These values are measured for an infinitely large submergence depth. At small 

 depths the measured added mass decreased. This agrees with the physical explanation 

 of the added mass phenomenon. The experiments were conducted for small-amplitude 

 motions and no separation occurred, hence the boundary effect is not considered. 

 This method can be used for rotary acceleration of a body. This experimental method 

 has important implications since it can be set up in a deep ocean simulating tank to 

 measure the added mass as well as the pressure distribution of any arbitrarily shaped 

 object under translational or rotary motion. 



For the unidirectional motion, the viscous and boundary effects must be 

 considered. Experiments for this type of motion have been conducted for a number 

 of bodies, but only that for spheres will be cited. Arbhabhirama'^ found that when 

 the ratio of the diameter of a sphere to the diameter of a fluid filling a concentric 

 spherical shell is 0.259, which is similar to a sphere oscillating in an infinite fluid, 

 the added mass is found to be 1.03 times the added mass obtained from potential flow. 



In summary, although some data is available on added mass coefficients in 

 oscillatory flow, most of the experiments have been conducted at small scale and 

 within the low Reynolds number regime. As an example, the following estimate of 

 the added mass of a complicated frame structure such as the STU described below, is 

 cited. Theoretically the oscillatory motion of a load being lowered to the ocean 

 floor and suspended by a cable is a damped simple harmonic motion. If the cable is 

 considered to be elastic, the equation of motion is 



M X + Cx + kx = 

 a 



where M is the virtual mass of the load, x is the elongation of the cable, k is the 

 ratio of the restraining force to the elongation of the cable, and C is the coefficient 

 of damping. The solution of this equation is quite complicated, but the period of 

 oscillation is the same bs for simple undamped harmonic motion: 



MqX + kx = 



Hence, the period T = 2ff (Mg/k). 



On 13 April 1965, a Submersible Test Unit (STU) was lowered by this Laborator/ 

 to the ocean floor to a depth of 2,500 feet using a 1.3-inch-diameter polypropylene 

 cable. The cable tensions were recorded as a function of time from the start o' 

 lowering operation. The curve of the graph (Figure 35) shows the oscillatory motion 

 of the STU, consequently the average period of 9.8 seconds was obtained while the 

 average tension of the cable in this interval (between 10 and 12 minutes as marked on 

 the figure) was 3,400 pounds. The breaking strength of the cable is 45,000 pounds 

 ("Braided Rope and Cordage Catalog," Samson Cordage Works, Boston, Mass.). From 

 the percent load of breaking strength versus the percent elongation curve of polypro- 

 pylene cables, the corresponding percent elongation of 4.0 is obtained. Since the 



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