352 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 59.11 



10,000 



8,000 



^ 6,000 



n 



8. 

 S4,000 



2,000 



480 



460 



420 



20 40 60 80 



Blade- Position Anale, deo 



Fig. 59.R Variation op Torque and Vertical and 



Horizontal Forces on a Victory Ship Propeller, 



A = 11,606 Tons 



The effect of the simphfying assumptions on the 

 calculations for these graphs creates some doubt 

 as to the validity of the results, especially because 

 of the first assumption of steady-state conditions. 

 Currently (1956), Tachmindji is refining the 

 method so that these assumptions will not have 

 to be made. Nevertheless, because of the im- 

 portance of this work in the design scheme, the 

 unrefined method used by Tachmindji for the 

 Lt. James E. Robinson calculation is outlined here. 



To determine the thrust and torque charac- 

 teristics for any blade section at a specific blade 

 angle, there are several methods that can be 

 employed. That of L. C. Burrill ["Calculation of 

 Marine Propeller Performance Characteristics," 

 NECI, 1943-1944, Vol. 60, pp. 269-294] is well 

 adapted to this operation and was utilized by 

 Tachmindji. It employs the circulation theory 

 with suitable correction factors to relate experi- 

 mental results with theory. 



The steps involved in the Burrill method are as 

 follows: 



(1) The angle ao (alpha) between the zero-hft line 

 and the base-chord line is determined by the 

 method of H. Glauert ["A Theory of Thin 

 Airfoils," ARC, R and M 910, 1924-1925]. The 

 angle ao is equal to a — a/ and is usually negative 

 for common hydrofoil sections, where the zero- 

 lift line lies toward the back of the section from 

 the base chord, as in Fig. 15. H. 



(2) The advance angle p is calculated by using 

 both the longitudinal wake fraction Wl and the 

 tangential wake component Wt . The reasons for 

 omitting the radial wake component are explained 

 in a previous paragraph. Hence 



tan (3 = 



2TvRn — Vwj 



(3) Burrill's formulas and graphs enable the 

 h3^drodynamic angle of attack ai to be determined 

 as a function of jS, Pi , and the geometry of the 

 blade section. But since /3i can not be determined 

 unless a J is known or assumed, the calculation is 

 one of successive approximations. Specifically, an 

 effective angle of attack is assumed. Then, since 

 iS, + ttf = — tto (where, as indicated in (1) 

 above, the zero-lift angle of attack a„ is usually 

 negative), /3/ is known temporarily, and the calcu- 

 lation is carried out to determine uj . The correct 

 values of fit and a/ are obtained when the assumed 

 ar equals the calculated aj . 



(4) The lift and drag of the blade section is then 

 determined as a function of aj , the relative 

 velocity, the correction factors, and the geometry 

 of the section. 



(5) Knowing the lift and drag, the thrust and 

 torque contributed by the blade section are then 

 determined. 



One calculation gives the thrust and torque of 

 one blade radius at only one blade angle. In 

 order to obtain the total thrust and torque it is 

 necessary to calculate the thrust and torque at 

 enough blade angles and blade sections so that 

 they can be integrated to determine the total 

 thrust and torque from one blade at any angle. 

 The position angle d of any one blade is assumed 

 to be measured from the upward vertical or 12 

 o'clock point, in a clockwise direction when 

 looking forward. Also 



T{x' , 6) is the thrust from the blade element at the 

 0-diml radius x' and the position angle d 



Q{x' , 6) is the torque from the blade element at 

 the 0-diml radius x' and the angle d 



Tz{6) is the thrust per blade at the angle d 



