Newman 



of wave energy. This result follows, too, from the stationary phase 

 approximation, which, in addition, tells us that the attenuation rate 

 is changed to R' on the cusp line. A uniformly valid expansion 



near the cusp line has been obtained by Peters [ 1949] and by Ursell 

 [ I960] . The latter work includes numerical computations. 



III. PHOTOGRAPHIC OBSERVATIONS OF SHIP WAVES 



Kelvin's ship-wave pattern, as developed in the preceding 

 section or as originally developed by Lord Kelvin using an initial- 

 value approach, is well known and widely accepted, since the final 

 results are consistent with our observations of ship waves. Never- 

 theless, and perhaps to the surprise of many, the author knows of no 

 definitive experimental confirmation of the Kelvin pattern. Aerial 

 photographs are generally of the near-field (e.g. , Guilloton [ I960] ; 

 Inui [ 1962]) or from oblique angles (Wehausen and Laitone [ I960] , 

 Fig. 23). Stoker's "Water Waves" contains striking high-altitude 

 photographs which are from directly above the vessels, but during 

 turning maneuvers or while in convoys. One exception to the above 

 may be a special volume on aerial reconnaissance prepared during 

 World War II, but this is not generally available, nor has it been 

 used at all for a comparison with theory. 



Two years ago I had the opportunity to obtain aerial photo- 

 graphs of the Ferry Boat M. V, UNCATENA, This vessel is 147 feet 

 long by 28 feet waterline beam and 9 feet draft, displaces 400 tons, 

 and operates at a speed of IBs knots between Woods Hole and Martha's 

 Vineyard, Massachusetts, Propulsion is from three propellers, 

 turning at 1,200, 1,000, and 1,200 rpm. The water depth in the 

 area where photographs were made ranges from 50 feet to 80 feet, 

 with depths of 70 feet predominant. Originally, this vessel was 

 chosen for observation because of the severe wave systems which 

 it generated, in consequence of its high (0,38) Froude number. Pre- 

 liminary observations from a surface vessel indicated the most severe 

 waves to be substantially shorter than those which are predicted on 

 the cusp line of the Kelvin wave system, but it is apparent from the 

 subsequent photographic observations that these waves, in fact, are 

 located inside the 19°28' boundary of the cusp line. 



Three of the photographs obtained are shown here as Figs. 

 3-5. These were made with a Hasselblad 2-1/4 X 2-1/4 inch camera 

 and a wide-angle lens of 38 mm focal length. Figures 3 and 4 were 

 taken consecutively, looking directly downward from an altitude of 

 1,000 feet. Figure 5 is an oblique shot from 1,600 feet. As is clear 

 from these photographs, the predominant waves generated are a 

 portion of the diverging wave system, lying inside of the 192° cusp 

 line. In Figs. 3 and 4 we have drawn in boundary lines ± 19^28' 



"Speed of Shipping," revised edition. Central Interpretation Unit, 

 revised November 1943. 



5 24 



