These results are equivalent to the induced velocities of the propeller 

 (Equation (26) in text) provided that 



da(r) ^ Q 



dr - ^ < ^ 



da(r) _ Z_ dr_(r) 1_ 



dr 2Tr dr r tan g . 



(r) hi<'<^ 



It follows that 



a(r) = 



Z /'^ dr(r') dr' 



/. 



2-n J dr' r' tan 3. (r') 



where the constant of integration is set so that a(R) = 0. For typical 

 propeller loading distributions, a(r) is negative over most of the disk, 

 corresponding to a sink distribution. 



76 



