Applications of Von Karman's Integral Method in Supersonic Wing Theory

Abstract

The present paper derives Van Karman's Fourier integral method in supersonic wing theory directly from the basic concepts of the harmonic source and doublet. The method is first applied to investigate the general solution of the wave drag of a tapered swept wing with a symmetrical diamond airfoil profile. The general solution includes all kinds of wing plan forms which may be swept backward or forward, and tapered or reversely tapered to any ratio. A number of the limiting cases are also investigated. For practical aerodynamic design, two families of wing plan forms with the fixed taper ratios 0.2 and O.5, any swept angle, aspect ratio, and Mach number are shown in graphs. Some particular applications are illustrated. The reversed-flow theorem on wave drag as shown by Van Karman and Hayes checks well with the consequence of the general solution. This method shows a certain elegance as no conical-flow assumption is needed and the mathematics is powerful enough to obtain a general solution covering all possible geometrical arrangements without detailed considerations.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1951
Accession Number
ADA382388

Entities

People

  • Chieh-chien Chang

Organizations

  • Johns Hopkins University

Tags

DTIC Thesaurus Topics

  • Aircrafts
  • Bessel Functions
  • Delta Wings
  • Differential Equations
  • Equations
  • Free Stream
  • Integral Equations
  • Integrals
  • Inverse Problems
  • Leading Edges
  • Mach Number
  • Pressure Distribution
  • Supersonic Flow
  • Swept Wings
  • Sweptback Wings
  • Trailing Edges
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Aerodynamics/Aeronautics.
  • Calculus or Mathematical Analysis

Technology Areas

  • Hypersonics