308 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 56.10 



0.2 0.3 0.1 a5 0.6 0.7 O.S 0.9 1,0 I.I 1.2 1.3 1.4 1.5 I 



Fig. 56.L Variation of Speed Exponent in Rbsiduart-Resistance Formula Rr = 



.6 1.7 I.S 1,9 2.0 2.1 



kV" FOR Nine Large Ships 



at the designed T^ of 0.544. This indicates that 

 the large volume on a given length, characteristic 

 of this ship, is carried at an unreasonably high 

 price in wavemaking resistance. The n-value is 

 only slightly over 3.0 at a T, of 0.4. This reveals 

 an acceptably low wavemaking drag for the lower 

 speeds customary with this type when it was 

 first developed into large sizes in the early 1900's. 



(c) For actual ships which are driven hard, 

 values of n exceeding 7.0, 8.0, and over are by no 

 means unusual. High-speed ships may reach the 

 greatest n-value at a speed less than the maximum, 

 with a greatly diminished n at that speed, as for 

 the heavy cruiser Pensacola and the destroyer 

 Hamilton in Fig. 56.L. The following footnote by 

 C. Rougeron is quoted from the U. S. Naval 

 Institute Proceedings, February 1953, page 190: 



"Actually, the speed-power ratio increases in a some- 

 what more complicated manner. In a recent French 

 flotilla leader the 'direct' resistance is found to vary in 

 proportion to the square of the speed at low speeds, to the 

 6th power of the speed in the vicinity of 28 knots; and only 

 to the 1.35 power of the speed for speeds in the vicinity 

 of 38 knots." 



(d) Some planing craft show pronounced knuckles 

 in the curve of Rr on V, with accompanying 

 sudden drops in the value of n, as in Fig. 30.B. 

 The data from which Fig. 53. D of Sec. 53.7 were 

 plotted show no such sharp discontinuities but 

 they do reveal that at several points the resistance 

 levels out so that it varies with V at some power 

 only slightly greater than 1.0. 



(e) For high-speed planing craft it may be 



expected that, at T^ values near the maximum, 



n will be negative. This occurs for the PT boat 



in Fig. 53.D. 



(f) There are irregularities in the n-curves 



unexplained on the basis of wave interference 



alone. 



56.10 Variation of Total Resistance of Model 

 and Ship with Speed-Length Quotient. It is use- 

 ful at times for the designer to be able to find 

 quickly the total resistance of a ship in some 

 everyday terms such as pounds of total resistance 

 per ton, expressed by flr/A, at say the designed 

 speed, when only the type of ship and the approxi- 

 mate Taylor quotient T, = F/vL or Froude 

 number F„ are known. For example, the Rt/^ 

 value for a large, modern Great Lakes freighter 

 at designed speed is about 2 lb per ton, that of an 

 Atlantic liner is some 10 lb per ton, and that of a 

 fast motorboat is of the order of 600 lb per ton. 

 H. M. Barkla has published a log-log plot showing 

 values of the ratio Rr/W on a base of T^ for 

 eleven sailing-yacht and motorboat hulls, as 

 listed on page 237 of his paper "High-Speed 

 Sailing" [INA, 1951, Vol. 93]. The range of T, is 

 from 0.4 to 10 and of Rr/W from 0.004 to 0.3. 

 Barkla's resistance-weight ratio is 1/2,240 times 

 the ratio Rt/^, when the latter is expressed as 

 pounds resistance per long ton of weight. 



To provide data for a greater variety of water 

 craft, both large and small, there have been 

 plotted on Fig. 56. M the values of flr/A, at the 

 designed speed, of a considerable number of 



