THE APPROXIMATE CALCULATION OF WAVE RESISTANCE AT HIGH SPEED 53 
Model 1,970 B. This is specified by 
a, = -4375 3 ag = — -4375 
21 = 16 ft. ; 2b = 1-5 ft. ; d= 1 ft. 
For comparison with the previous case we take the same subdivision : no 
horizontal section, and transverse sections at x = 0, + 4/1, + 3/1. The approxi- 
mate source distribution could be shown on a diagram of the longitudinal 
ection of the model ; it is given here in Table 2, with the divisions not drawn 
to scale. 
TABLE 2 
— -485 | = Byi/ | — 188 | 188 | S27 | “485 
These numbers, when multiplied by vM/4r, give the source strengths. The 
depth of the sources is 3d, while the longitudinal distances from the midship 
section are found to be x// = + -349, + -638, + -879. 
Comparison may be made with the distribution for the previous model 
with a, = a,= 0. Since we have not taken any horizontal section, the dif- 
ferences correspond to those on the curves of sectional area—or, rather, to 
the differences in the gradients of those curves. Using these coefficients for 
the sine series we calculate R from (13). Using the same notation as in Table 1, 
the comparison between calculated values from the complete integrals and 
from the approximation is shown in Table 3. 
TABLE 3 
i 303 341 404 522 607 884 
Ra 5-82 4-23 8-67 21-74. | 24-9 28-4 
R, 5-34 431 8-83 eT 27-9 
Model 1970 C. In this case 
a, = °8125 ; ay = — 1-3125 
A = 16 ttt, 8 Ap = leit, & al il it, 
With the same subdivision, we find the distribution shown in Table 4. 
TABLE 4 
— -456 | = Bhs) | = cilsf) | “159 | “385 
For the horizontal location of the sources, we obtain. 
edi se Sith ae WSL se COL 
For comparison with experimental results, the calculated values have been 
expressed in terms of ©,=R { 25-41/8 tv}?, where 8 is the displacement and v the 
velocity. The results are shown in Fig. 1, in which the two curves have been 
reproduced from Wigley’s paper. One curve is for the residuary resistance, 
obtained in the usual way by deducting from the total measured resistance the 
part due to skin friction calculated from Froude’s coefficients ; the other 
curve is for the wave resistance calculated from the theoretical integrals, without 
viscosity correction. The results obtained by the present approximation are 
shown by a cross for each of the speeds for which calculations were made. 
Model 2038 C. This model is specified by 
a, = —0:5'; a, = 0; 
DI N6itt. 2 bI—s leita —1O-5tts 
In addstion to the wariations,in the parameters, we have larger beam and only 
half the draught. Taking the same sections we obtain the scheme in Table 5. 
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