On the construction and calculation of optimal nonlifting critical airfoils

  • D. W. Schwendeman
  • M. C. A. Kropinski
  • J. D. Cole
Original Papers


Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM for a given thickness ratio δ and tail angle θ t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM and δ for various θ t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM →1, δ → 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding δ and θ t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.


Numerical Calculation Mach Number Mathematical Method Free Stream Thickness Ratio 
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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • D. W. Schwendeman
    • 1
  • M. C. A. Kropinski
    • 1
  • J. D. Cole
    • 1
  1. 1.Dept of Mathematical SciencesRensselaer Polytechnic Institute TroyNew YorkUSA

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