372 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 60.9 



devised to take direct account of the factors which 

 develop the thrust-deduction force, is based upon 

 the rate of variation of — Ap with fore-and-aft 

 distance ahead of the propeller, and that of 

 -|-Ap abaft it. The assumption is made that these 

 pressures vary with distance in very nearly the 

 same manner as for a screw propeller working in 

 open water or an airscrew working in open air, 

 indicated by diagram 3 in Fig. 59.G. It is further 

 assumed that, following D. W. Taylor's patent 

 previously referenced, the — Ap's are so small at 

 2 diameters ahead of the disc position that they 

 can be neglected. 



The method is based upon a summation of 

 longitudinal forces exerted upon certain selected 

 transverse sections of the ship, lying within an 

 imaginary cylinder concentric with the propeller 

 axis. This cyhnder has the propeller diameter D, 

 and extends both forward and aft from the disc 

 position. 



A similar imaginary cylinder in this position 

 was shown by G. Kempf many years ago [STG, 

 1927, Vol. 28, p. 180]; also by E. F. Hewins as a 

 method of determining the wake fraction w 

 [Osbourne, A., "Modern Marine Engineer's Man- 

 ual," 1943, Vol. II, p. 2311], 



For the analysis described here, the transverse 

 sections are at 2.0Z), l.OD, and 0.5Z) ahead of the 

 disc position. A fourth section is taken through 

 the maximum-area section of whatever rudder, 

 rudder post, or horn combination lies abaft it. 

 Any other transverse-section positions could be 

 used if desired, and they could extend for more 

 than 2D ahead of the disc position. 



It is assumed that the — Ap values at the three 

 positions ahead have the relative multipliers 

 or weights of 5, 2, and 1, respectively, indicated 

 by the tabulation at the bottom of Fig. 67.V. 

 The rudder section is given a multiplier or weight 

 of 7 because it is usually closer than 0.5Z) to the 

 disc and the 4-Ap's in the outflow jet are greater 

 numerically than the — Ap's in the inflow jet for 

 a screw propeller producing thrust. These multi- 

 pliers are based upon the relative ordinate 

 magnitudes of the — Ap and -|-Ap curves at the 

 transverse sections selected. They are still 

 somewhat arbitrary, and could be varied for a 

 re-analysis. 



Expanding the disc circles by amounts cor- 

 responding to the enlargement of area of the 

 propeller inflow jet at the three selected forward 

 disc positions is considered not justified. The 

 same applies to contraction of the after disc 



circles. The jet area increases rather slowly 

 immediately ahead of the propeller, even for the 

 large thrust-load factors expected in the free- 

 running operation of a normal ship with a not-to- 

 large propeller, as indicated in diagram 1 of 

 Fig. 59. G. The values of — Ap are relatively so 

 small, farther forward of the propeller, that the 

 refinement of increasing the disc areas seems not 

 justified by the approximate nature of the overall 

 method. Moreover, the presence of the ship and 

 its appendages, either ahead of or abaft the 

 screw-propeller position, distorts the jets out of 

 their normal axisymmetric shape. Little is known 

 of what happens when they are so distorted, of 

 the amount of hull surface covered by the water 

 in them, and the differential pressures in that 

 water. 



The foregoing "cylinder" procedure assumes 

 that the rudder always develops a thrust-deduc- 

 tion force in the form of a drag, acting opposite 

 to the direction of motion, and that it always 

 contributes to the thrust deduction. However, in 

 the case of a contra-rudder, and some forms of 

 streamlined rudder, each lying in a propeller 

 outflow jet, it is known that the hydrofoil action 

 on the rudder produces a forward component of 

 lift which exceeds the drag. The rudder then 

 exerts a thrust force on the ship, and helps to 

 push it along. Theoretically, the net thrust force 

 Tr exerted by the helping rudder, mentioned in 

 Sec. 34.8 of Volume I, should be subtracted from 

 the thrust-deduction force exerted on the hull 

 or appendage ahead. This can only be done when 

 the amount of this thrust force is better known. 



In practice, the "cylinder" procedure involves 

 the following steps: 



I. On the afterbody lines plan of the ship lay off 

 special stations at O.SZ), l.OZ), and 2.0Z) forward 

 of the propeller-disc position. A fourth station is 

 laid off through the maximum-thickness position 

 of the rudder. Using the coordinates of these 

 special stations, draw the corresponding sections 

 on the body plan, as in Fig. 33. A of Part 2 in 

 Volume I or in Fig. 67. V of Part 4. If a rudder 

 horn is thicker than the rudder, or if any other 

 appendage lies anywhere in the propeller outflow 

 jet, draw a section (or sections) representing the 

 maximum transverse thickness of the horn or 

 appendage. 



II. Draw on the body plan, over the section lines 

 of the special stations, three circles, each repre- 

 senting the propeller-disc outline if moved sue- 



