Accession Number : ADP005029

Title :   Bifurcation Theory Applied to Aircraft Motions,

Corporate Author : WATERLOO UNIV (ONTARIO)

Personal Author(s) : Hui,W. H. ; Tobak,Murray

Report Date : NOV 1985

Pagination or Media Count : 14

Abstract : Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (subcritical). For the pitching motion of a flat-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with experiments.

Descriptors :   *AERODYNAMIC STABILITY, BIFURCATION(MATHEMATICS), NONLINEAR ANALYSIS, THEORY, AIRCRAFT, EQUATIONS OF MOTION, COEFFICIENTS, PITCH(MOTION), ROLL, SLENDER BODIES, DELTA WINGS, OSCILLATION, TRIM(AERODYNAMICS), ANGLE OF ATTACK, HIGH ANGLES, SUPERSONIC FLIGHT, HYPERSONIC FLIGHT, HYSTERESIS, CANADA

Distribution Statement : APPROVED FOR PUBLIC RELEASE