598 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.11 



that which gives the maximum propeller efficiency 

 Tjo under the trial or designed-load conditions 

 specified. 



While the design procedures described by 

 examples in this chapter give n as a part of the 

 solution, several practical requirements are to be 

 met before this value can be approved, as it were. 

 The first involves the ability of the selected or 

 probable type of propelling machinery to deliver 

 the required torque and power at the specified 

 rate of rotation. This situation is discussed at 

 some length by J. E. Burkhardt [ME, 1942, Vol. I, 

 pp. 28-33]. It is assumed here that no problems 

 are presented because of the type of engine and 

 of the reduction gear or transmission system 

 employed. 



K. E. Schoenherr illustrates a procedure 

 whereby the effect on propeller efficiency tjo of 

 varying n, P/D, and certain other variables is 

 readily determined [PNA, 1939, Vol. II, p. 172 

 and Tables 19, 20]. 



Finally, the vibration characteristics of the 

 ship, the engine, the shafting, and the machinery 

 foundations must be considered when selecting 

 the rate of rotation. However, this is primarily 

 a matter of the number of blades, and as such is 

 discussed in Sec. 70.12. 



70. 11 The Proper Pitch-Diameter Ratio ; Pitch 

 Variation with Radius. Assuming that the rate 

 of rotation for the designed maximum or other 

 specified power is fixed, or that it is to he within 

 certain limits, the pitch of the propeller is the 

 next factor which logically evolves, since for 

 zero real shp the effective pitch is the average 

 speed of advance divided by the rate of rotation. 

 However, for analysis and ship-design purposes 

 the pitch-diameter ratio is found to be a preferable 

 parameter. 



In Sec. 34.15 the effects on propeller efficiency 

 of too high and too low a P/D ratio are described 

 and illustrated. In practically all propeller-series 

 design charts it is possible to pick a P/D ratio 

 which gives the maximum propeller efficiency 

 rjo for a given set of working conditions. In Fig. 

 70.B, for example, it is noted that there is a 

 curve of optimum efficiency jjodua:;) for thrust-load 

 factor Ctl ■ A line normal to the inclined double 

 scale for Ctl and A cuts the heavy line for 

 lodnnx) at the best J-value. Interpolation between 

 the values of Kt for the various pitch-diameter 

 ratios, along the normal line mentioned, gives the 

 optimum P/D values. A point vertically above 

 this intersection, on the curves of efficiency tj for 



the selected P/D ratio (interpolated if necessary), 

 gives the working efficiency r; to be expected. 



When propulsion is by a piston-type internal- 

 combustion engine in which the mean effective 

 pressure in the cylinders is limited to a maximum 

 value, it becomes necessary, as pointed out in 

 Sec. 69.8, to match the rate of rotation and the 

 torque very carefully in order to achieve the 

 maximum or rated brake power. In other words, 

 if the full power of the engine is to be utilized, 

 deUvered at a certain rate of rotation and at 

 none other, the power absorbed by the propeller 

 connected to it has to be exactly the same, 

 neglecting transmission losses. It is most im- 

 portant, therefore, that after the engine is selected 

 both the pitch and the diameter of the propeller 

 be correct for the shaft power and rate of rotation 

 available. 



Experience through the past several decades 

 indicates that inaccurate predictions almost 

 always err on the side of designing a propeller 

 which absorbs too much power at the specified 

 rate of rotation. If slowed down to match the 

 power of the engine, the rate of rotation is usually 

 less than for maximum engine power. The common 

 remedy is to cut off the blade tips; this enables 

 the engine to run up to rated speed (and power) 

 but often spoils the shape of a useful part of the 

 propeller. 



There is a great deal of discussion in the litera- 

 ture on screw propellers concerning the wisdom 

 or the necessity of attempting to match the 

 pitch at each radius with the average wake 

 velocity at that radius. This matching is under- 

 taken on the basis that the blade element at each 

 radius should work at an effective angle of attack 

 that is efficient for that radius. Obviously, some 

 elements should not be underloaded while others 

 are overloaded, by any reasonable method of 

 reckoning. Furthermore, overloading the extreme 

 blade tips involves excessive tip-vortex losses. 



Three situations are to be considered here, in 

 which there may be: 



(I) An appreciable variation of wake velocity 

 (or wake fraction) with radius from the propeller 

 axis, combined with a reasonably uniform wake 

 velocity around the circumference at any radius. 

 This situation occurs abaft most bodies of revolu- 

 tion, like torpedoes, when the propeller axis 

 coincides with the body axis. 



(II) Some consistent variation of wake velocity 

 with radius from the propeller axis, but in which 



