The added mass coefficient is determined from experimental measurements by means of equations 

 (CI) and (C2) wiiich combine to give 



2 



V^/rm 'J 



fA 



fu 



(C3) 



Since /^ and fw are usually close, particularly at low frequencies, a small error (1 or 2%) in one or 

 both often results in relatively large variations in Cam(— 10-40%). For this reason it is helpful to also 



consider the ratio of the virtual and actual masses which, according to equation (C2), is the square of 



f 



the frequency ratio . Most of the conclusions in this section related to the added mass effect for 



fw 



/a 

 marine cables are based on the measured values of -7—. 



Jw 



The added mass coefficient Cam was determined from equation (C3) for a variety of marine cable 

 materials and constructions. The results are plotted against the "vibration Reynolds number," 

 Re,, = fD^llv in Fig. C5 and the legend for the data points is given in Table C2. The cables were taut 

 for all of the conditions tested and discussed here. The dashed line in Fig. C5 represents the classical 

 added mass prediction developed by Stokes (see Rosenhead, reference C3). This predicted value of 

 Cam 'S given by the equation 



r=X^l m (C4) 



Table Cl 



Marine Cable Model Physical Characteristics 



DTNSRDC Towing Tank Experiments (C1,C2) 



Cable Model/Type 



Nominal 



Nominal 



Weight 



Virtual 





Diameter 



Length 



In Air In water 



Mass 





(ft) 



(cm) 



(ft) 



(m) 



(lbs/ft) 



(N/m) 



(lbs/ft) 



(N/m) 



(slugs/ ft) 



(kg/m) 



Double Armored Steel (DAS) 



0.051 



1.55 



14.38 



4.38 



0.520 



7.59 



0.391 



5.71 



0.0202 



0.967 



Uniline 



0.050 



1.52 



14.27 



4.35 



0.190 



2.77 



0.069 



1.01 



0.00967 



0.463 



Small Diameter 



0.0058 



0.177 



14.25 



4.34 



0.0065 



0.095 



0.0048 



0.070 



0.00025 



0.012 



(Piano wire) 























143 



