17 



The measured transition points should be behind the neutral stability points and 

 forward of the self-excited transition points owing to the small amount of natural turbulence 

 in the wind tunnel. Examination of Table 1 confirms this. The reason for the large difference 

 between the measured transition point and the self-excited transition point on Model B is due 

 to the favorable pressure gradient, 0.40 < l/L < 0.61, which tends to delay the development 

 of self-excited transition. 



In order to obtain the neutral stability and transition points, it is more convenient to 

 use nondimensional relations. From [36] there results 



It also follows that 



1 \UnoJ .„= « 



[51] 



V dx \Rr I 



(t) <r) 



[52] 



Thus, from [47] 



e'^ dU = i, _ J.. 



dx 



45 





(t) 



"Mt) 



i 



I" m^ - <£ 



[53] 



The neutral stability point or self-excited transition point is determined graphically by the 

 intersection of a curve representing the appropriate parameters of the given boundary layer 

 with the curves of Figure 3 or 4, as the case may be. 



The position of transition on a body in a wind tunnel or other flow facility depends, 

 to a great extent, upon the scale and intensity of the turbulence in the free stream. To 

 simplify the analysis the representative measure of turbulence in the stream will be taken as 

 the ratio of the root mean square of the velocity fluctuations in the a;-direction to the mean 

 velocity of the free stream or yu"^/ U . Data for flat plates without pressure gradient from 



tests in wind tunnels ^^'^^'^^ are plotted in Figure 5, the ordinates being the difference in 

 the boundary-layer Reynolds numbers for transition and that for neutral stability Ra ^^ - Ra ^, 

 and the abscissae being the percentage of turbulence \u^/V^ in the free stream. It is to 

 be noted that for flat plates the neutral stability point seems to be the limiting position of 

 transition for streams of increasing turbulence while the self-excited transition point is the 

 limiting position of transition for streams of decreasing turbulence. 



