Appendix A 



ANALYSIS OF CABLE AND PAYLOAD DYNAMICS FOR 

 RAISING AND LOWERING LOADS IN THE DEEP OCEAN 



The analysis presented here is essentially that given in BuShips Technical 

 Report No. 1370863, "Stress Analysis of Ship-Suspended Heavily Loaded Cables for 

 Deep Underwater Emplacements," by Arthur D. Little, Inc. ' 



The cable and load are considered to be in a vertical position as shown in 

 Figure 1; i.e., the deflection of the cable due to currents is small. Any displace- 

 ment of the cable support point will cause the dynamic displacement u(x, t) at time 

 t of an element of cable originally located at x; see Figure 1. Displacement 

 u(x, t) is of a form which satisfies the equation for the propagation of waves in the 

 cable: 



2 2 



p S^-^ = SE^^ - k4^ (A-1) 



' Bt2 Sx2 ^' 



where p = density of the cable 



S = material cross section of the cable 



E = modulus of elasticity of the cable 



K = constant of friction on the cable due to the surrounding water 



In an actual lowering or raising operation, the length of the cable, L, varies 

 with time. However, it is assumed that L may be considered constant over short 

 periods of time; i.e., the net vertical motion of the load and cable does not influ- 

 ence the dynamic displacements due to the cable support-point oscillations. 



The following nondimensional variables and parameters may then be defined: 



and Equation A-1 becomes 



p ' c p cS 



c "^c 



2 2 



S u , „ Su S u 



+ ^.^ = — - 0) 



(St')2 ^ ^^' (Sx') 



58 



