Added Mass of High-Altitude Balloons

Acoustic theory is used to find the added mass for several rigid, immersed bodies. The classical cases of a thin circular disk and a sphere are used to determine the mesh fineness required for engineering accuracy. A family of five Smalley-shaped balloons (zero circumferential stress in the film) is then considered, at different inflation ratios. Acoustical boundary elements are used. The fluid is assumed incompressible and, therefore, the added masses are identical in spirit with those from hydrodynamics. Although not important for this study, compressibility effects can be included for other bodies, if needed. Both vertical and horizontal accelerations are considered. Results show that the pear-shaped balloons behave in an intermediate way between spheres and cylinders, as expected. Such accurate values for added mass will allow better simulation of balloon flight, particularly for dynamic motion resulting from ballast or pay load drop. A major feature of this article is to demonstrate the feasibility of calculating added masses for arbitrarily shaped bodies using acoustics. The authors feel this approach will become a standard working tool for studies of immersed bodies such as balloons, parachutes, and submarines because of the ease of computation. The method uses commercial finite element preprocessors for building the model, calculation of enclosed volumes, and transferring rigid body information to the acoustic computer program.