<DOC>
<DOCNO>
1342
</DOCNO>
<TITLE>
the calculation of aerodynamic loading on surfaces of any shape .
</TITLE>
<AUTHOR>
falkner, v.m.
</AUTHOR>
<BIBLIO>
r + m 1910, august 1943 .
</BIBLIO>
<TEXT>
the object of the report is to establish a routine method for the calculation
of aerodynamic loads on wings of arbitrary shape . the method
developed is based on potential theory and uses a general mathematical
formula for continuous loading on a wing which is equivalent to a double
 fourier series with unknown coefficients . in order to evaluate the
unknown coefficients the continuous loading is split up into a regular
pattern of horseshoe vortices, the strengths of which are proportional
to the unknown coefficients and to standard factors which are given in a
 table . the total downwash at chosen pivotal points is obtained by
summing the downwashes due to the individual vortices, a process which
is simplified by the use of specially prepared tables of the properties
of the horseshoe vortex . by equating the downwash to the slope of the
wing at each pivotal point, simultaneous equations are obtained, the
solution of which defines the unknown coefficients .
the first layout involves a total of 76 vortices over the wing, and a
second layout, involving a total of 84, is shown to be of superior
accuracy . the effect on the solution of the number of pivotal points is
 investigated and it is concluded that by a suitable choice, it is unnecessary
to use a large number . results for a rectangular wing at
with those obtained by other workers and it appears that there may be
errors in published results in at least one of these cases . immediate
development includes the application to the calculation of the characteristics
of actual sweptback wings, including rotary derivatives, and
 future development includes also applications in wind tunnel design and
 technique .
</TEXT>
</DOC>
