LIMITS TO HUMAN FLIGHT — WIMPEMS 583 



is again at its original value. This diagram shows in a simple way 

 that merely pushing up the height of flight without paying attention to 

 the way in which the engine is affected by that height would be 

 foolish. Merely pushing up the altitude will not give greater speed. 



Moreover, increase of altitude brings in other effects which we must 

 not ignore. One is that when flying near the ceiling, the angle of 

 incidence is increased, and with that increase comes a growth in the 

 relative proportion of induced drag to parasitic drag; this formerly 

 quite small fraction now becomes too large to be ignored and its 

 effect is to bring down the speed attained. Further, there has to 

 be considered the effect of change in Reynolds number with height of 

 flight. 



The Reynolds number is too well known to need description, but it 

 is less well known that change in that number as an airplane climbs 

 to a height has an important and adverse bearing on the drag coeffi- 

 cient. For a given wing, wing loading, and angle incidence, the 

 dynamic pressure (%pV 2 ) is the same at any altitude. But since 

 Reynolds number is proportional to both density and air speed 

 (ignoring for the moment any change in the viscosity of the air which 

 affects but does not change the conclusion), it follows that the Rey- 

 nolds number must fall as the air speed rises; hence the Reynolds 

 number at a high altitude of flight, despite the higher speed, will be 

 lower than at a less altitude. 4 Any lowering of the Reynolds number 

 means an increase in the drag coefficient for both laminar and turbu- 

 lent skin friction. Hence for flight at altitude one must allow a higher 

 drag coefficient than would correspond to sea-level conditions. This 

 is a factor adverse to attaining great speed at height. 



Apart from these particulars, the question of getting the highest 

 possible speed is one of providing an airplane which, while comfortably 

 containing pilot and engine, will have the minimum amount of 

 "wetted" area in proportion to engine power. Obviously, the body, 

 must be such as to house the pilot comfortably; this provides a certain 

 cubic capacity for the engine space in front of him, which in turn 

 governs the amount of power that can be derived from the engine. 

 Would one get any more speed by building a more spacious airplane? 

 Since a 10 percent increase in dimensions would put up the engine 

 power possibilities by 30 percent and the wetted area by only 20 

 percent, it is clear that one could, although with the disadvantage of 

 an increased landing speed. For any size of airplane, however, the 

 amount of power available related to the drag coefficient which cor- 

 responds to turbulent skin friction, gives a definite limit to the speed 

 attainable unless some method of getting still more engine power from 

 that given space, or of reducing (if we know how to) some part of the 

 drag to the lower level which corresponds to laminar flow. As Relf 



» Of. Von Karman on The problem of resistance in compressible fluids, Rome, 1936. 



