Since the wave pattern forms a V in the wake, the wave crests off the centerline 

 build up some distance aft of the model. The wave heights reach a maximum value and then 

 decay slowly downstream. The wave heights of the highest crests at each athwartship sta- 

 tion are plotted in Figure 18 as a function of towing speed. 



Irregularities in the wave structure in Figures 10 through 16 result from the wave 

 interference between the source and sink of the Rankine ovoid singularity representation. 

 This interference is particularly noticeable in the off-centerline wave profiles at the higher 

 towing speeds. At the very low speeds shown in Figure 16, the centerline wave profile is 

 very irregular immediately behind the model. 



The length of the steady-state wave train increased with the distance the model 

 traveled from the starting point to the measuring station. Figure 19 shows the growth of the 

 steady-state wave pattern at one towing speed as the measuring station is moved farther and 

 farther from the starting point. The longest steady-state wave profile was obtained at Meas- 

 uring Station 4. Measuring Station 5 was 187 ft from the start of the run, and the model had 

 stopped before all of the wave train reached the wave transducer. The deceleration of the 

 model may have produced spurious surface disturbances. 



DISCUSSION OF RESULTS 



Although a complete wave analysis is not available at the Model Basin for comparing 

 measured wave height with theory, certain quantative observations can be made from the 

 measured wave heights. A limited portion of the wave train on the centerline can be com- 

 pared with stationary-phase theory. Since two similar ovoid models were tested, it is also 

 possible to evaluate the accuracy of Froude scaling. 



STATIONARY-PHASE WAVE PROFILES 



Stationary-phase wave profiles computed from Equation [4] for several of the centerline 

 wave conditions are compatible with the wave measurements which Livingston obtained in a 

 coordinate system which moved with the model. Figure 20 compares one of his wave profiles 

 obtained with the 9-ft Rankine ovoid with the stationary-phase waveform. With this large 

 model, there was only a short interval between the first and third wave crest where the theory 

 showed good agreement with the experimental results. 



The stationary-phase wave profile in Figure 19 is superimposed on the experimental 

 data obtained with the 4.5-ft ovoid at four measuring stations over the length of the run. Al- 

 though these experimental data were not obtained in a moving coordinate system, it is evi- 

 dent that a steady-state wave pattern was set up which increased in length as the measuring 

 station is moved away from the starting point. In the steady-state portion of the wave pro- 

 file, the stationary-phase analysis showed reasonable agreement with experiment up to the 

 first wave crest. 



22 



