boundary layers are assumed to be thin, so that the flow can be treated as inviscid, 



except for the calculation of frictional drag. 



The nonrotating coordinate system, (x ,y ,z ), and rotating coordinate system, 

 a J 'ooo 



(x,y,z), fixed to the blades are shown in Figure 1. The x-axis of the fixed and 



rotating system are coincident, as are the (y,z) and (y ,z ) planes. The defini- 

 d J J ■> -^oo 



tion of the angular coordinates in the fixed system, 6 , and in the rotating sys- 

 tem, 9, are also defined in Figure 1. The propeller rotates at a constant angular 

 velocity, ^ = -fii^. A field point, P, in the fluid with angular coordinate, 9, in 

 the rotating frame has an angular coordinate 



6 = 9 - fit (1) 



o 



in the fixed frame for a right-handed propeller shown in Figure 1. 



The blade geometry is defined relative to a midchord line, which is para- 



metrically defined by the radial distribution of skew, 9 (r), and total rake, 



s 



i (r). The pitch angle, (j)(r), and chord length, c(r), define the angle and extent 



of the sectional nose-tail line along the pitch helix on the surface of a cylinder 



of radius r. The meanllne offset, f(r,x ), and thickness distribution, t(r,x ), 



' ' c c 



describe the section characteristics of the blade as a function of radius, r, and 

 nondimensional arc length, x , along the nose-tall line. The meanline, f, is 

 measured along the cylindrical surface at right angles to the nose-tall line. The 

 thickness, t, is measured perpendicular to the meanline.* 



The blades and vortex wake are represented by straight-line vortex and source 

 lattice elements of constant strength, distributed over the meanline surface of the 

 blade (see Figure 2) and the assumed surface of the trailing vortex sheet. The 

 vortices are arranged in the traditional horseshoe configuration (see Figure 3) so 

 as to satisfy Kelvin's conditions automatically, and the strength of each horseshoe 

 vortex is determined by solving a set of simultaneous equations, each satisfying 

 the flow tangency condition at a blade control point. Source strength is deter- 

 mined from the slope of the thickness distribution and resultant onset speed. 



* At DTNSRDC, the thickness is conventionally measured perpendicular to the 

 nose-tail line. In linear theory the differences of these two specifications is 

 of higher order. 



