### naca-report-846

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National Advisory Committee for Aeronautics, Report - Flutter and Oscillating Air Force Calculations for an Airfoil in a Two Dimensional Supersonic Flow

A connected account is given of the Possio theory of non-

stationary flow for small disturbances in a two-dimensional

supersonic flow and of its application to the determination of the

aerodynamic forces on an oscillating airfoil. Further applica—

tion is made to the problem of wing flutter in the degrees offree-

dam—torsion, bending, and aileron rotation. Numerical tables

for flutter calculations are provided for carious values of the

lunch number greater than unity. Results for bending-torsion

wingjlutter are shown in figures and are discussed. The static

instabilities of dirergence and aileron reversal are examined

as is a one-degree-of-freedom case of torsional oscillatory

instability.

The problem of flutter or aerodynamic instability for

high-speed aircraft is of considerable importance and hence

interest is directed to the aerodynamic problem of the oscil-

lating airfoil moving forward at high speed. Although for

conventional aircraft the subsonic and the near-sonic or

transonic speed ranges are still of main interest, the super-

sonic speed range is becoming increasingly significant.

A theoretical treatment of the oscillating airfoil of infinite

aspect ratio moving at supersonic speed has been given by

Possio (reference 1). This treatment is based on the theory

of small perturbations to the main stream, thus is essentially

an acoustic theory, and leads to linearization of the equation

satisfied by the velocity potential. The airfoil is therefore

assumed to be very thin, at small angle of attack, and the

flow is assumed nonviscous, unseparated, and free from

strong shocks.

The small-disturbance linearized theory, being much less

complicated than a more rigorous nonlinear theory, is to be

regarded as an expedient which allows an initial theoretical

solution. The theory permits the occurrence of weak (in-

finitesimally small) shocks and thus the basic trends and

effects of the parameters of the simplified problem can be

indicated. The theory reduces to that of Ackeret in the

stationary (static) case and, like it, is not expected to be

valid too near M' =1. In view of the restrictions and as-

sumptions in the analysis, important modifications may be

required in certain cases for thick finite ail-foils; but even

here the simple theory for thin wing sections may serve as a

basis.

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