ABSTRACT 



A linearized theory is developed for the motions of a 

 slender body of revolution, with vertical axis, v/hich is float- 

 ing in the presence of regular waves. Equations of motion 

 are derived which are undamped to first order in the body 

 diameter, but second-order damping forces are derived to 

 provide solutions valid at all frequencies including resonance. 

 Calculations made for a particular circular cylinder show^ 

 extremely stable motions except for the low frequency range 

 where very sharp maxima occur at resonance. 



INTRODUCTION 



The motions of a vertical body of revolution, which is floating in the 

 presence of waves, present a problem of interest in several connections. 

 The naotions of a spar buoy, of a wave-height pole, and of floating rocket 

 vehicles are important examples of such a problem. The same methods 

 developed for these motions may be applied to find the forces acting on 

 offshore radar and oil-drilling structures. 



A theoretical discussion of this problem, which also treats the sta- 

 tistical problem of motions in irregular waves, has been presented by 

 Barakat. However, this analysis is restricted to the case of a circular 

 cylinder and is based upon several semi-empirical concepts of applied 

 ship-motion theory. An alternative procedure is to formulate the (inviscid) 

 hydrodynamic problem as a boundary-value problem for the velocity po- 

 tential and to employ slender-body techniques to solve this problem. The 

 latter approach is follow^ed in the present w^ork, leading to linearized equa- 

 tions of motion which may be solved for an arbitrary slender body with a 

 vertical axis of rotational symmetry. The particular case of a circular 

 cylinder, whose centers of buoyancy and gravity coincide, is treated in 

 detail and curves are presented for the amplitudes of surge, heave, and 



References are listed on page 27. 



