Milgram 



relatively little experimental data, whereas Moses presents a considerable 

 amount for a variety of pressure distributions which is in excellent agreement 

 with his semi-empirical theory. 



The Design of a Chordwise Pressure Distribution for High Lift 



The dominating effect on boundary layer growth in an adverse pressure 

 gradient is the work done against the force of the adverse gradient by the fluid 

 in the boxindary layer. To minimize this work, the maximum pressure on the 

 suction side of the airfoil should be made as small as possible. The lift coeffi- 

 cient is given by 



PUo 



J^/aP(x) 



(40) 



where the suction side pressure is AP/2 for a very thin airfoil. Clearly, the 

 way to minimize the strength of the peak suction while retaining a given lift 

 coefficient is to make AP(x) constant. However, just ahead of and just behind 

 the airfoil the pressure must be equal to free stream pressure, but streamwise 

 pressure jumps are not realizable. Furthermore, it has been found that if the 

 approach of the pressure to free stream pressure at the trailing edge is faster 

 than linear, separation is likely. Most experiments indicate that the value of 

 H for turbulent flow just following transition is 1.4 (see, e.g.. Von Doenhoff and 

 Tetervin, 1943). In an adverse pressure gradient, H rises with increasing 

 downstream position. Since separation is avoided by keeping h small and since 

 transition from laminar to turbulent flow occurs just aft of the point of maximum 

 suction, it seems desirable to have the point of maximum pressure difference 

 relatively far aft. Putting the above facts together indicates that a pressure 

 distribution giving relatively high lift without separation might have the form 

 shown in Fig. 5. The results of the boundary layer calculation, by the theory of 

 Moses (1964) with a lift coefficient of 1.9, on this pressure distribution are 

 shown in Fig. 6. The maximum attainable lift coefficient without flow separa- 

 tion is about 1.9. The section shape needed to attain this pressure distribution 

 in two-dimensional flow with a lift coefficient of 1.9 has been calculated by use 

 of the thin airfoil theory and is shown in Fig. 7. 



Fig. 5 - Pressure distribution for a 

 high-lift section 



1418 



