The Potential Theory Of Unsteady Supersonic Flow

This classic monograph on unsteady transonic flow — the flow of air encountered at speeds at or near the speed of sound — is of continuing interest to students and professionals in aerodynamics, fluid dynamics, and other areas of applied mathematics. After a brief Introduction, Swedish physicist Mårten T. Landahl presents a chapter in which the two-dimensional solution is derived, succeeded by a discussion of its relation to the subsonic and supersonic solutions. Three chapters on low aspect ratio configurations follow, covering triangular wings and similar planforms with curved leading edges, rectangular wings, and cropped delta wings, and low aspect ratio wing-body combinations. The treatment concludes with a consideration of the experimental determination of air forces on oscillating wings at transonic speeds.

Division II: Aerodynamics, Volume 7: Wing Theory in Supersonic Flow examines the cases of isolated simple wings, wings with vertical plane tail, cruciform wings, and simple or cruciform wings fitted with a body. This book presents the method for the actual calculation of isolated wings or of more complex system. Organized into 12 chapters, this volume starts with an overview of the basic equations in the mechanics of inviscid fluids. This text then presents a unified theory that is established for angularly shaped wings in supersonic flow. Other chapters consider the method for calculating the characteristics of drag, lift, and moments for various shapes of the trailing edge line. This book discusses as well the wings of ordinary shapes, delta wings, yawed wings, polygonal wings, trapezoid wings, and arrow-head or swept-back wings. The final chapter deals with a delta wing with a central fusiform body. This book is a valuable resource for teachers, students, and specialists engaged in modern aerodynamics.

The method of integral relations is applied in a one-strip approximation to the perturbation equations governing small motions of an inclined, sharp-edged, flat surface about the mean supersonic steady flow. Algebraic expressions for low reduced-frequency aerodynamics are obtained and a set of ordinary differential equations are obtained for general oscillatory motion. Results are presented for low reduced-frequency aerodynamics and for the variation of the unsteady forces with frequency. The method gives accurate results for the aerodynamic forces at low reduced frequency which are in good agreement with available experimental data. However, for cases in which the aerodynamic forces vary rapidly with frequency, the results are qualitatively correct, but of limited accuracy. Calculations indicate that for a range of inclination angles near shock detachment such that the flow in the shock layer is low supersonic, the aerodynamic forces vary rapidly both with inclination angle and with reduced frequency.

Linearized slender-body theory is applied to the computation of aerodynamic forces on an oscillating, or deforming, body in supersonic flow. The undeformed body is a body of revolution and the deformed body is represented by movement of a line through the centers of the cross sections which are assumed to remain circular. The time dependence is based on sinusoidal motion. For a body of vanishing thickness the slender-body theory yields the apparent mass approximation as it is obtained for incompressible crossflow around a cylinder. Both linearized slender-body theory and the apparent mass approximation are used to calculate the pitching-moment coefficients on a rigid slender body with a parabolic arc nose cone, and these coefficients are compared with some experimental results. (Author).

Areader who achieves a substantial command of the material con tained in this book should be able to read with understanding most of the literature in the field. Possible exceptions may be certain special aspects of the subject such as the aeroelasticity of plates and sheIls or the use of electronic feedback control to modify aeroelastic behavior. The first author has considered the former topic in aseparate volume. The latter topic is also deserving of aseparate volume. In the first portion of the book the basic physical phenomena of divergence, control surface eflectiveness, flutter and gust response of aeronautical vehicles are treated. As an indication of the expanding scope of the field, representative examples are also drawn from the non aeronautical literature. To aid the student who is encountering these phenomena for the first time, each is introduced in the context of a simple physical model and then reconsidered systematicaIly in more compli cated models using more sophisticated mathematics.