589 T. H. Havelock. 
With the use of the graphs in fig. 1 and the expressions in (21), caiculations 
were made from (22), (23) and (24) for about fifteen values of /p in each case. 
The results are shown in the continuous curves of fig. 2, the curves being marked 
with the corresponding value of 8. 
7. The curves show the increasing influence of smaller draught at the higher 
velocities. Although, from the differences in the expressions for the resistance, 
the maxima and minima due to interference of bow and stern systems probably 
do not occur at exactly the same positions, it is important to notice that 
the differences in this respect are inappreciable. This agrees with a similar 
phenomenon which has been observed experimentally in the resistance of a 
submerged model at different depths ; although the magnitude of the interference 
effects varies with the depth, the positions of the maxima and minima are 
practically unaltered. Another point to note in the theoretical curves of fig. 2 
is that at the smaller draughts the effect of interference is less pronounced. 
But the chief purpose of the calculations was to find whether, with a draught 
similar to that of actual ship models, the calculated resistance was in reasonable 
agreement with experimental results. 
The values which have been chosen for the ratio of draught to length, namely, 
one-twentieth and one-tenth, cover ay proximately the usual range in practice. 
It must, of course, be remembered that the calculated results correspond to a 
model with vertical sides and constant horizontal cross-section ; therefore one 
cannot expect more than agreemrnt in order of magnitude. Three examples of 
experimental curves have becr selected and are shown in the discontinuous 
curves of fig. 2. 
The curves marked 0-0475 and 0-0385 have been drawn from results given by 
R. E. Froude* for the residuary resistance of two models of the same length 
and beam and having the given ratios of mean draught to length. The results 
were given as the resistance in tons for a ship of 400 ft. length, and have been 
recalculated here in the non-dimensional co-ordinates of fig. 
Froude’s ship A with displacement 5,390 and 4,090 tons respectively. In 
both cases there was a certain amount of parallel middle body. 
The third curve, marked 0-083 in fig. 2, has been obtained by similar reduc- 
tions from experimental results given by J. L. Kent}; it refers to his model 
112K, which had no parallel middle body, but had hollow lines at the bow. 
The curve has been filled in approximately from a smaller number of points 
2; the two cases are 
thanin the previous cases ; one can, however, observe the effect of the hollow lines 
* KR. E. Froude, ‘ Trans. Inst. Nay. Areh.,’ vol. 22, p. 220 (1881). 
j J. L. Kent, ‘ Trans. Inst. Nav. Arch.,’ vol. 57, p. 154 (1915). 
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