The forces acting on the array are inertia, gravity, buoyancy, and 

 friction. The downward displacement of the array, Uj(t), must obey the fol- 

 lowing differential equation: 



M 



dt = 



= W + gpV 



B - Vs a p A 



du 



^) 



(33) 



The second term in the right side of the above equation accounts for the gravity 

 on a volume V of water trapped in the array and moving with it. For the cyl- 

 indrical array discussed thus far, gpV will be approximately equal to B , 



and the solution of this equation satisfying the conditions that at t = , 



du, 

 u, = — L = is: 

 1 dt 



= V t, 

 o ^ 



.n cosh — 



(34) 



where V = (2W ) / (a p A) 



t, = 1.41 M (a DAW )"* . 

 I a a 



and t = 1 sec. 



is the ultimate velocity of the array and 

 For the 50-ton cylindrical array, V =5.3 ft/sec 



To determine the degree of buckling, u and u 



plotted as indicated below. 



u must be 

 s 



VELOCITY 



TIME 



30 



artbur Jl.littbJnt. 



