Kim and Mevciev 



2T 2 /A 



(42) 



2 m . 2 

 fw 



IZ. /pgA I 

 Sw w 





where Z>- w is the wave -induced vertical force evaluated without taking 

 into account the damping term. 



Since, at resonance. |Zv r /pgA„ I < 1 , and for slender vertic- 



9 , 9 HP (W D W 1 



al floats T z /A w »l and -^L 1 < 1 , then c/c c «l and z/f»l . For 

 example, for T/R Q = 30, g R a /R = 1 - 8 and L a / T = °- 5 > the 

 calculated "wave-damped" resonant heave motion z/f would be almost 

 8000 I Wave -associated damping is inadequate for slender floats and 

 viscous damping controls the resonant motion. 



Results of tests on a l/13th-scale model of a Manned Open 

 Sea Experimentation Station (MOSES) reported by the Oceanic Institute, 

 Waimanalo, Hawaii [53] , showed that a ratio of damping to critical 

 damping of 0.075 could be achieved. This was discovered in tests of 

 the model with about 18 external rings attached to a slender shaft. The 

 rings, which are intended to provide structural stiffening, have out- 

 side diameter about 15% larger than the shaft. Complementary tests 

 were carried out with acetate sheet wrapped tightly around the rings 

 to present a smooth, unbroken surface. With this shroud the damping 

 was about 1% of critical. 



Damping coefficients will, in general, be obtained most ef- 

 fectively by experiments, or will be estimated on the basis of empiric- 

 al results. It has been known since Froude's investigations in 1874 [54] 

 that the drag coefficient for an oscillating bluff body can be very differ- 

 ent from that for the same body in steady flow. As in all model ex- 

 perimental work, it is important to be sure that the model conditions 

 correspond to the full scale : thus, for dynamic similarity to exist, 

 the model should be geometrically similar and the flow kinematically 

 similar to the full size. 



Certain experience from investigations of roll damping of ships 

 with appendages can give insight into questions relevant to damping of 

 platforms oscillating in waves. It is important to recognize that a 

 small ambient current, due to oceanic circulation or induced by wind, 

 can have an appreciable effect on energy dissipation, as has been found 

 by many investigators into the rolling of ships [54-58] . This is because 

 the model, in the course of its cyclical motion, must impart motion to 

 fresh, previously unentrained water. Consider that for a current speed 



830 



