626 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.33 



z t 



1.0 O 



0.8 



1.4 



1.2 



.0 o 



1. Reduce to S-Bloded Propeller of Equivalent Area [Ae/AqIs =(3/2)(Ae/Ao) 

 2. Read k| for A= 0.4 and Qa^/AqJj =1.00 from Curve of Diagram 1 for the Series of Values of x' 

 3. Read Correction Foctor Vz fc Equivalent (A e/Ao)3, in this case 0.358, and for x' Volue5 from Diag.S 

 4. Read Correction Factor kj for Proper A from Dioqram 3 

 5. Muliipl\) ki.kg., and kj to Obtain Final Correction Ftictor for Use in Eq. (70.x\(l) 



Fig. 70.N Graphs for Flow-Curvature Corrections 



fc is the correction for the curvature of the 

 propeller flow. 



The application of this correction and the cal- 

 culation of maximum camber are shown in 

 Table 70.i on page 622. 



All the calculations made thus far are for a 

 non-viscous liquid. In order to compensate for 

 the decrease in lift which occurs in actual water, 

 a small viscous-flow correction angle is added to 

 the hydrodynamic pitch angle at each section. 

 This correction depends upon the meanline. For 

 a symmetric meanline, as embodied in the circular- 

 arc or a = 1.0 sections, the correction is given by 

 the following equation: 



(1 -m) 



C. 



0.1097 



(TO.xvii) 



where a^ is the added viscous-flow correction 

 angle, in deg 



M is the viscous-flow factor. 



In this equation 0.1097 is the slope of the lift 

 curve for infinite aspect ratio; in other woi'ds, 

 the increase in lift for an increase of 1 deg in 

 angle of attack. The viscous-flow factor can be 

 taken as follows: 



(a) For a circular-arc meanUne, ju = 0.80 



(b) For an a = 1.0 meanline, /i = 0.74 



(c) For an a = 0.8 meanline, p. is approximately 

 1.0, so that «! becomes zero. 



For the ABC design, using a circular-arc mean- 

 line, this viscous-flow correction is simplified to 



ai^ 1.8Cx,(indeg). 



The hj'drodyuamic pitch angle /J/c is then 

 increased by a^ and a new and final PjD ratio is 

 calculated, using Eq. (70. ix). The pitch angle <^ 

 is now equal to /3/c -(- "i . These calculations are 

 shown in Table 70.i. The final P/D values are 

 hsted in Col. P of Table 70. i and are plotted as 

 the upper hne on Fig. 70.1 in Sec. 70.29. 



Attention is called to the fact that the pitch 

 distribution shown in the upper curve of Fig. 

 70.1 is not typical for a normal single-screw 

 merchant ship of the 1950's. The ABC ship has a 

 transom stern and an unusually thin skeg; the 

 latter probably contributes most to the unusual 

 local wake variation shown in Fig. GO.M. The wake 

 fraction for a normal single-screw ship is low at 

 the tip, increasing rapidly to high values near 



