424 T. H. Havelock 
model does not contribute much to the wave-making. We shall not 
examine the wave profile in this case. For the wave resistance we have 
Ren) { ne + BY) cos 6 dé, (22) 
where 
A— iB = — aoe { -@ a 1) e-ixoh sec 4 I}, 
=i 
pis we [ema gh. (23) 
0 
This leads to the result 
— l6pb*c? (2 (1 + 48%) | 16(1 + 168%) , 48 
CE ea 8 ag 
— ap Pa Op) + $8 P, @p) + 8p, an) — 8p, en 
Ml =D ae WGP ca 
a C75) p, (p) + 20 Pp, @-— P, (4p) 
i “et P, ap}. (24) 
This expression may be written as 
R=Ry+ BR, + BRo. (25) 
The form (25), with 8 a positive quantity less than unity, applies to the 
model when going bow first. It is easily seen that the corresponding 
result for motion stern first, assuming the same reduction factor 8, is 
R = #R, + PR, + Rg. (26) 
Numerical calculations have been made from these expressions for 
6 = 0-6, and from these curves have been drawn showing the variation 
of R/c® with speed, on a base of c/4/(g/); these are given in fig. 3. 
The curve A in fig. 3 is for motion bow first, the curve B for motion 
stern first. The curve C is for (24) with 8 = 1, that is, it is the resistance 
curve for motion in either direction when no allowance is made for 
frictional effects. There are few experimental data available for com- 
parison ; but in any case it should be noted that, apart from other simpli- 
fying assumptions, the preceding calculations are for a model of very 
great draught. However, reference should be made to some experimental 
curves given by Wigley ;* in fig. 3 of his paper there are three resistance 
* * Trans. Inst. Nav. Arch.,’ vol. 72, p. 216 (1930). 
405 
