An Application of Matrix Methods to Wing Theory

Citation

Fischer, Harold S. (1940) An Application of Matrix Methods to Wing Theory. Master's thesis, California Institute of Technology. doi:10.7907/E1VN-SQ19. https://resolver.caltech.edu/CaltechETD:etd-11142008-094640

Abstract

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.

Thesis Files