Influence of Ballonet Motions on the Longitudinal Stability of Tethered Aerostats

Abstract

To date tethered aerostat stability analyses have assumed the ballonet air to be frozen with respect to the rest of the aerostat. Also, it was assumed that the least stable, and hence most important, longitudinal mode of motion was the first mode, where the cable's and aerostat's motions are so coupled as to approximate an upside-down pendulum. The present analysis shows that when motion of the internal air and gas is allowed, a third mode appears whose stability may be equal to, or less than, that of the first mode for current aerostat designs. The degree of the third mode's stability is primarily controlled by the ballonet's fore-and-aft constraint and damping, and current design practices applied to larger and higher altitude aerostats could give rise to systems with serious stability problems at lower altitudes. However, this investigation also shows that moderate increases in constraint and damping, which should be achievable by ballonet redesign, would strongly stabilize the third mode. Nomenclature A = matrix of coefficients from the dynamic Eqs. (25) B = total buoyant force of the aerostat c = characteristic length of the aerostat C = damping coefficient defined by Eq. (23) ca,cg = damping coefficients of the hull's internal air and gas, respectively Cx, Cz = nondimensional aerodynamic forces in the x and z directions, respectively Cm = nondimensional aerodynamic moment about the y axis dxa/dO = axial ballonet constraint term used in Eq. (30) D( ) = nondimensional time derivative, (c/2U 0 )(') = matrix of coefficients from the dynamic Eqs. (25) = ballonet fullness, % = gravitational acceleration = vertical body-fixed aerostat coordinate shown in Fig. 2 = moments of inertia about the y and z axes, respectively = product of inertia with respect to x and z axes = spring constant defined by Eq. (24) = spring constants of the hull's internal air and gas, respectively