construction of a set of numerical tables for the principal non-dimensional quantities. Recommendations are made for extension of the present analysis, particularly to the case of steady turns involving three-dimensional cable configurations.