Since the vortex/source sheet on the blade surface is represented by "discrete" 

 singularity elements, each discrete element represents a certain area. Therefore, 

 when computing the velocity jump across the vortex sheet, we have to redistribute 

 this concentrated vortex/source over the area. 



Consider a two-dimensional airfoil illustrated in Figure 5. The discrete 

 bound vortices/sources are located on the meanline at the quarter chord of each 

 meanline segment to approximate the continuous distribution of the vortex/source 

 along the meanline. Suppose F. is the strength of the bound vortex at the i 

 segment whose length is Ac. Then the distributed vortex strength, y., over this 

 segment can be approximated by: 



assuming the vorticity is uniformly distributed over the segment. The velocity 

 jump across the vortex sheet is related to the local vortex strength, Y-» ss 

 follows : 



Y . Y . 



(V^)^ = -^ and (V^)^ = - -T" ^^^ 



where the plus sign represents the upper surface and the minus sign the lower sur- 

 face. In this two-dimensional case, the velocity jump is tangent to the surface 

 in the chordwise direction. 



Similarly, the distributed source strength, q., over the same segment will be; 



Q, 



(4) 



Ac, 



where Q. is the strength of the discrete source element. The source sheet induces 

 a jump in normal velocity, that is related to the local source strength, q., as 

 follows: 



+ ''i - '^i 



(V )^ = ^ and (V ). = - -^ (5) 



n 1 2 n 1 2 



