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National Advisory Committee for Aeronautics, Technical Notes - Numerical Determination of Indicial Lift of a Two Dimensional Sinking Airfoil at Subsonic Mach Numbers from Oscillatory Lift Coefficients with Calculations for Mach Number 0.7

The reciprocal equations for relating the incompressible circula-
tory indicial lift to the lift due to harmonic oscillations have been
modified to include the noncirculatory lift associated with apparent—
mass effects. Although the apparent-mass effects are impulsive in
nature in incompressible flow, the lift due to apparent-mass effects in
compressible flow is a time-dependent function. The corresponding
reciprocal equations for the total compressible lift are given. By use
of the reciprocal equations for compressible flow; the indicial lift and
moment functions due to an airfoil's experiencing a sudden acquisition
of vertical velocity are determined numerically for Mach number 0.7.
Lack of sufficient flutter coefficients prevents the calculation of
these functions at other Mach numbers.

Although the indicial lift and moment fUnctions due to penetration
of a sharp-edge gust may be obtained from the oscillatory tab or aileron
coefficients by a similar analysis, sufficient coefficients are not
available at the present. However, an approximate method is shown for
determining a portion of this unsteady-lift function.

When a comparison is made of the indicial lift functions at Mach
numbers 0.0 and 0.7, it is noted that the growth of lift to the steady
state appears to be less rapid for the compressible case than for the
incompressible case. Consequently, the calculation of the gust load
factor at high subsonic Mach numbers utilizing the two-dimensional
incompressible indicial lift functions and an over—all correction for
compressibility such as the Prandtl-Glauert factor might be conservative;

A knowledge of transient flows is important in many aeronautical
problems. In the study of transient flows, two types of airfoil motions
have had special significance — a harmonically oscillating airfoil and
an airfoil experiencing a sudden change in angle of attack. The lift
function for an airfoil experiencing a sudden change in angle of attack
and the lift function associated with the growth of lift on an airfoil
due to penetration of a sharp—edge gust are commonly referred to as 4
indicial lift functions. The present paper is concerned with the use
of reciprocal relations for determining for compressible flow the
indicial lift functions directly from the lift data that are available
for the airfoil oscillating harmonically.

The indicial lift functions‘have been derived for two-dimensional
incompressible flow; the function for a sudden change in angle of
attack was derived by Wagner, see reference 1, while the penetration
function was derived by Kfissner, reference 2. An account of the rela-
tions that exist between these indicial lift functions and the lift
coefficients for a two-dimensional oscillating airfoil is given by
Garrick in reference 3.