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National Advisory Committee for Aeronautics, Technical Notes - Tables of Wing Aileron Coefficients of Oscillating Air Forces for Two Dimensional Supersonic Flow

Wing-aileron coefficients of oscillating air forces for two-
dimensional supersonic flow are tabulated for Mach numbers of 10/9,
S/h, 10/7, 5/3, 2, and 5/2. Various ratios of control-surface chord
to airfoil chord are employed in the calculations, namely, 0.1, 0.2,
0.3, 0.1;, 0.5, 0.6, 0.7, 0.8, and 0.9 and for each combination of
chord ratio and Mach number approximately 35 values of reduced frequency
are utilized. For completeness,-the exact and some approximate expres-
sions for the tabulated quantities are given. The approximate expres-
sions are useful for extending the tables to lower values of the fre-
quency and also for interpolation between Mach numbers. The tables
presented can be used directly in oscillating—air-force or flutter
calculations.

In recent years various authors have worked on the theory of
nonstationary flow past airfoils at supersonic speeds (see, for example,
reference 1). This theoretical work, in particular for harmonically
oscillating airfoils, is of special interest in discussions of flutter
at supersonic speeds. In reference 1 various applications to flutter
of wings and control surfaces have been considered, and in particular
a detailed treatment and discussion of numerical results have been
given for the special subcase of wing bending-torsion flutter. various
numerical tables of interest for application to this case of wing
flutter are presented in reference 1 but no numerical tabulations or
results are given for flutter involving control surfaces. Some graphical
values for oscillating aileron coefficients have appeared but these are
of a qualitative interest and do not take the place of, or fulfill the
need for, tables.

The present paper is devoted to the listing of tables that can
be used in calculations of flutter and in the determination of oscil—
lating air forces of wing-aileron combinations in two—dimensional
supersonic flow. various Mach numbers and ratios of control—surface
chord to airfoil chord have been employed in the calculations. Six of
the Mach numbers that were employed in the tables of reference 1 have
been used, namely, 10/9, 5/h, 10/7, 5/3, 2, and 5/2, and the range of
chord ratio is 0.1 to 0.9 in increments of 0.1. For each combination
of Mach number and chordiratio approximately 35 values of reduced
frequency were employed. The tables have been prepared principally
by the use of a general-purpose automatic-sequence relay-type computing
machine of the Bell Computing Section at the Langley Laboratory and
checked by manual computations.