This paper considers the problems of dynamically modeling and automatically controlling the motion of a small maneuverable flight vehicle that is being towed by a much larger one. Mathematical models of the components of the system, including the towing aircraft, tow cable reel mechanism, tow cable, and vehicle aerodynamics, are described. The development of an autopilot for stability augmentation and maneuvering of the towed vehicle is discussed. An overview of the implementation of the models in a digital computer simulation program is provided, and some typical results obtained using the program are presented. A comparison of theoretical and experimental results is also made. ROM the early days of powered flight, there has been an interest in towing objects from aircraft. Objects that have been towed include antennas, banners, gliders, and targets. Because of the interesting, and sometimes troublesome, characteristics of the motions of some towed objects and the cables, or towlines, the dynamics of the cables and the towed objects have been studied by several investigators at various times during the last 60 years.1'10 The problem of describing the motion of a towed cable/ object system is far from trivial. The equations of motion are, in general, coupled, ordinary, and partial differential equations (i.e., hybrid equations). Various approaches have been taken in studying such systems. Glauert1 and Phillips2 did some pioneering work on the stability of the motion of bodies towed from aircraft. Phillips3 also analyzed the stability of the motion of a cable used to tow a nonlifting body. He used a continuum model for the cable and studied the effects of towing speed on the stability of lateral oscillations of the cable and concluded that the oscillations would be damped out if the speed of flight were less than the speed of propagation of vibrational waves along the cable.

Dynamics and Control of Maneuverable Towed Flight Vehicles

A non-linear mathematical model for the study of the dynamics of an extensible cable subjected to aerodynamic forces generated by a uniform flow field is formulated. Solutions are found considering large displacement caused by suddenly applied loads (i.e., gusts, shock waves, turbulence) for a range of flow speeds and cable lengths. Transition from overdamped to oscillatory motion is observed when flow speed and cable length are increased and decreased respectively. The stability of the system is discussed.

The Dynamical Behaviour of a Flexible Cable in a Uniform Flow Field

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Dynamic Simulation of Low Altitude Aerial Tow Systems

A representation of fluid forces in finite segment cable models

The three-dimensional equations of motion of a flexible towed cable are developed. A closed-form approximation for the equilibrium shape of a cable subjected to arbitrary aerodynamic loading is developed and used in the study of a heavy, vibrating tow cable. Natural frequencies of vibration and cable shapes are computed for typical cables and are shown to be in good agreement with exact, numerically obtained values.

Dynamical Behaviour of a Materially Damped Flexible Towed Cable

Equilibrium configuration and tension of flexible cable in uniform flow field, considering tangential drag force and weight effects

T. C. Cannon

Papers

Equilibrium configuration and tensions of a flexible cable in a uniform flowfield.