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National Advisory Committee for Aeronautics, Report - Theoretical Study of the Transonic Lift of a Double Wedge Profile with Detached Bow Wave

A theoretical study is described of the aerodynamic character-
istics at small angle of attach: of a thin, doubleuedge profile in
the range of supersonic flight speed in which the bow wave is
detached. The analysis is carried out within the framework of
the transonic (nonlinear) small-disturbance theory, and the
efiects of angle of attack are regarded as a small perturbation on
the flow previously calculated at zero angle. _ The mired flow
about the front half of the profile is calculated by relaxation
solution of a suitably defined boundary—value problem for the
transonic small—disturbance equation in the hodograph plane
(i. e., the Tricomi equation). The purely supersonic flow about
the rear halfisfound by an extension of the usual numerical
method of characteristics. Analytical results are also obtained,
within the framework of the same theory, for the range of speed
in which the bow wave is attached and the flow is completely
supersonic.

The calculations provide, for vanishingly small angle of
attack, the following information as a function of the transonic
similarity parameter: (1) chordwise lift distribution, (2) lift-
curve slope, and (3) position of center of lift. As in previous
studies, the aerodynamic characteristics of a profile of given
thickness ratio show little variation with free-stream Mach num—
ber as the Mach number passes through 1. As the Mach
number is increased to higher values, however, the lift—curve
slope rises to a pronounced maaimum in the vicinity of shock
attachment and then declines. Correspondingly, the center of
lift moves forward toward the leading edge and then returns aft.

These findings are in marked contrast to the behavior of the drag'
coefl'icient at zero angle of attack, which was found in earlier
work to decrease monotonically as the Mach number increased
above 1. At Mach numbers above that for shock attachment, the
results of the present calculations tend toward those given by
classical linear theory.