Design of Low-Resistance Hull Forms 



noted above concerning the tanker end of the data) intended to represent mini- 

 mum powers achieved by current optimum designs when subject to the minimum 

 of extraneous practical requirements. 



Conclusions from Part 1 



It has been shown that the propulsive shaft horsepowers P^est > °^ those 

 present-day ships which for a given displacement A and speed V have the least 

 resistance, approximately fit the formula 



Pbest ^ "^^ ^^''^ [0.845 Cp(R^) + 0.5x 10"^ + 0.3x 10"^ N'*] , (10) 



where 



Cp(R„) = 0.075 (logjo R,-2)-^ (5) 



R„ = 2.66 X 10^ VAi/3 _ (7) 



and 



N = 0.228 VA- 1/6 . (9) 



It is unlikely that, however much design can be improved, the power could ever 

 be brought down much below 



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



to achieve which, wavemaking would have to be virtually eliminated without in- 

 creasing the frictional drag per ton above that of a fully submerged optimum 

 airship form. The difference between P^est ^^^ Pmin? therefore, represents 

 the margin there is for improvement on present-day designs. 



Three points should be borne in mind. 



1. Equation (10) represents an envelope for different ships, each "opti- 

 mised" (by empirical processes) for its particular operational conditions, and 

 so it does not represent what happens to a given hull form as its speed is varied. 

 Thus the N'' factor cannot be identified simply with wave resistance, though un- 

 doubtedly it forms an important part of the wave resistance. 



2. A ship whose propulsive power greatly exceeds P^est ^^ ^^^ necessarily 

 a badly designed ship, since Eq. (10) represents only a hydrodynamic optimum, 

 and a more resistful ship may well be cheaper to build and hence a more eco- 

 nomic design than one conforming to Eq. (10). The latter form may also be un- 

 able to meet practical requirements of stability, draught limitation, etc. 



3. Nevertheless, Fig. 2 suggests that even for very beamy, and hence short 

 and cheap, ships, the viscous component of resistance need not necessarily 

 greatly exceed its optimum value. If, therefore, we were sufficiently adept at 

 reducing wave resistance for large beam-to-length ratios, we ought to be able 

 to design a ship which was not only cheap to build, but which also compared 

 favourably with Eq. (10). 



715 



