The Wave Generated by a Fine Shtp Bow 
stabilize at about 1.7 in. See Figure 4, parts (b) to (e), in which 
the rise varies between about 1.5 and 1.9 in. while the speed in- 
creases from 5.0 to 11.5 ft. /sec. (Note : the white mark on the 
bow here is at the 16 in. draft. ) 
(iv) The region in which the bow wave dominates the picture in- 
creases steadily with forward speed. (The analysis predicts that the 
peak of the bow wave moves aft in proportion to U , the speed.) In 
the lowest-speed tests, there is a clear wave-trough behind the bow 
wave. See, for example, Figure 4, parts (a) and (b) : The lowest 
visible white marks are on the still-water waterline. The trough is 
not predicted in the present analysis, and so we see that there are 
non-negligible waves at low speed which simply are not evident under 
the assumptions which have been made here. We cannot say whether 
the same kind of troughs occur at the higher speeds, because the 
model length was not great enough to observe the phenomenon, 
From Figure 2, it was clear that we have a "universal'' 
bow-wave curve which is supposed to apply to all wedges at all speeds 
at all drafts - within some unknown limits. To check this conclusion 
quantitatively, we measured just the amplitude and longitudinal po- 
sition of the peak of the bow wave. For the finer wedge, the results 
for the wave amplitude are shown in dimensional form in Figure 5 ; 
the corresponding data for the longitudinal position of the peak are 
shown in Figure 6. These dimensional data are shown only to provide 
the reader with an impression of the scale of what was observed. The 
nondimensional wave-peak data are shown in Figure 7 ; according to 
the analysis, the nondimensional amplitude, Z,,3,, should always 
have the same value, approximately 1.6. Figure 7 shows clearly 
that this is only roughly substantiated in the experiments. In fact, 
there are two ways in which the analysis is obviously deficient : 
1) The assumption that made our analysis distinct from the 
usual slender-body theory was that the bow flow is essentially a 
"high-Froude-number"' problem, in some sense. The depth-Froude- 
number is the only reasonable Froude number to consider in the bow 
region, and one can hardly expect the analysis to give good answers 
when Fy 0. In fact, it gives terrible answers then ! 
2) At the higher Froude numbers, the wave peak occurs at 
a considerable distance from the bow, ata place where the '"'thin- 
ship" representation of the body is probably quite invalid. We used 
the ''thinness"' twice, first in satisfying the body boundary condition 
approximately, then in evaluating the wave height on the body. (We 
simply set y= 0 in passing from (16) to (16').) The worse agree- 
ment for the wider wedge suggests that this ''thinness'' assumption 
LSLS 
