405 



09 

 10 Kq 



08 

 ^0 



O 01 02 03 04 05 06 07 08 09 10 



J 

 PROPELLER A 



PROPELLER B 



MEASURED 

 Re^ . 2 9 X 10° 

 CALCULATED L, SURF 

 CALCULATED L LINE 



09 

 10 Kq 

 08 



01 02 03 04 05 06 07 08 09 10 

 PROPELLER D 



FIGURE 7. Propeller open-water characteristics. 



So Eq. 6 has to be corrected to obtain a three- 

 dimensional lift curve. At one point of the lift 

 curve, at the ideal angle of attack, results of 

 systematic lifting surface calculations are avail- 

 able [Morgan et al. (1968)] and they can be expressed 

 as correction factors on cairiber, K^, and the angle 

 of attack, Kqi. Van Oossanen (1974) used these 

 correction factors to define the three-dimensional 

 lift curve over the whole range of angles of attack 

 instead of at the ideal angle of attack only. He 

 wrote 



/dC^ 

 Vda 



3d 



dC^ 

 da 



and 



= (K -l)a. 



3d 



(8) 



(9) 



where a-;^ is the ideal angle of attack of the 

 propeller section. Substitution of these three- 

 dimensional values in Eq. 6 makes it possible to 

 solve the set of Eqs. 5-7, resulting in a radial 

 distribution of Bj^, a.^, and Cl. 



In Figure 7 the calculated open-water character- 

 istics using this approach are compared with experi- 

 ments. The agreement between measurements and 

 calculations is acceptable. Propeller B could not 

 be calculated since the regression formula's for 

 K^ and K^^ in the program were restricted to a 

 maximum pitch ratio of 1.4. 



Viscosity is taken into account by assuming a 

 viscous lift slope 



(^)/2^ 



0.947-0.76 



