Towed vehicle system in a coordinated turn.

Abstract

Analytical methods are developed to study the equilibrium configurations assumed by a towed cable (with towed body attached) moving in a uniform flowfield, when the towing vehicle executes a coordinated turn. With appropriate assumptions closed form solutions for the governing nonlinear differential equations are obtained for the coordinates of the towed body with respect to the towing vehicle. The exact two point boundary problem is then solved numerically, and good agreement is shown to exist between both solutions. Nomenclature C D = coefficient of drag of the towed body C N> C T = coefficients of drag on the cable in its normal and tangential directions d -diameter of the cable / = length of the cable M = mass of the towed body m = mass per unit length of the cable R = turn radius of a point on the cable S = cross-sectional area of the towed body s = spatial coordinate measured (along the cable) from the towed body to a point on the cable T = cable tension U, V, P = tangential, normal and binormal components of cable velocity u,v,p = tangential, normal and binormal components of wind velocity W = velocity of the towing vehicle X, Y, Z -inertia! coordinate system shown in Fig. 1 a = mR 0 /M P = P C N dR 0 2 a) 2 /M y,6 = angles defined in Fig. 1 B = -P C D SR 0 /2M p = density of the media 0 = local angle of attack of the cable co = angular velocity of the towing vehicleSubscripts 0 = subscript used to denote variables measured at the towed body 2 = subscript used to denote variables measured at the towing vehicle