610 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.21 



when the design requirements are so unusual, or 

 the situation is so special, that there is no existing 

 design from which to work. New waters must be 

 traversed, so to speak, which are not only un- 

 familiar but for wliich there are few reliable 

 sailing directions. One such situation occurs when 

 cavitation is to be expected — and avoided. 

 Another occurs when wake surveys show an 

 unusual distribution of velocity at the propeller 

 position, or when it is desired to take full advan- 

 tage of a more-or-less normal wake variation. A 

 third might arise if it were desired to eliminate 

 all possibility of tip-vortex cavitation cores, 

 requiring the blades to be almost completely 

 unloaded at their tips. 



For problems of this kind, and for developments 

 of the future leading to appreciable improvements 

 in propeller performance, it is necessary to fall 

 back upon an analytic method. This in turn must 

 be based on the fundamental hydrodynamics of 

 the problem, in this case the theory of circulation 

 as applied to a screw propeller. There are to be 

 found in the literature at least six papers dealing 

 with this subject and making use of the successive 

 developments of the theory up to the time each 

 paper was prepared and published. These are: 



(1) Schoenherr, K. E., "Propeller Design by the Betz- 



Prandtl-Helmbold Circulation Theory," PNA, 1939, 

 Vol. II, Chap. Ill, Sec. 10, Art. 3, pp. 168-170 



(2) Van Lammeren, W. P. A., "Design of a Wake- Adapted 



Screw by Means of the Circulation Theory," 

 RPSS, 1948, Chap. II, Sees. 138-140, pp. 248-250 



(3) HiU, J. G., "The Design of Propellers," SNAME, 



1949, pp. 143-192 



(4) Van Manen, J. D., and Troost, L., "The Design of 



Ship Screws of Optimum Diameter for an Unequal 

 Velocity Field," SNAME, 1952, Vol. 60, pp. 442^68 



(5) Van Manen, J. D., and van Lammeren, W. P. A., 



"The Design of Wake-Adapted Screws and their 

 Bahaviour Behind the Ship," lESS, 1954-1955, 

 Vol. 98, pp. 463-482 



(6) Eckhardt, M. K., and Morgan, W. B., "A Propeller 



Design Method," SNAME, 1955, pp. 325-374. 



For the design of what is called a wake-adapted 

 propeller, the procedure is to employ the funda- 

 mental hydrodynamic concepts of circulation set 

 forth in Chap. 14. At the present stage of the art 

 it is necessary to call upon certain semi-analytic 

 and experimental sources for information which 

 will enable a propeller designer to start with his 

 requirements and end with a screw-propeller 

 design. To do this, the designer need have only 

 the knowledge that is set down in Volumes I 

 and II of this book. 



In most discussions of the design of wake- 



adapted propellers by the circulation theory, 

 there are gaps and omissions which make it 

 practically impossible for anyone except an expert 

 in the field to carry through a design by the 

 methods described. The sections to follow in this 

 chapter give a complete and continuous story 

 for a new method, recently (1954) developed by 

 Dr. H. W. E. Lerbs of the David Taylor Model 

 Basin staff. It is a short-cut method based on the 

 theory he described completely in his paper 

 "Moderately Loaded Propellers with a Finite 

 Number of Blades and an Arbitrary Distribution 

 of Circulation" [SNAME, 1952, pp. 73-123]. 



No attempt is made to give here a theoretical 

 explanation of the principles involved. There are 

 quoted only the formulas actually employed, 

 accompanied by a written and tabular explanation 

 of their use. 



Lerbs' short-cut method was chosen for several 

 reasons: 



(i) It has not been published before in this form 

 and thus offers a new approach to the problem 

 (ii) It produces the answer rather directly and 

 involves a minimum of reliance on intuition, 

 background, and previous propeller-design ex- 

 perience 



(iii) It gives promise of becoming an excellent 

 method of rational design for a wide variety of 

 screw propellers 



(iv) It is backed up by Lerbs' theoretical papers 

 and is based on sound hydrodynamic principles 

 (v) Design calculations using this short method 

 were checked by parallel calculations with Lerbs' 

 rigorous method, described in his referenced 

 paper. The results gave satisfactory agreement. 



Lerbs' theory for moderately loaded, wake- 

 adapted propellers is based on the assumption 

 that the induced-velocity components of the 

 second and higher degree can be neglected. In the 

 development of the short-cut method two addi- 

 tional assumptions are made; first, that the 

 induced velocity is always perpendicular to the 

 resultant relative velocity and second, that the 

 Goldstein function may be applied, relating the 

 behavior of a propeller with a finite number of 

 blades to that of one with an infinite number of 

 blades. 



The propeller design is carried out in this 

 chapter along the following lines. The terms 

 fisted are defined and described as the discussion 

 proceeds: 



