The wave length of the waves on the centerline is 



A = %nV 2 /g [5] 



If the wave heights of the two singularities are added, the wavemaking of the Rankine ovoid 

 has the nondimensional form 



SRO -.1/2 . /p/^2 



= B{2nf/R) L/Z sin (R/fF f 2 - Sn/i) [6] 



plus higher order terms in 1/R. 



8M I 1 , 



exp [- ] sin [7] 



f 2 UF f \ F f 2 J fF f 2 



R is now the distance to the center plane of the ovoid, and F f is the depth Froude number. 



The Froude number is defined as the ratio of the inertia to the gravity forces; the 

 depth Froude number is 



F,='U/JiT [81 



/ 



where U is the towing speed, 



g is the acceleration of gravity, and 



f is the submergence depth. 



If B is plotted as a function of depth Froude number, the conditions for maximum and 

 minimum wave heights can be seen in Figure 2. These minima can be calculated from Equa- 

 tion [7] by setting c/fF , equal to nn. For c/f = 1.393, minimum wave heights occur at depth 

 Froude numbers of 0.66, 0.470, 0.392, etc. as shown in Figure 2. The maximum heights are 

 more complicated functions of the parameters. 



TEST EQUIPMENT 



Two Rankine ovoids were towed at several depths below the free surface in the MASK 

 facility. This facility is 360 ft long, 240 ft wide, and 20 ft deep. The basin is large enough 

 so that reflections from the walls did not interfere with the primary wake pattern. The ovoid 



