Drag Reduction by Suction 

 M= 1.0 + -^ (2.26 K' - 1.26) (2) 



Q 



where 



BL 



K' = 1.0 for ^^ < -045 



K' = 1.0 + 1.48f-^ - .045'^ for ^ > .045 



gj = local velocity head outside boundary layer. 



According to the reference for laminar stability, the Reynolds number based 

 on Uj, the local velocity outside the boundary layer, and the boundary layer 

 thickness should not exceed approximately 3400. In this case, the boundary 

 layer thickness was defined as the value of 5 for which u/u^ = 0.707. 



A velocity profile through the boundary layer of the form 



-2X1-7) 



u, 



was assumed. In lieu of calculating the actual boundary layer profile, this 

 seemed to be a reasonable choice since when based on the displacement thick- 

 ness, this profile lies between that of Blasius and the asymptotic suction profile. 



These results were then substituted into the Karman momentum integral 

 equation and the boundary layer thickness obtaining by numerically integrating 

 along the length of the body for different values of AQ/Q^j^. 



At each increment in length, x, along the body the value of the boundary 

 layer Reynolds number was compared to the critical value quoted by Ref . 1. 



K Rg equalled, or possibly slightly exceeded 3400, the value of x was 

 printed out and Q through the slot at the X location calculated from 



Q=2,.„(^)q3,. (3) 



s immediately after the slot was calculated from Eq. (1) and the numerical in- 

 tegration continued to the next slot location where Rg once again reached a 

 value of 3400. In this manner the slots were located along the body and the total 

 suction flow requirement determined as the sum of all the Q' s obtained from 

 Eq. (3). 



After a series of trial designs, a value of ^Q/Q^^ of 0.17 was selected. This 

 resulted in slots 0.007 inches thick spaced every 2 inches starting 6 inches back 

 from the nose. These continue back to within 7 inches from the tail at which 

 point the axial flow pump is installed. On the recommendation of Ref. 1, the slot 

 thickness was chosen equal to the boundary layer thickness. The required suction 



1003 



