Figure 7 shows the growth of the centerline wave pattern of a Rankine ovoid towed at 

 10 ft/sec at a 3-ft submergence depth to the axis of the body. 7 After the body had traveled 

 through a distance of 72 ft, the wave pattern was fully developed for two crests only. As 

 time increased, the third crest continued to increase in amplitude and other crests began to 

 develop downstream. After a run of 132 ft, steady-state conditions had developed up to the 

 second and possibly the third crest. 



4.5-FOOT, 7 TO 1 RANKINE OVOID 



A 4.5-ft Rankine ovoid was constructed for the new series of tests. Tests were run at 

 several velocities with the axis of the ovoid 1.5 ft below the free surface. Wave heights were 

 measured with both sonic and resistance-type wave probes. The output of these transducers 

 were recorded on a Series 350 Sanborn Recorder and on DIDAS. 



The wave patterns were measured at five longitudinal stations approximately 48, 63, 

 95, 133, and 187 ft from the starting position of the model. Measurements were made at two 

 lateral locations on each run. In one set of runs measurements were taken directly over the 

 path of the model and 22.75 ft to beam. In the other set of runs the carriage was moved 

 laterally, and measurements were taken 11.275 and 34.125 ft to beam. Figures 8 and 9 show 

 the measuring stations and the locations of the wave-measuring probes with respect to the 

 line of tow of the model. Extensive wave measurements were made at speeds of 6.0, 7.3, 

 9.0, and 10.0 ft/sec. Other wave measurements were made at towing speeds between 3.2 

 and 5.5 ft/sec. A total of 194 test runs were made. Representative data from these runs 

 are presented in Figures 10 through 18; original data from some of these runs have been re- 

 ported informally in Hydromechanics Laboratory Test Report 105-H-01. 



Figures 10 through 18 show centerline and three off-centerline time-varying wave 

 profiles produced at different towing speeds. These records were made at Measuring Station 

 4 which was between 130 and 135 ft from the start of the run. The longest steady-state 

 wave pattern was obtained at this station. It became difficult to measure off-centerline data 

 below velocities of 6 ft/sec. 



As the model approached the centerline wave probe, the pressure built up over the 

 nose of the model and a wave crest formed, known as the Bernoulli hump. As the model pas- 

 sed, the pressure became negative over the midsection and a wave train formed aft of the 

 body. The wave crests in the wake immediately behind the model were usually the highest. 

 The later crests decayed monotonically and became uniform in period far downstream. The 

 height of the wave crests were functions of the towing velocity, submergence depth, body 

 length, and displacement. Figure 17 shows the variation of the wave heights of the first and 

 fifth centerline wave crests with velocity produced by the 4.5-ft Rankine ovoid at 1.5-ft sub- 

 mergence. The wave crests have maximum values at a velocity of 7.3 ft/sec which corre- 

 sponds to a depth Froude number of 1.05. 



12 



