Motion characteristics of a tethered spherical float, undergoing oscillatory motion in sinusoidal waves, have been studied theoretically using potential flow theory. Equation of motion is developed in terms of mass, damping and restoring characteristics of the float and amplitude of float motion is determined for a single degree of freedom. Linearised drag force is introduced in the dynamic equation, even though hydrodynamic coefficients are estimated, based on potential theory. Variation of float displacement has been investigated for various wave periods, wave heights, float sizes, water depths and depths of submergence of float. Variations of various force terms with respect to the above parameters are also briefly explained. Float displacement increases with increase in wave period and wave height and decreases with increase in float size and depth of submergence. Theoretical results are compared with experimental results and those available in the literature.
Extensive studies are made on motion response of large floating bodies such as ships and large cylinders. But studies are very limited for small bodies like tethered floats. The interaction of floating bodies with waves is a quite complex phenomenon and very little is known on the motion characteristics of tethered spherical floats. This may probably be due to the rare utility of spherical shaped structures in offshore activities. However, there are spherical shaped structures such as data buoys, marine observation buoys, tethered float breakwaters, etc. for which a realistic analysis is very much essential. As performance of any floating system is primarily governed by the response of the system to ocean waves, it is important to analyse the motion characteristics of the system in ocean waves. Dynamic characteristics of offshore structures could be well studied if wave forces are accurately predicted. In this context, potential flow theory is followed in the present analysis.