—2. = 1 when V = L 



where : 



(T = Stress value (Ib/in^) 



U = dynamic extension of line 



U = amplitude motion of the line at the surface end (ft) 



9 



E = modulus of elasticity for the line (lb/in") 



k = wave number = JL 



c 



where: '^ = frequency of ship's roll (cycles/sec) 



c = speed of sound of line (ft/sec) 



U = amplitude of motion of line at som.e point along cable (ft) 



/ = length along line (ft) 



m = mass of ALVIN at end of line (slugs) 



P = density of line (slugs) 



S = material cross-sectional area of the line (ft ) 



= Constant 



m 

 Cq = coefficient of drag 



■2 



2 



A = projected area of load (ALVIN) (ft^) 

 P M/ = density of seawater (slugs) 



NOTE: 



(1) Data sheets in this appendix indicate the loads and stresses imposed on the three 

 lines when the vertical amplitude, U^ , and period of oscillation, T, are varied. 



(2) The accompanying graphs are plots of total loads taken from the same data sheets. 



78 



