F^ = FqM + 0.59C ^'^^ '"H (A-2) 



where C = empirical constant 



w = maximum frequency or maximum energy in wave 

 spectrum (rad/sec) equaling 2.26//H. , for 

 Pierson-Moskowite spectra 



V = towing velocity (KT) 



H ,„ = height of one-third highest waves 



Assuming a Pierson-Moskowite spectra for the ocean and a value of 

 C = 0.23 [2], Equation A-2 becomes 



^o 6 + o.308/H:;^y 



Fj^ = F^fl + 0.308yH, /,/vr (A-3) 



Added to this is the wind force, F„, which is 



W 



F = 1/2 C p vl fS (A-4) 



W D a a 



3 

 where p = density (slug/ft ) of air 



V = wind velocity (ft /sec) 



f = freeboard height (ft) 



3 

 Taking C = 1.5 and p = 0.00269 slug/ft , Equation A-4 becomes 



F„ = 0.00576 fS V^ (A-5) 



W a 



V is now wind velocity in knots. 



The total drag force on a length of boom in catenary tow is given 

 by the sum of Equations A-3 and A-5. For a 1,000-foot length of boom in 

 a catenary with a 500-foot opening these equations were used to obtain 

 the force values in Table A-1. Type I Class 1 (12 inch), Type I Class 2 

 (24 inch) , and Type II (36 inch) . 



35 



