620 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.30 



distribution than the fraction 1/2 shown there. 



The calculations for the lift-coefficient product 

 and the lifting-surface correction are given in 

 Table 70.g. 



Having applied the lifting-surface correction 

 factor to the hydrodynamic pitch angle, it is 

 possible to calculate the initial hydrodynamic 

 P/D ratio for each 0-diml radius by the formula 



(P/D)^. = irx' tan 4, 



(70.ix) 



where 0(phi) is the pitch angle and is equal to 

 /3/c at this stage of the design. This calculation 

 is also shown in Table 70. g. A plot of the P/D 

 ratios is given by the lower curve of Fig. 70.1. 

 The upper curve in this figure is explained later. 



Fig. 70.1 Plots op Pitch-Diameter Ratio on 

 Radius Fraction 



70.30 Finding the Blade-Thickness Distri- 

 bution. The next step is to make an estimate of 

 the blade-thickness distribution along the radius. 

 This is based on a simplified strength calculation 

 given by Eq. (70.x) which follows. The first term 

 of this equation represents the compressive stress, 

 the second term shows the increase in the com- 

 pressive stress due to the centrifugal-force effect, 

 and the right-hand side of the equation is the 

 allowable stress. 



C,Ps 



4.123nD 



m 



+ 



Dn^i4>i 



12,788 



= Sc + 



12,78? 



(70.x) 



where Ci is a coefficient depending upon the 



P/D ratio at the 0.7i?. It is obtained from Fig. 



70.J [RPSS, 1948, Fig. 180, p. 270; S and P, 1943, 



Fig. 161, p. 138] 



Ps is the shaft power per blade 

 n is the rate of rotation in rpm 

 to/D is the blade-thickness fraction 



2.8 § 



2.7 rH= 



2.6, 



2.5 



2.4, 



2.3 d 



2.2 



0.5 0.6 0.7 0.8 0,9 1.0 i.l 1.2 1.3 1.4 

 Pitch-Diameter Ratio P/D at 0.7 Radius 



Fig. 70.J Graphs of D. W. Taylor's Ci and 04 

 ON Pitch-Diameter Ratio at O-lRua^ 



D is the propeller diameter in ft 



i is the tangent of one-half the angle of rake 



<l>i is a coefficient depending upon P/D at 

 0.7R, obtained from Fig. 70.J [RPSS, 1948, 

 Table 22, p. 270]. 



Sc is the maximum allowable stress. For 

 manganese bronze, Sc is 6,000-7,000 psi for 

 merchant ships or other ships that cruise near 

 their maximum power. It is 13,000 psi for warships 

 or other vessels that operate at full power only 

 infrequently. 



Eq. (70.x) is usually solved by assuming values 

 of to/D. A plot is made of the values of the left 

 side of the equation on a basis of to/D. The 

 required to/D is found where the curve crosses 

 the line given by the right-hand side of the 

 equation. 



For the ABC design, the second term of Eq. 

 (70.x), showing the centrifugal-force effect, be- 

 comes zero since the rake angle is zero. The 

 equation is thus directly solvable for to/D. 



P. = 



13,250 13,250 



= 3,312.5 horses 



n = 97.2 rpm Z) = 20 ft 



i = {P/D)o.,a = 1.166 



C, = 908 from Fig. 70. F Sc = 6,000 psi 



