FROUDE NUMBER SCALING EFFECTS 



Since Livingston's ovoid was 9 ft long and was towed at a depth of 3 ft, it was postu- . 

 lated that a 4.5-ft ovoid towed at a depth of 1.5 ft would yield similar results. Therefore, if 

 tests were run at the same Froude number, the body should be towed at 1A/2 times the former 

 velocity. The ensuring wave heights would then be one-half as high. Absolute values of the 

 dimensionless wave heights of the first centerline wave crests from the two sets of data are 

 plotted as functions of depth Froude number in Figure 21. Superimposed on these data is a 

 theoretical curve obtained from the stationary-phase analysis. The small differences may be 

 attributed to viscous effects, secondary wave effects, and inadequacies of the source-sink 

 representation of the body in proximity to a free surface. 



In Figure 22, data obtained with the 4.5-ft model have been converted to conditions 

 for a 9-ft model using Froude scaling. There are two sets of curves which compare the wave 

 profiles of the 4.5- and 9-ft Rankine ovoids at Froude numbers 1.4 and 1.005. As in Figure 

 21, there was reasonably good agreement over the steady-state portion of the wave profile. 



ACKNOWLEDGMENTS 



The development of equipment and techniques reported here was the work of several 

 investigators over a period of five years. Richard M. Ralston designed the towing equipment 

 and conducted the first experiments. Walter Livingston made the second set of measurements 

 with the help of Mr. John L. Power. Mr. D. A. Shaffer conducted the third set of experiments 

 and prepared the final report. 



The author gratefully acknowledges the assistance of Messrs. Richard Rothblum, ■ 

 William Souders, and L. Bruce Moore in conducting the experimental work. He also wishes 

 to express his thanks to Mr. Walter Livingston for allowing him to draw freely from his notes 

 and to Dr. Avis Borden for her critical review of this report. 



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