The Calculation of Downwash Behind Wings of Arbitrary Plan Form at Supersonic Speeds

Abstract

Exact and approximate methods based upon linearized supersonic flow theory have been developed for the calculation of the velocity potential and the downwash from thin wings of arbitrary plan form. Particular attention is given to the evaluation of the downwash in the plane of the wing. The applicability of the method inherently depends upon a knowledge of the load distribution over the plan form of the wing. General expressions for the velocity potential and downwash have been derived. Simple modifications if these expressions produced formulas for the velocity potential and downwash from arbitrary curved lifting lines. A complete development of all formulas, starting with the basic solution of the linearized potential equation for supersonic flow, is given. Although the paper contains many new results, some of the results presented have been obtained by other methods and are given here solely for completeness. The general formulation of the downwash equations can easily be used in finding exact and approximate expressions for the other velocity components. The results of the theoretical development are used to determine the downwash from a pitching rectangular wing and to determine the expression for the local angle of attack necessary to give a specified load distribution. Comparisons of the exact and approximate values of the downwash for several lifting-line configurations are also presented.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1950
Accession Number
ADA380569

Entities

People

  • John C. Martin

Organizations

  • National Aeronautics and Space Administration

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Aeronautical Laboratories
  • Delta Wings
  • Differential Equations
  • Equations
  • Flow
  • Flow Fields
  • Free Stream
  • Leading Edges
  • Lifting Surfaces
  • Load Distribution
  • Mach Number
  • Partial Differential Equations
  • Pressure Distribution
  • Supersonic Flow
  • Thin Wings
  • Trailing Edges
  • Trailing Vortices

Readers

  • Aerodynamics.
  • Structural Dynamics.
  • Systems Analysis and Design

Technology Areas

  • Hypersonics