the natural period of oscillation of a single degree of freedom, 

 spring-mass system without damping: 2 



(1) 



\Ke/ ' 



VKg 



where T is the natural period of oscillation in seconds, W is the 

 total system weight in air", g is 32.2 ft/sec^ and K is the 

 spring rate in pounds buoyancy per foot of the surface-piercing 

 section. 



Practical experience has shown that a cross section with a K 

 of 3 lb/ft gives adequate reserve buoyancy to a spar for sea- 

 worthiness and a section modulus capable of withstanding the 

 bending stresses encountered in handling. By solving Eq. (1) for 

 required system weight, using 30 sec for natural period and 

 3 lb/ft for K, a guideline parameter for the spar can be deter- 

 mined. With these values, and the limitations of maximum spar 

 length and weight capable of being launched from the ship, the 

 final spar dimensions were determined „ The exact spar buoyancy 

 constant, K, and system weight put back into Eq. (1) give a 

 natural period of 31.4 sec. (W = 2327 lb and K = 2.89 lb/ft.) 



A rough check of these calculations was made in Lake 

 Washington on a very calm day with the full-scale spar. The 

 array was simulated by an equivalent weight, adjusted to compen- 

 sate for the difference in density between fresh and salt water. 

 The spar was marked every 3 in. for a distance of several feet on 

 either side of the neutral position. Observations of the 

 magnitude and elapsed time of excursions both positive and 

 negative, caused by releasing the spar from an initial vertical 

 displacement, were recorded. Fig. 2 shows a curve of displacement 

 versus time for the oscillatory motion resulting from an initial 

 displacement of 5 ft. Three complete cycles can be easily dis- 

 tinguished before motion damps beyond recognition. These tests 

 showed an average period of 33 to 34 sec for initial displace- 

 ments up to 5 ft. Displacements over 5 ft showed longer initial 

 periods as would be expected with nonlinear damping, but the 

 periods always ended the same. Varying the system mass gave 

 changes in period corresponding to calculated values, thereby 

 increasing confidence in the testing scheme o 



includes array weight and weight of captured water 



170 



