Analyses of Multiple-Float-Supported Platforms in Waves 



of only one knot past a moored platform, the fluid which is 'entrained" 

 by the motion of a platform may convect about 17 feet during a 10-sec 

 period ; such a period is common for ocean waves, and the distance is 

 about half of a typical column diameter for a large semi-submersible 

 drill rig. Entrained fluid energy can be convected away at an appreci- 

 able rate by modest currents producing important effects on damping 

 and, hence, resonant response. 



Indeed, when the damping force is non-linear and, hence, 

 superposition cannot be applied, it may be inappropriate to apply an 

 oscillatory drag coefficient obtained for a particular structural element 

 from tests with rectilinear oscillatory motion [43-45,47-51] to the 

 somewhat different kinematic conditions of the orbital velocity pattern 

 of waves. The differences may be modest but the question should be 

 posed and, hopefully, investigated. 



The question of scale effects is persistently present and model 

 experimenters must be alert (and somewhat intuitive) to recognize 

 when it may be appreciable. When phenomena are recognized to be 

 predominantly viscous in origin, we are likely to suspect the possibi- 

 lity of scale effect. This is, of course, due in large part to the hi- 

 story and experience of testing ship models for resistance. Very 

 little is known about scale effects on oscillatory hydrodynamic forces 

 which may be relevant to platform motions testing and analysis. Some 

 years ago, however, a program of experiments to study scale effects 

 on roll damping of circular cylinders with and without appendages was 

 undertaken by the Naval Ship Research and Development Center and 

 Davidson Laboratory. While these studies were not directed to plat- 

 form motions, the results are relevant to the phenomena of oscil- 

 latory damping in general and since they are the only results with 

 which we are familiar which show the effect of model size, it may be 

 useful to discuss them. Three cylinders with diameters of 6-in, 12-in 

 and 24 -in were suspended vertically in water by torsion springs. Three 

 kinds of appendages were symmetrically attached to the models, as 

 shown in Figure 35 for the smallest (6-in-diam) cylinder. Curves of 

 decaying oscillation from various initial angular displacements were 

 recorded and analyzed to obtain "square-law" damping moment coef- 

 ficients of the form 



damping moment 



C = ~~ I *—* q ■ • (43) 



m (p/2)AR 6 01 01 



c.a. 



where A is the frontal area of both appendages and R c#a . is the 

 radius from the axis of rotation to the center of area of the appendage. 

 The results are tabulated in Table 15. 



831 



