. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. 1909.] The Wave-making Resistance of Ships. 299 velocity-the resistance being zero after that point. In practice, we know that there are no such discontinuities in the resistance curves, and there are certain considerations which go to account for this difference. First, as regards the transverse waves alone, the preceding formulae show that 'the amplitude tends to become infinite at the critical velocity, although the corresponding resistance at uniform velocity remains finite ; but, e
. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. 1909.] The Wave-making Resistance of Ships. 299 velocity-the resistance being zero after that point. In practice, we know that there are no such discontinuities in the resistance curves, and there are certain considerations which go to account for this difference. First, as regards the transverse waves alone, the preceding formulae show that 'the amplitude tends to become infinite at the critical velocity, although the corresponding resistance at uniform velocity remains finite ; but, even''apart from the effects of viscosity, there is a highest possible wave with a velocity depending partly upon the amphtude. Secondly, we have left out of consideration the diverging waves; but these must become more important m the neighbourhood of the critical velocity, for we may regard the two systems as coalescing into one solitary wave in the limit as the critical velocity is reached. After this point the diverging waves persist, so that the effect of these would be of the order of halving the drop in the resistance as the critical velocity is passed. Finally, we must consider the frictional resistance, which increases steadily with the velocity; so that the fall is finally a smaller percentage of the total resistance than might appear at first. The curves given in fig. 11 give an estimate of a maximum effect of this kind, considering only the transverse wave system. §7. Further Types of Pressitre Distrihutmi. The preceding formula have been built up on the effect of a travelling pressure disturbance of simple type; we consider now another type which we may use as an illustration. Let the pressure system be given by The type of distribution is graphed in fig. Proceeding as in §2, we have ("00 7 2 2 <^ (k) = 2A J^ ^^a~",^,co3 Kco dco = 7rA«e-«*. (30) 57. Please note that these images are extracted from scanned page images that may have been digitall
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