54 THE APPROXIMATE CALCULATION OF WAVE RESISTANCE AT HIGH SPEED 
The sources are at depth 3d, and the longitudinal positions are x/J = + -327, 
627, *869. Making calculations with this plan it was found that the 
values at the lower speeds tended to be too large. This is probably due to 
the large source strength in the middle compartments compared with the 
previous cases, and possibly to the shallower draught. It was decided to 
take additional transverse sections so as to divide each middle compartment 
into two of equal strength ; this can be calculated from the general formule 
(10) and (11). Thus the scheme finally adopted is 314, 342, O72, 
— 172, :172, -172, :342, -314, with the longitudinal positions given by 
x/l = + -227, + -418, 627, -869. The depth is the same as before. 
The consequence is that we have now four sine terms to evaluate. The results 
are shown in Fig. 1, the curves being reproduced from Wigley’s paper and 
the values from the present approximation denoted by crosses. 
TABLE 5 
The agreement shown in Fig. 1 between the two sets of calculated values is 
reasonably good. The four cases which have been examined, taken together, 
give some idea of the scope of the approximation and of the measure in which 
it responds to changes in the form of the model. It is not the present purpose 
to compare calculated results with experimental, but the latter have been 
included in Fig. 1 for the last two cases. It should be noted that viscosity 
effects have been neglected, but these are comparatively small at the speeds 
under consideration ; moreover, the residuary resistance has not been corrected 
by any allowance for form effect upon the frictional resistances, or similar 
refinements. It is generally considered that the main difference between 
calculated and experimental values of wave resistance at these speeds is due to 
sinkage and trim of the model. From the point of view of the present work, 
this would be reflected mainly in an increase in the effective area of the mid- 
ship section ; and it can be seen from the formule that the values are very 
sensitive to changes in this factor. 
Models with Non-mathematical Lines 
10. We proceed now to apply the method to models with lines not given by 
mathematical equations, for which the wave resistance has not hitherto been 
calculated. For obvious reasons, in view of the range of speeds under con- 
sideration, it is not possible to deal with recent models. Data have, however, 
been obtained for two models ; these include complete plans and dimensions, 
together with the record of actual measurements of resistance. (I am indebted 
to Mr. J. L. Kent, Superintendent of the William Froude Laboratory, for per- 
mission to use this material, and to Mr. W. C. S. Wigley for much valuable help.) 
Model A. The body plan and other data for this model are shown in Fig. 2. 
It is obvious that the problem is more complicated than for the simple 
model, symmetrical fore and aft and with similar transverse sections through- 
out. After some preliminary calculations it was decided to take the following 
subdivision : one horizontal section throughout at half draught ; in the upper 
half, transverse sections at stations 1, 2, 5, 8 and 9; and in the lower half, 
transverse sections at stations 2, 5, and 8. The various sectional areas and 
the depths of their centroids, and the corresponding volumes were obtained 
from the plans. From the sectional areas in the upper and lower halves, we 
obtain the source diagram shown in Table 6. 
507 
