Aerodynamics of a rectangular wing of infinite aspect ratio at high angles of attack and supersonic speeds Page: 3 of 115
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NACA TN 3421
at angles of attack beyond the validity of the second-order theories
developed in references 4 to 6. At the present time, little published
information can be found on the aerodynamic derivatives at finite angles
of attack and supersonic speeds.
The only published papers associated with these aerodynamic deriva-
tives that have come to the authors' attention are the analyses of Ivey
(ref. 7), Carrier (refs. 8 and 9), and Chu (ref. 10). The analyses by
Carrier and Chu make use of the linear perturbation theory for rotational
flow (refs. 11 to 13) which allows first-order estimates to be made of
the flow variables behind a strong shock attached to the leading edge of
a two-dimensional wedge or within the region bounded by the lower surface
of an airfoil at finite angles of attack and the strong shock from the
leading edge of the airfoil.
The present paper contains a first-order evaluation of a number of
aerodynamic derivatives for a rectangular wing of infinite aspect ratio
at finite angles of attack, based upon the linear perturbation theory for
rotational flow. This analysis, including the development of the line-
arized rotational-flow equations, was performed independently of previous
analyses, an attempt being made to present a completely unified treatment
leading directly to the evaluation of aerodynamic stability derivatives.
Wherever possible, similarity of results from the present and previous
analyses are noted.
The results are valid for the ranges of Mach number and angle of
attack for which the flow behind the shock from the leading edge is
supersonic. A first-order evaluation of the following aerodynamic deriva-
tives is made: the lift-curve slope C I, the rate of change of pitching
moment with angle of attack C , the damping in roll C Zp, the lift due
to constant pitching CLq, and the moment produced by a constant rate of
Simple approximate relations for CL, Cm , C1p,, CLq, and Cm -
are derived. These approximate relations yield results which are in good
agreement with the exact first-order values, except at angles of attack
near the angle where the flow behind the shock is sonic. In addition,
approximate expressions are determined for CL& and Cm&, the lift and
pitching moment due to a constant vertical acceleration. It should be
noted that, although- the shock-expansion theory can be used to calculate
CL, and COm (see ref. 7) with relatively little effort, the use of
this theory to evaluate the remaining derivatives becomes difficult, if
not impossible. The methods used herein yield the first-order evaluation
of the aerodynamic derivatives for the airfoil considered with relatively
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Martin, John C. & Malvestuto, Frank S., Jr. Aerodynamics of a rectangular wing of infinite aspect ratio at high angles of attack and supersonic speeds, report, July 1955; (digital.library.unt.edu/ark:/67531/metadc57675/m1/3/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.