• Current meters should not be allowed to in- 

 cline more than 15° from the vertical. 



• Wind drag will be considered negligible. 



• All hardware used shoidd have a safety fac- 

 tor of 5 :1. 



The total tension on the mooring line was cal- 

 culated using the Circular Arc Approximation 

 (G. B. Shick, 1964). The shape of the mooring 

 line was assumed to be a circular arc (Figure 3). 

 The only force considered was the form drag 

 on the array. The form drag (F) acting on each 

 component of the taut-line array was calculated 

 from: 



F=0.5pv=LDCd (2) 



where: F = pressure drag, lbs 



P = density of seawater, slugs/ff 

 v= current velocity, ft/sec 

 L=length of component, ft 

 D=diameter of component, ft 

 Cd = drag coefficient 



The uncertainties in determining the drag force 

 arose from our lack of knowledge about the ac- 

 tual current profile and the drag coefficient. 



The current velocity was assumed to be con- 

 stant from the ocean surface to the bottom. 

 This assumption was made to facilitate the cal- 

 culation of F and to introduce a "worst case" 

 situation. In 1970, a current velocity of 1.68 

 ft/sec (0.51 m/sec) was used; in 1971 the value 

 was increased to 2.48 ft/sec (0.76 m/sec). 



Selection of the drag coefficient (d) was based 

 on the Reynolds Number (Re) and the shape of 

 the component. Reynolds Number, the ratio of 

 inertial forces to viscous forces, is defined as: 



Re = -:^=^ 

 V n 



where: /3 = density of fluid, slugs/ft' 



V = velocity of flow, ft/sec 



/i = coefficient of viscosity, lb-sec/ft= 



v = kinematic viscosity, ft-/sec 



J = characteristic length, ft 



A value of Re was calculated, using equation 3, 

 for each component in the array. Values of Re 

 ranged from 3 X 10= to 5 X 10^ The calculated 

 value of Re was used as the entering argument 

 for determining Cd from a graph of Re versus Cd 

 (Bretsclmeider, 1966). The drag coefficient for a 

 right circular cylinder ranged from 0.90 to 1.20. 



(3) 



A Cd equal to 1.80 was used in the final calcula- 

 tions for the current meters, release device, and 

 the nylon line to allow an extra safety factor and 

 to compensate for such factors as strumming of 

 the mooring line. Strumming occurs when a 

 cylinder is free to vibrate laterally imder the 

 effect of alternating lift forces generated by vor- 

 tex shedding. Strumming increases turbulent 

 flow behind the mooring line, resulting in in- 

 creased drag. Since no graph of Re vs. Cd was 

 available for chain, a Cd equal to 2.0 was selected 

 based on a value used by Woods Hole Oceano- 

 graphic Institution. 



The equivalent spring constant (K) was cal- 

 culated for each size nylon line considered for 

 use in the array. K was calculated from the 

 equation : 



T,-Ti 



K = 



(4) 



CoX — eiX 



where: K = spring constant, lbs/ft 

 T.&Ti= tension, lbs 

 e2&ei= percent elongation 

 x = unstretched length, ft (x + per- 

 cent initial elongation times x 

 = water depth) 



The values of T and e were taken from first load- 

 ing curves for line similar to that actually used 

 in the construction of the arrays (Figure 4). 

 The expected working range was between 5% 

 and 15% of the average breaking strength of the 

 nylon line. In 1971, the values of K calculated 

 were 



• 20 lbs/ft for ?iG inch line at the shallowest 

 water depth (490 ft). 



• 22 lbs/ft for % inch line at the shallowest 

 water depth (490 ft). 



• 40 lbs/ft for % inch and %o inch line at the 

 deepest water depth (870 ft). 



The total tension (T) in the mooring line was 

 then computed using the Circular Arc Approx- 

 imation. A value of T was assumed and the 

 angles ni and a-, were comj^uted : 



ai=arc sm — =^ — (5) 



where q:i = surface angle of inclination 

 Di= surface buoy drag, lbs 

 T= assumed tension, lbs 

 and 



Qi2 = arc sm „ (6) 



