Gadd 



water, it would of course make waves. Let us imagine, however, that its shape 

 could be modified so that its wavemaking were reduced virtually to zero, without 

 altering its immersed volume or appreciably increasing its frictional drag. The 

 resistance of such an imaginary ship would then be half that given by Eq. (2) 

 with V set equal to twice the immersed volume, since the water surface would 

 remain practically flat and would be equivalent to a plane of symmetry for a 

 deeply immersed body. Correspondingly, the power needed to drive this ship 

 with 70 percent propulsive efficiency would, from Eq. (4), be given by 



Pn,in = 0-845 V^ A2/3 Cp(RJ , (6) 



where 



R^ = 2.66 X 10^ VAi/3 ^ (7) 



V is the speed in knots, and A the salt-water displacement in tons of the im- 

 mersed part of the hull. This implies that, in the usual notation, the minimum 

 value of C is l8.9/(logjQ r^ - 2)^, remarkably close to Hughes' estimate (4), 

 derived by quite different procedures, for the minimum viscous contribution 

 to C . 



In reality, of course, a greater power is likely to be needed, since the mod- 

 ifications in shape required to reduce the wavemaking of the half-immersed 

 body of revolution would almost certainly increase frictional drag. Neverthe- 

 less Eq. (6), in conjunction with Eq. (5) and Eq. (7), provides a reasonable datum 

 with which to compare actual ship performances. 



In Table 3 the actual powers P^ of a number of ships, whose details are 

 given in published literature, are compared with the P^-^ values calculated 

 from A and V using Eq. (6). Speed-to-length ratios v/\T7 are also given, where 

 L is the LBP in feet. Some of the data of Table 3 are quite probably in error; 

 although we have tried to ensure that the stated power corresponds to smooth- 

 water smooth-hull operation at the stated displacement and speed, this may not 

 be true in every case. Sometimes, for example, the displacement given may be 

 a service one, whereas the speed may be a trials result obtained at a different 

 displacement. Likewise, the power quoted may contain an appreciable service 

 margin to enable the ship to reach the given speed even in rough-weather con- 

 ditions and when the hull surface has deteriorated with time out of dock. Thus, 

 some of the results for Pg/Pniin "^^Y ^^ subject to quite large errors. 



It can be seen that the ratios Pa/Pn,in vary widely, even for ships of roughly 

 the same speed-to-length ratios. For large values of V \1^, typical of fast war- 

 ships, Pg/Pniin is large, in the region of 3 to 5. It is interesting that the power 

 ratios of postwar warships are somewhat lower than those for prewar ones; this 

 presumably reflects improvements in hull design and the use of welded rather 

 than riveted construction. Among the vessels with V/vTT in the region of 1, cargo 

 liners with displacements in the region of 10,000 to 20,000 tons are much supe- 

 rior to passenger ferries; the latter have to be made beamier because of draught 

 limitations and for stability reasons. Large tankers and bulk carriers show a 

 wide range of performance, the best of them having a power ratio of as low as 

 1.5, whilst some have ratios of well over 2. 



710 



