where f,, = natural frequency (Hz) 



n = mode number (1, 2, 3 ...) 



L = cable length (ft) 



T = cable tension (lb) 



Mj. = virtual mass of cable (slug/ft) 



= mass of cable + mass of 

 equivalent volume of water 



vibrations, if present, will probably be of small 

 amplitude. 



Increased Drag Due to Strumming. The follow- 

 ing equation has been developed to predict the 

 maximum drag coefficient (values for Cjj when 

 f^=f„) that can be expected in short sections of a 

 strumming, smooth, circular cable [103, 1041 : 



Cp[l + 10(d2/M^)2l 



(4) 



it has also been shown that the approximate 

 frequency of vortex shedding from relatively short* 

 cylinders and cables perpendicular to flow may be 

 characterized by the Strouhal Equation [103, 104]. 

 The Strouhal relation is 



where C 



f. 



SV„/d 



(2) 



where f^ = Strouhal frequency (Hz) 



S = Strouhal number = 0.2 when 

 2x 10^ <R<1 x 105 



Vjj = free stream velocity (ft/sec) 



d = diameter of cable (ft) 



R = Reynolds Number 



When the cable is inclined to the flow by an 

 acute angle d between the free stream and the cable, 

 then the Strouhal relation is: 



f^ ^ (SV„sin0)/d 



(3) 



When the Strouhal frequency is found to be 

 nearly the same as the natural frequency of the cable, 

 the maximum vibration amplitude (for example, the 

 worst strumming) occurs. The first step in investi- 

 gating a cable segment for its propensity to strum- 

 ming is to assign preliminary design values to the 

 parameters in the string and Strouhal equations and 

 then to determine if the resulting frequencies are 

 nearly the same. If the frequencies are close, large- 

 amplitude cable strumming may occur; if the fre- 

 quencies are not close for several mode numbers, 



= drag coefficient for strumming 

 cable 



Cjj = drag coefficient for stationary 

 cable 



d = cable diameter (ft) 



Mj, = virtual mass of cable (slug/ft^) 



Equation 4 has been verified for small-diameter 

 (0.057 in. < d < 0.140 in.) smooth cables of mass per 

 unit length from 1.16 x 10"^ to 9.3 x 10""^ slug/ft 

 over a range of Reynolds numbers from 300 to 1,300. 

 No verification of the equation has been made for 

 stranded cables. 



Strumming Suppression. If strumming must be 

 reduced or eliminated in a cable, changes can be made 

 to the cable system so that the natural frequency and 

 Strouhal frequency are much different or a cable 

 fairing can be added to disrupt the vortex-shedding 

 process. Figure 2 shows how four cable fairings com- 

 pare in terms of strumming drag coefficient and 

 strumming force over a range of Reynolds numbers. 

 In Table 5, several additional fairings are described 

 and performance characteristics listed. It should be 

 noted that for some fairings the drag coefficient is 

 increased over that of a bare cable even though strum- 

 ming force or vibration amplitude is reduced. 



To summarize, analysis and design procedures to 

 predict, describe, and suppress strumming in long 

 cables under oceanic conditions are not possible. 

 Today's procedures consist of comparing the natural 

 frequency of a cable (Equation 1) with the Strouhal 

 frequency for the cable in flow (Equations 2 or 3) to 

 determine if strumming is likely. If strumming is 

 predicted on this basis, changes are made to the 

 system or some fairing is added to the cable. 



* A shon cable is one that docs not exhibit large variations in normal velocity component due 

 to cither streaming (bending* of the cable or nonuniform current profiles. 



