602 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.15 



of the known and unknown scale effects, it is not 

 yet safe to make full-scale predictions from a 

 model experiment. Swirl cores and hub vortexes 

 have been and can be observed on ships through 

 special glass viewing ports installed in proper 

 locations in the shell. 



70. 1 5 Determination of Expanded-Area Ratio ; 

 Choice of Blade Profile. For design purposes in 

 this book the blade area of a propeller corresponds 

 to the expanded area of all the blades. This is 

 usually expressed as the ratio of the expanded 

 area Asto the disc area .4o . As a means of arriving 

 at the blade outUne or profile, use is made of the 

 mean-width ratio, represented by the ratio of 

 the average expanded chord length c^f of one 

 blade to the propeller diameter D. The high and 

 low limits for these ratios, in recent and current 

 propeller design, are given by K. E. Schoenherr 

 and W. P. A. van Lammeren [PNA, 1939, Vol. 

 II, p. 157; RPSS, 1948, p. 227]: 



the area ratio of the parent model (s) may be 

 expected to give the performance indicated by 

 the chart. Variations from the parent values 

 have in the past usually been left to the experience 

 and judgment of the designer, with little to rely 

 upon if he does not have that kind of experience. 



Only recently there have appeared a new 

 series of graphs and a procedure based upon 

 cavitation characteristics of the models of certain 

 propeller series, devised by J. D. van Manen, 

 whereby values of the proper developed-area 

 ratio may be determined [Inter. Shipbldg. Progr., 

 1954, Vol. 1, No. 1, pp. 39-47]. Data derived by 

 this method are presented at the end of Sec. 70.6. 



In the example of the Lerbs' method of design- 

 ing a wake-adapted propeller by the circulation 

 theory, described in Sees. 70.21 through 70.38, 

 in which cavitation is definitely to be avoided, 

 the chord widths of the sections at the outer 

 radii are selected to give —Ap values which will 



The total expanded area of the Z blades of a 

 propeller must be: 



(1) Large enough, when combined with the 

 differential pressures -j-Ap and —Ap, to develop 

 the lift and thrust forces required 



(2) Small enough to avoid excessive blade 

 surface and resulting large friction drag [van 

 Lammeren, W. P. A., RPSS, 1948, pp. 226-227] 



(3) Large enough to develop the required thrust 

 at high blade velocities (and possibly also low 

 hydrostatic pressures) without objectionable cavi- 

 tation 



(4) Large enough to satisfy the requirements for 

 retardation in the case of emergency stops or 

 sudden reversals 



(5) Large enough so that the blade elements at 

 the several radii have sufficient section modulus 

 to give the blades the necessary strength and 

 rigidity. 



Unfortunately, propeller-series charts do not 

 give direct answers as to the proper expanded- 

 area (or developed-area) or mean-width ratios. 

 They indicate only that a new propeller with 



not drop the pressure on the back below the 

 vapor pressure of water. The chord lengths of the 

 sections at the root are fixed by a combination of 

 the amount of metal required and a thickness 

 ratio tx/c that is not too large. With chord lengths 

 fixed for the inner and outer radii, and a fair 

 profile drawn around them, the expanded area 

 is more or less fixed, and with it the ratios Ae/Ao 

 and tx/c. 



Despite the large variety of blade-profile types 

 illustrated in Fig. 32. L there are few estabUshed 

 design rules for the choice of the best or most 

 appropriate profile for any given case. The 

 profile is narrow or wide, depending upon the 

 expanded area required. It is skewed if it is 

 desired to spread the pressure field developed by 

 one blade over a sizable sector of the disc circle. 

 The expanded profile has a certain minimum 

 width if the propeller is to be free of cavitation. 

 Within the limits of normal shape, any profile 

 may be selected, without a detrimental effect 

 upon performance, which meets any other 

 requirements for the propeller design in hand. 



Comments in the literature on blade outline are 

 to be found in: 



