594 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.6 



(ii) The basic factors br or Bu are known 

 (iii) The basic factors bg or Bp are known. 



For the study on the ABC ship, the propeller 

 diagram for the B.4.40 series is selected. This 

 series number indicates that the propeller has 

 four (4) blades and that its expanded-area ratio 

 Ab/Ao is 0.40. The mean-width ratio is only 

 0.189, from the information block in the upper 

 right corner, but this group of propellers appears 

 to correspond most nearly to that desired. 



The first step is to find the thrust-load coefficient 

 Ctl , using the expression Ctl — T/{Q.5pAqVI). 

 The thrust T is obtained by dividing the total 

 resistance Rt oi 172,000 lb by (1 - ^ = 0.889; 

 it is found to be 193,476 lb. The speed of advance 

 V A is the ship speed, 20.5 kt, times [(1 — w) = 

 0.739], or 15.15 kt. The thrust-load coefficient then 

 becomes 



Ltl — 



193,476 



(0.5)(1.9905)(0.7854)(20)'[(1.6889)15.15]' 

 = 0.945. 



Prohaska's chart. Fig. 70.B, is entered on the 

 lower of the pair of upper right-hand diagonals, 

 marked Ctl ■ Draw a perpendicular to this line 

 at the value of Ctl = 0.945, marked on the 

 diagram by an arrowhead. Where this perpendic- 

 ular crosses the graph marked "tjmsx for Ctl ," 

 interpolate for the correct value of P/D from the 

 series of five Kt curves for various P/D ratios. 

 The optimum P/D value corresponding to the 

 crossing marked with an "x" on the diagram is 

 1.02. 



From this crossing draw a vertical line to the 

 top of the diagram. Where this line cuts the series 

 of r/o efficiency curves, at a point corresponding 

 to a P/D of 1.02, marked by a small solid circle, 

 read the corresponding efficiency value ?jo • From 

 the scales at the right or left the open-water 

 efficiency is 0.68. 



Continuing up the vertical fine to the lower 

 horizontal scale at the top, the value of the ad- 

 vance coefficient J is read off as 0.703. From the 

 relationship J = Vo/inD) or ra = Vo/{JD), 

 calculate the rpm as follows: 



Vo_ _ Vj_ _ 1.6889(15.15)60 



= 109.2 rpm. 



JD JD (0.703)20 



If this rate of rotation appears to be not suit- 

 able, for some reason or other, it may be necessary 

 to sacrifice some propeller efficiency for a desired 

 rate which is faster or slower. The amount so 

 sacrificed is determined by following the procedure 



described, except that instead of picking r/o and 

 J values for the crossing of the Ctl perpendicular 

 and the graph of "r/Max for Ctl or A," they are 

 picked for the crossings of that perpendicular 

 with the several Kt graphs for a range of P/D 

 values. The latter crossings are marked by small 

 open circles. The values derived for the complete 

 range of P/D available on the chart are listed 

 in Table 70.a. 



TABLE 70.a — Variation op Epficienct with Rate 



OF Rotation and P/D Ratio 

 The data listed here are for the Wageningen B.4.40 series 

 propellers from Prohaska's logarithmic chart, Fig. 70.B. 



The efficiency drops off only one point at the 

 most, from 0.680 to 0.670, for a rather wide 

 range of P/D ratio and rate of rotation. As a 

 matter of interest, H. F. Mueller's data in Fig. 

 59. A show that for a Ctl of 0.945, as used here, 

 the P/D ratio for maximum efficiency could be 

 as high as 1.2. The expected propeller efficiency 

 would be 77, (from Table 34. a) = 0.835 times 

 (j/n/j?/ = 0.794) or 0.663. 



To determine whether the blade shapes, areas, 

 and sections of the B.4.40 series are the best, 

 the propeller designer is required to go through 

 the same steps for the Wageningen B.4.55 series. 

 A check for the ABC ship, not given here, revealed 

 that with its wider blades the B.4.55 series is 

 considerably less efficient. 



Using Schoenherr's charts, the problem is that 

 represented by category l.(a) [PNA, 1939, Vol. 

 II, p. 159]. As before, the designed ship speed V 

 is 20.5 kt, the effective power P e is 10,827 horses, 

 and the propeller diameter D is 20 ft. From 

 Schoenherr's Chart 1, Fig. 20, on pages 160 and 

 161 of the reference, 



K,i = 



58.913 



(sp.gr.)(l - 0(1 - wY VD'' 

 58.913 10,827 



1.027(0. 889) (0.739)^ (20.5)'(20)' 

 = 0.371245 = 0.371 



