Newman 



the relatively weak transverse wave system of this vessel, and the 

 fact that aerial photographs from directly above tend to emphasize 

 the shorter, and hence steeper, diverging waves.) 



As can be seen in all three photographs, but most noticeably 

 in the downstream portion of Fig. 5, the diverging wave system 

 includes three discrete groups of waves, separated by relatively 

 calm regions or "nodes. " The observation of three wave groups is 

 also noted by Wehausen in the text adjoining Fig. 23 of Wehausen 

 and Laitone [ I960] . The explanation of this phenomenon is sonnewhat 

 controversial. One possibility is in terms of the conventional "bow" 

 and "stern" waves, and possibly others associated with the shoulder 

 or knuckle of the vessel. My own view is that, while this synthesis 

 is applicable near the ship, it is inappropriate in the far-field where 

 the stationary phase approximation developed in the previous section 

 is valid. Indeed, if two discrete "bow" and "stern" wave systems 

 are superposed, in the Kelvin stationary phase approximation, the 

 res.ult is only one wave system, provided that the observation distance 

 downstream is large compared to the separation distance between the 

 two disturbances. There will, of course, be interference effects, 

 with regions of reinforcement and other regions of cancellation, just 

 as in the simpler radiation and diffraction patterns which we associ- 

 ate with nondispersive wave problems. In the present context these 

 will be introduced via the amplitude function A(0) , and my own view 

 is that the nodal regions between the three observed wave systems 

 correspond to zeros of the function A(9) for this particular vessel. 

 Indeed, it is not difficult to perceive, in some parts of these photo- 

 graphs, a phase difference of 180*-* across the nodal regions. In 

 principle, there should be additional nodal lines and discrete diverg- 

 ing waves in the interior portion of the wave system, but these will 

 correspond to relatively short waves which are not so strongly 

 generated by this vessel, and more quickly attenuated by viscous 

 and other effects. 



As one possible measure of the validity of Froude's hypothesis, 

 that ship- wave effects are dependent only on the Froude number and 

 the hull form, a series of photographs have also been made with a 

 scale model of the UNCATENA. For this purpose a six-foot (scale 

 ratio of 24) fiberglass model was constructed, and equipped with a 

 single battery-powered electric motor and screw propeller, and a 

 radio-controlled rudder system. Figures 6 and 7 show the model, 

 as fitted with its single propeller and rudder, with an antenna mast 

 for the radio control receiver. Test runs were made with this model 

 on the Charles River, with photographic observations from the Boston 

 University Bridge at a height of approximately 50 feet. These photo- 

 graphs were made with a Minolta 35 mm camera and 28 mm focal- 

 length lens. Figures 8-10 show the model wave system from various 

 oblique angles. Unfortunately, no observations could be made from 

 directly above, so that measurements of the wave angles are not 

 obtainable for the model scale. Figures 8-11 show indeed that 

 close to the model discrete bow and stern wave systems are 



5 28 



