Table I. Comparison of Typical Values of I^^qxI °^ Computed by Digital 

 Computer Program and as Calculated From Equation 13 



^ 



M 



1 max! 

 Computed by Digital 



Computer Program 



max 

 Calculated from 



Equation 13 



Percentage 

 Difference 



0.50 

 1.00 

 5.00 



0.10 

 0.10 

 0.10 



112.1 



142.32 



514.09 



110.1 

 139.5 

 503.5 



1.80 

 2.01 

 2.10 



The parameters /3 and ji are representative of the damping and the ratio of the 

 weight of the cable to the virtual mass of the load respectively. As was noted in the 

 A. D. Little report, the variations of K^q^I ^'*^^ '^'r ^' °"*^ /^ °'^^ '" agreement 

 with known results for simpler systems. As the mass of the load is decreased, i.e., 

 fi "• 00, the system reduces to that of a free-ended spring, with the resonant frequencies 

 approaching 77/2 and 37r/2, etc. As the mass is increased, /i ~* 0, the resonant fre- 

 quencies approach TT, 277, etc., which agrees with the case of a fixed-ended spring. 



The damping parameter, jS, has a slight effect on the resonant frequencies but 



a far more important effect on the amplitude of ll' „| at resonance. A conclusion 



' '^ ' maxi 



in the A. D. Little report indicated that the maximum dynamic stress amplitude at 

 resonance increases when the damping is increased beyond a certain value. From 

 the above calculations it can be seen that the amplitude at resonance increases 

 generally with increased damping; i.e., there is no minimum amplitude as implied 

 by the above conclusion. This result is compatible with the concept that as the 

 damping increases, the system becomes equivalent to a fixed-ended spring giving 

 resonances at 77, 277, etc., and amplitudes tending to infinity, restricted only by 

 internal and external damping of the cable. This argument considers the damping 

 effects, a function of jS, to be divorced from the inertial effects, which are 

 dependent upon JLI. 



In view of the dependence of the maximum dynamic stress amplitude on j8, 

 and since /3 depends on the parameters of the load — i.e., the cross-sectional 

 area, the mass, and the density of sea water, which are fixed — and on the coef- 

 ficient of drag, the value of Cp assumed for a given load configuration is of 

 particular importance. This can be seen from the results given above where a 

 change of ]3 from 1.00 to 3.00 results in a change in K/nax| °^ resonances from 

 142 to 370. If U^Qxl '^ interpreted as an allowable stress which when exceeded 

 results in an unsafe condition for the operation, as implied in the design procedure 

 which follows, then the value of Cq used in the calculation of /3 becomes critical. 

 For poor hydrodynamic shapes such as blunt bodies or open frameworks, it is not 

 possible within the present state of development of theoretical fluid dynamics to 

 calculate Cq from the basic equations of fluid flow. The alternative, therefore, is 



