<DOC>
<DOCNO>
704
</DOCNO>
<TITLE>
a systematic kernel function procedure for determining aerodynamic
forces on oscillating or steady finite wings at subsonic speeds .
</TITLE>
<AUTHOR>
watkins, c.e., woolston, d.s. and cunningham, h.j.a.
</AUTHOR>
<BIBLIO>
nasa tr r-48, 1959 .
</BIBLIO>
<TEXT>
a detailed description is given of a method of approximating solutions
to the integral equation that relates oscillatory or steady lift and
downwash distributions on finite wings in subsonic flow . the method of
solution is applicable to general plan forms with either curved or
straight leading and trailing edges . moreover, it is directly applicable
to control surfaces such as all-movable tails but modifications
are needed to apply it to controls in general . applications of the
method involve evaluations of numerous integrals that must be handled by
 numerical procedures but systematic schemes of evaluations have been
adopted that are well suited to the routines of automatic digital computing
machines . these schemes of evaluation have been incorporated in
a program for an ibm 704 electronic data processing machine . with this
machine, a pressure distribution together with such quantities as section
or total lift and moment coefficients or generalized forces can be
determined for a given value of frequency and mach number and for
several /four or five/ modes of oscillation in about 4 minutes of
machine time . in the case of steady downwash conditions corresponding
quantities can be obtained in about 2 minutes of machine time .
in order to illustrate applications of the method, results of several
calculations are presented . in these illustrations total forces and
moments are compared /1/ with results of analytic procedures for a circular
plan form with steady downwash conditions, /2/ with results of
other theories and with experiment for a rectangular plan form of aspect
 ratio 1 at a uniform angle of attack, and /3/ with some experimental
results for a rectangular plan form of aspect ratio 2 undergoing pitching
and flapping oscillations . also included in the illustrations are
results of flutter calculations compared with experimental results for
an allmovable control surface of aspect ratio 3.50 and for a cantilevered
rectangular plan form of aspect ratio 5.04 .
</TEXT>
</DOC>
