Vertical-Axis Propeller Efficiency 47 
| o (Mf (0,242 | 
Fig. 3. The deformable profile A — B 
along the cycloid 
On this cycloid the turning point T corresponds to the parameter value f = m = wt. Al- 
though the segment A — B changes its radius of curvature we assume the distance s of some 
point of the profile to the point T, measured along the cycloid, to be constant. Trailing and 
leading edge are given by s = a and s=a+ 
The magnitude of the velocity V(Q) of the points of the profile is assumed to be equal 
to the velocity of the pivotal point 7. Using the relation @ = wt for the parameter of position 
of this point we find 
Veo)i= oR /f + 22 Sen cos © (2.2) 
The density of the bound vortices I'(~,s) is a function of the two variables 9 and s 
with 
