McCormick 

 The dimensionless velocity u^ is found from the static pressure distribution, 



^ , _ _i_ ^ (12) 



dx 2uj dx 



where Cp, the pressure coefficient is defined by 



P-P 



i^"c 



The numerical integration is started close to the nose by estimating s* on 

 the basis of the exact solution of viscous flow near a stagnation point. S is then 

 assumed to be equal approximately to 3 s*. Actually the ensuing integration 

 depends very little on the initial choice of S. Knowing s, Cp(x) and specifying 

 v^, one can now integrate Eq. (10) numerically along x with the aid of Eqs. (6), 

 (7) and (8). 



This integration has been carried out for the two Reynolds numbers of 

 2.3 X 10^ and 39x10^ and for Cp values from to .0003. The lower Reynolds 

 number is typical of the wind tunnel tests while 39X10^ represents the design 

 value. The results of these calculations are presented in Figs. 7 and 8. In each 

 case the suction was assumed distributed uniformly over the body starting 6 

 inches back from the nose. Also included on each figure are the stability limits 

 predicted from Figs. 5 and 6. 



These results are very interesting and in agreement with the experimental 

 observations. From Fig. 7 for zero suction, the transition point is predicted to 

 lie between 8 inches to 14 inches back from the nose. With a Cq of .0001, the 

 shape parameter H predicts transition 33 inches from the nose while K predicts 

 it at 9.5 inches. Finally for a C^ of .0002 both criteria predict laminar flow 

 over nearly the entire length of the body. Observe that the lines of critical Rg* 

 and actual R^* , a-s Cq increases, become nearly parallel. Hence as Cq is in- 

 creased slightly above some value close to .0002, the transition point shifts sud- 

 denly from the nose rearward. This predicted behavior was observed experi- 

 mentally. It should be noted also that the flow is stable at a Cq of .0002 not 

 simply because the suction is inhibiting the growth of the boundary layer but, 

 equally as important, because the suction is causing the profile to become more 

 stable. 



Now consider the predictions of Fig. 8 made at the design Reynolds number. 

 Both shape criteria predict transition before the first suction slot at 3 or 4 

 inches from the nose. Thus it appears that transition may be occurring before 

 the suction can take effect. In fact it appears as if the velocity would have to be 

 reduced to about 17 fps in water to move the transition point behind the first 

 suction slot. However, calculations, not presented here, have shown that a Cq 

 starting 3 inches back from the nose would be sufficient to prevent transition. 



1012 



