Appendix A 

 HYDRODYNAMIC FORCES 



During field use, a boom assembly experiences forces resulting 

 from the relative currents and wave action on the boom skirt and flota- 

 tion and from wind action on the boom freeboard area. 



In catenary tow, the hydrodynamic forces on the boom include the 

 steady drag force caused by (1) the relative towing velocity and (2) the 

 more complicated, unsteady surge and impact forces from the waves. Waves 

 in an actual seaway are difficult to characterize in simple analytical 

 form. Based on a statistical analysis, it is_common to use the significant 

 wave height of the one-third highest waves, H ,„,* as the significant 

 wave height for the irregular ocean waves. An energy spectrum found to 

 correlate the irregular waves of the ocean is the Pierson-Moskowite 

 spectrum [1]. This spectral description is used below to estimate the 

 drag force on a boom under catenary tow. 



For the straight-line tow, the drag force is estimated using the 

 results for frictional drag, Fq, on a flat plate in turbulent flow. 



CATENARY TOW 



For a steady towing velocity the drag force on the skirt of the 

 boom can be approximated by the relation for drag on a vertical flat 

 plate, i.e. , 



F = 1/2 C^ p v^ hS (A-1) 



o D 



where C = drag coefficient 



3 



p = mass density of water (slug/ft ) 



V = towing velocity (ft /sec) 



h = skirt depth (ft) 



S = catenary opening (ft) 



For the total force including the effect of unsteady wave action. 

 Miller, et al. [2] obtained an empirical relation for estimating the 

 drag. The total drag force, Fp, on the boom skirt can be computed by 

 the expression 



Significant wave height is determined by sampling the height of a 

 population of waves over a given length of time, dividing the popu- 

 lation into thirds by height, and then averaging the heights obtained 

 for the highest one-third of the wave population. 



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