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National Advisory Committee for Aeronautics, Report - Theory of Wing Sections of Arbitrary Shape

This paper presents a solution of the problem of the
theoretical flow of a frictionless incompressible fluid
past airfoils of arbitrary forms. The velocity of the 2~
dimensional flow is explicitly expressed for any point
at the surface, and for any orientation, by an exact
expression containing a number of parameters which are
functions of the form only and which may be evaluated by
convenient graphical methods. The method is particu-
larly simple and convenient for bodies of streamline
forms. The results have been applied to typical airfoils
and compared with experimental data.
The theory of airfoils is of vital importance in aero-
nautics. It is true that the limit of perfection as
regards efficiency has almost been reached. This
attainment is a result of persistent and extensive
testing by a large number of institutions rather than
of the fact that the important design factors are known.
Without the knowledge of the theory of the air flow
around airfoils it is well-nigh impossible to judge or
interpret the results of experimental work intelligently
or to make other than random improvements at the
expense of much useless testing.
A science can develop on a purely experimental basis
only for a certain time. Theory is a process of sys-
tematic arrangement and simplification of known facts.
As long as the facts are few and obvious no theory is
necessary, but when they become many and less simple
theory is needed. Although the experimenting itself
may require little effort, it is, however, often exceed-
ingly difiicult to analyze the results of even simple
experiments. There exists, therefore, always a ten-
dency to produce more test results than can be digested
by theory or applied by industry. Alarge number of
investigations are carried on with little regard for the
theory and much testing of airfoils is done with insuffi-
cient knowledge of the ultimate possibilities. This
state of affairs is due largely to the very common belief
that the theory of the actual airfoil necessarily would
be approximate, clumsy, and awkward, and therefore
useless for nearly all purposes.