Design of Low-Resistance Hull Forms 



We now attempt to find a formula for the power required to propel a ship of 

 salt-water displacement A tons at a speed of V knots, when this ship is designed 

 by the best current procedures to have minimum resistance, with no other re- 

 strictions imposed. A reasonable form of expression, based on Eq, (6), is 



Pbest = V' A2/3 [0.845 Cp(RJ + F(N)] , (8) 



where N, approximately equal to V/VU, is given by 



N=-0-228V .J 



from Eq. (1), where we put t equal to 0.15, as for the optimum body of revolu- 

 tion, and V equal to twice the displaced volume in cu ft of the ship, or 70A, Eq. 

 (8) was fitted to the best data of Table 3 and of a further collection of trials 

 data, not reproduced here. These best data were: 



Tanker A = 24,230 tons V = 13.78 knots P^ = 4,120 hp 



Cargo liner A = 11,070 tons v = 22 knots P^ = 11,290 hp 



Frigate A = 2,700 tons V = 28 knots P^ = 20,000 hp 



and so we obtained an approximate relation 



Pfaest = ^^ ^^^^ [0.845 Cp(R^) + 0.5x 10"^ + 0.3 X 10-3 N'*] . ^qj 



An alternative, equally plausible, relation roughly fitting the same optimum data 

 is 



Pbest = V^ A2/3 [1.20 Cp(R^) + 0.3x 10-3 N''] . 



This does not differ much from Eq. (10) in the low Reynolds number range, but 

 shows up most of the large tankers in an even poorer light* than does Eq. (10), 

 which we therefore assume to be more appropriate. In a sense, this may be de- 

 parting from the intention that Ptest should represent the minimum power at- 

 tainable, since large tankers, which provide most of the low Froude-number 

 data, are always designed with very bluff lines, and there is little doubt that a 

 finer-lined ship of the same displacement and speed would require less power. 

 To this extent, therefore, Eq. (10) may represent some compromise with prac- 

 tical requirements. This compromise could perhaps have been avoided by using 

 model results in deriving Eq. (10). However, we have consistently used full- 

 scale data to avoid uncertainties in ship-model correlations and to include ef- 

 fects of any hull-surface imperfections which may be normally present on the 

 full scale. There is a scarcity of full-scale data for large fine -lined ships at 

 low Froude numbers, but, since most tanker powers are considerably in excess 



*That is, of course, when looked at purely fronn the point of view of resistance. 

 As pointed out earlier, practical considerations (in this case the desirability 

 of minimizing length, so reducing construction costs) nnay often require large 

 departures from the minimum-resistance "optimum." 



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