8 WAVE PATTERNS AND WAVE RESISTANCE. 
Notice first the magnitudes of the terms in (13). The bow and stern systems are 
factored by c?/g1l, while the effect of the curved sides has the factor c*/g21?. Hence at 
low speeds the bow and stern provide the greater part of the wave system, but as the 
speed increases their relative importance becomes less. Then we have the effect of the 
amplitude factor cos 6 in the last two terms of (13). Remembering the distinction between 
transverse waves and diverging waves in a simple pattern, and that cos @ diminishes from 
unity at 0° to about 0-8 at 35° and then to zero at 90°, we may describe the result in 
general terms: the effect of the gradual change of slope along the curved sides of the model 
compared with the finite angle at bow and stern is to diminish the relative importance of 
the diverging waves. This point is amplified further in the following model. 
8. In this model one end, say the stern, is drawn out to a fine point. The model is 
again of great draught and is of uniform horizontal section throughout. Fig. 6 shows the 
form of the horizontal section. Sa 
-p----------fo 
Fig. 6. 
Taking the origin O at the bow, as in the diagram, the equation of the curved side 
OCB is 
276 
Y= aay 2 til) Bye gs etna Se ach ee I) 
The maximum beam 26 occurs at one-third of the length from the bow. 
The wave pattern in the rear is given, in our abbreviated notation, by 
gee eae eC. c2\2 CN oa 
= al sin (7, y) — 4 G) cos 6 cos (@, y) — 6 G cos? @ sin (x, y) 
2\ 2 2\3 
—2 (5) cos 8 cos (x + 1, y) + 6 (5) cos? 6 sin (x ++ J, ofa @ (15) 
Here we have five simple patterns, the first three focussed at the bow and the last 
two at the stern. The first term in (15) is the simple sine pattern due to the finite angle 
of the model at the bow; we notice there is no similar term for the stern because the angle 
has been smoothed away completely at the stern. The last four terms of (15) taken together 
represent the resultant effect of the curved sides OCB and ODB of the model. The 
general inferences are the same as for the previous model; but we notice that we have 
now, in (15), patterns with an amplitude factor cos? 6, and for such the relative importance 
of the diverging waves is still further diminished. 
Errect oF DRAUGHT. 
9. Another point about which we may make some broad deductions from the formule 
for the wave patterns is the effect of the draught of the model. In the previous cases 
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