584 T. H. Havelock. 
The first point to be noticed is the prominent hump on the resistance 
curves in the neighbourhood of V/,/L=1. This is a well-known feature 
of ship resistance; it has been stated as an empirical rule that this hump 
occurs at V = 1:05,/L, or again that it occurs at V = 1:34,/(PL) where P 
is the prismatic coefficient. In fig. 2 the values of V/,/L for the more 
normal models A and B are 1:04 and 1:03 respectively, while for the more 
extreme forms C and D with hollow lines they are about 1:02 and 0:98; the 
model D has obviously lines which are unusually fine at the bow. 
In the figure the humps and hollows are, in general, more pronounced 
than in experimental curves. The familiar pattern of ship waves is usually 
described as made up of transverse waves and diverging waves, the former 
being the chief factor in the wave resistance; there is also a tendency to 
associate the transverse waves with the stream-lines which travel along the 
bottom of the ship and the diverging waves with the action of the vertical 
sides of the ship at the bow, but this is misleading. In the present calcula- 
tions we have models in which none of the stream-lines can go underneath 
the ship; they are all forced sideways from the bow. It appears that the 
effect of the flat bottom of the ship, and of its finite draught, may be rather 
to smooth out the oscillations in the resistance curve. A general feature 
of the curves which is in agreement with experiment is that the oscillations 
become progressively less prominent as we take the models in the order 
A,B, GC, D; this is especially noticeable in models C and D, which have 
hollow lines. 
The most interesting and important characteristic of the set of curves is 
their intersection in pairs at values of V/,/L ranging from 1:12 to 1:18. 
Compare, for instance, models C and A. At low speeds C, with its finer 
entrance, has a decided advantage ; at 1:18 the resistances are equal, while 
above this speed the advantage remains with model A, with blunter ends 
but with less beam. It has been remarked that one cannot make exact 
comparison with experimental results from ship models, but a general 
survey of the data bears out these calculations. Without going into detail, 
it may suffice to give a few references to standard treatises on ship resistance 
where the results are summarised. 
G. S. Baker remarks: “In the section dealing with the relative merits of 
hollow versus straight lines, and elsewhere, it has been shown that for vessels 
of fine form intended to work at speeds in the neighbourhood of V = ,/L 
there is a decided gain in working the level lines with some hollow in them. 
Tt has also been known that for such fine forms at very high speeds the 
hollow should be reduced to get the best effect.” * 
*@.S. Baker, ‘Ship Form Resistance and Screw Propulsion,’ p. 87, 2nd edn. 
1920. 
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