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An Application of Matrix Methods to Wing Theory


Fischer, Harold S. (1940) An Application of Matrix Methods to Wing Theory. Master's thesis, California Institute of Technology. doi:10.7907/E1VN-SQ19.


The calculation of spanwise lift distribution of a wing by a new method proposed by Theodore von Karman and W. R. Sears* depends on knowledge of certain "characteristic values" (eigenvalues) and "characteristic functions" (eigenfunctions) of the wing planform. These functions are solutions of a homogeneous boundary-value problem of the third kind.

In the present paper the eigenvalues and the eigenfunctions, in series form, are calculated for a class of planforms by the method of successive multiplication of matrices.

The class of planforms considered is that of trapezoidal wings with rounded tips. The eigenvalues and eigenfunctions are calculated for taper ratios 1:1, 2:1, 3:1, and 4:1; they are independent of aspect ratio. It is found, that for intermediate taper ratios they can be determined with reasonable accuracy by graphical interpolation.

* To be published shortly.

Item Type:Thesis (Master's thesis)
Subject Keywords:Aeronautics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • von Kármán, Theodore (advisor)
  • Sears, William Rees (advisor)
Thesis Committee:
  • von Kármán, Theodore (chair)
  • Stewart, Homer Joseph
  • Rannie, W. Duncan
  • Sears, William Rees
Defense Date:1 January 1940
Record Number:CaltechETD:etd-11142008-094640
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4559
Deposited By: Imported from ETD-db
Deposited On:21 Nov 2008
Last Modified:08 Feb 2022 00:28

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PDF (Fischer_h_1940.pdf) - Final Version
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