On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow

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This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 ... continued below

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Watkins, Charles E; Runyan, Harry L & Woolston, Donald S January 1, 1955.

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This report is part of the collection entitled: National Advisory Committee for Aeronautics Collection and one other and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 87 times . More information about this report can be viewed below.

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  • Main Title: On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow
  • Series Title: NACA Technical Reports

Description

This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.

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  • : 93R21532
  • URL: http://hdl.handle.net/2060/19930092242 External Link
  • Report No.: NACA-TR-1234
  • Center for AeroSpace Information Number: 19930092242
  • Archival Resource Key: ark:/67531/metadc60623

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National Advisory Committee for Aeronautics Collection

The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915 to undertake, promote, and institutionalize aeronautical research. On October 1, 1958 the agency was dissolved, and its assets and personnel transferred to the newly created National Aeronautics and Space Administration (NASA).

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This selection of materials from the Technical Report Archive and Image Library (TRAIL) includes hard-to-find reports published by various government agencies. The technical publications contain reports, images, and technical descriptions of research performed for U.S. government agencies. Topics range from mining, desalination, and radiation to broader physics, biology, and chemistry studies. Some reports include maps, foldouts, blueprints, and other oversize materials.

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  • January 1, 1955

Added to The UNT Digital Library

  • Nov. 17, 2011, 5:13 p.m.

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  • Feb. 3, 2017, 4:14 p.m.

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Watkins, Charles E; Runyan, Harry L & Woolston, Donald S. On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow, report, January 1, 1955; (digital.library.unt.edu/ark:/67531/metadc60623/: accessed October 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.