— (9) 



/G 



The curvilinear distance is measured along the helix on the reference surface 

 from the 9=0 plane to the leading and the trailing edges, denoted by S and S , 

 respectively. The chord length of the propeller blade at any radius is 



c(r) = S t (r) - S £ (r) (10) 



VELOCITIES DUE TO SINGULARITIES 

 Both a source distribution with strength m(r,9) per unit area and a vortex 



distribution with strength G(r,9) per unit area are distributed on each blade- 

 reference surface. Then, the 

 derived from potential theory 



reference surface. Then, the velocity u caused by the source distribution is 



u m (x,r,9) = - -L Jm(p,<J)) V x (|) H dpd* (11) 



— G 

 The velocity u caused by the vortex distribution is derived from the Biot- 



Savart law 



u G (x,r,9)=MG( P> «^B (12) 



where 



!(x-0 2 +r 2 +p 2 -2rp cos(<J>+6,-6) 



- - 2k(k-l) 

 *k Z 



1/2 



(13) 



(14) 



