624 



HYDRODYNAMICS IN SHIP DESIGN 



Sfc. 70J] 



where T'^ is the resultant velocity approaching 

 the blade element 



(Ts is the cavitation number at each blade 

 element, with the blade in the upper vertical or 

 12 o'clock position, based on the ship speed V 



a is the cavitation number, based on the 

 resultant velocity Vn 



Poo is the static pressure at the shaft axis, or the 

 atmospheric pressure plus the hydrostatic pressure 

 with the ship at rest 



e is the vapor pressure of salt water at an average 

 service temperature, taken here as 0.36 psi or 

 52 lb per ft' 



x'{Rm^x)w is a term to correct the cavitation 

 number to each blade element, with the blade in 

 the upper vertical or 12 o'clock position 



w is the specific weight of standard salt water = 

 64.043 lb per ft' 



x' is the 0-diml ratio R/Rm^x ■ 



For the ABC ship the shaft centerline is 15.5 

 ft below the designed waterline. The wave crest 

 or hollow due to the wave profile at the designed 

 speed is ignored in these calculations. In the 

 ABC ship, the positive wave height resulting 



l.0f? = Rr 



Expanded Blade Outline From 

 CoYitotion Criteria 



. Rodiol Disc Line / 

 / 



Faired Outline 



OA H 



0.3 R 



-Expanded Width at 0.2R 



II Petermined lyy Strength and 

 O.Z R^.^ I Riqidity Considerotions 



Fio. 70. L Expanded Blade Outlines with Minimum 

 Widths for Cavitation Prevention 



from the crest at the stern adds a shght margin 

 of safety against cavitation. 



p. = 14.7(144) + 15.5(64.043) = 3,110 lb per ft' 

 Po, - e = 3,110 - 52 = 3,058 lb per ft' 



The remaining calculations for cavitation 

 numbers and for the maximum-camber ratio 

 rux/c, the chord length c, and the lift coefficients 

 of the blade elements at the various radii are 

 shown in Table 70.h. 



When entering Fig. 70.K to pick the ratios 

 rrix/c and ix/c, the value of <r is reduced by 15 

 per cent, as shown in Col. M of Table 70.h. It is 

 customary to do this for all merchant ships as a 

 safety factor to guard against intermittent cavi- 

 tation which may arise from the non-uniformity 

 of the wake in a peripheral direction. For ships 

 in which there are highly concentrated wakes, 

 such as those behind a bossing or a large strut, the 

 reduction should be as much as 20 per cent. For 

 high-speed, high-powered vessels with fast-run- 

 ning propellers, where it is almost impossible to 

 avoid cavitation, no reduction in a is made. 



There are additional limiting factors in the 

 propeller design which must be considered at 

 this time. First, the blade-thickness ratio tx/c at 

 the hub section or at the 0.2/2 section should not 

 exceed values of 0.16 for destroyer-type propellers, 

 and 0.18 to 0.20 for merchant-ship propellers. 

 Above these limiting values, the drag-to-lift 

 ratio of a blade section begins to rise rapidly. 

 Second, the lift-coefficient Cl for any blade 

 section should not exceed about 0.6. Values 

 greater than this give propellers with poor stop- 

 ping and backing characteristics and increase the 

 liability of air leakage from the surface. 



Using the values of 0.85(7 and C tic/tx), calcu- 

 lated in Tables 70.h and Fig. 70.K, the blade- 

 thickness ratios tx/c and camber ratios mx/c are 

 found only for the 0.5 to 0.95 radii. The inner 

 radii are off the chart, which means that cavitation 

 is of little or no concern at these blade sections. 

 In this case, a limiting value of tx/c of 0.20, 

 mentioned in the preceding paragraph, is assumed 

 at the Q.2R section. The Q.2R chord length is 

 then calculated. This length, together with those 

 determined from Fig. 70. K, are laid down on a 

 sketch and a smooth expanded blade outline is 

 drawn. The result is illustrated in Fig. 70.L. 

 The expanded blade lengths are, for the time 

 being, laid out symmetrical to the radial disc line. 

 The method of introducing skew-back is described 

 later. 



