FUNDAMENTALS OF NONSTATIONARY AIRFOIL. THEORY

Four distinctive ranges of speed, classified according to the magnitude of the free-stream Mach number M, are considered in aerodynamics. These are:

1. The “incompressible” speed range, in which M2 1 and the fluid may be considered incompressible.

2. Subsonic-speed range, M < 1, and below the Mach number of “divergence” (cf. § 4.3).

3. Transonic-speed range, M ~ 1.

4. Supersonic-speed range, M> 1.

This classification is based on a theoretical point of view, particularly on the method of analysis. There is no essential difference in the flow patterns between ranges 1 and 2. But, in range 1, which is a limiting case of 2, considerable mathematical simplifications are possible.

Since airfoil characteristics vary with the speed ranges, the most efficient configuration of an airplane is likely to be different for different design speeds. Thus sweptback wings become favorable for airplanes designed for high subsonic and transonic speeds, and thin delta wings and wings of small-aspect ratios are favored in transonic and supersonic designs. Such differences in the geometrical configurations and the corresponding differences in the structural constructions have important effects on the method of aeroelastic analysis.

In this and the next three chapters the aerodynamics of an oscillating airfoil is studied. We shall consider harmonic oscillations of small amplitudes only, so that in most cases the principle of superposition is applicable. In case the aerodynamic equations may be linearized, the aerodynamic response to an arbitrary motion can be obtained from the response to harmonic oscillations by an integration.

Of the four speed ranges mentioned above, the aerodynamics of an incompressible flow has been exhaustively developed; that of the sub­sonic and supersonic flows is also developed to certain extent. But, in the transonic-speed range, much theoretical and experimental work remains to be done before a reliable analysis can be made.