A Study of the Longitudinal Low Frequency (Phugoid) Motion of an Airplane at Supersonic and Hypersonic Speeds

Citation

Walter, Uso (1967) A Study of the Longitudinal Low Frequency (Phugoid) Motion of an Airplane at Supersonic and Hypersonic Speeds. Engineer's thesis, California Institute of Technology. doi:10.7907/CNZT-1P02. https://resolver.caltech.edu/CaltechETD:etd-11152005-105053

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The character of the longitudinal low frequency (phugoid) motion of a rigid airplane with controls fixed is investigated for the flight Mach number range from 1.25 to 8.0 using the physical and aerodynamic data of the North American X-15 research airplane. The validity of the simplifying assumptions made in most low speed airplane stability investigations (symmetry of the airplane and of the air flow, small perturbations) is established for the problem under consideration. The equations of longitudinal motion have been solved for the flight altitudes: sea level, 20,000 ft., 40,000 ft., and 60,000 ft.; and in, addition the roots of the simplified equations resulting from the phugoid approximation have been calculated for the same flight situations. It is found that the deviation of these approximate solutions from the solutions of the complete longitudinal equations is below 5 per cent throughout the considered range of flight conditions, and for most calculated points is less than 2 per cent. The phugoid roots are complex at 60,000 ft. altitude and real at sea level, with transition from one mode to the other at the intermediate flight altitudes. The real part of the roots is always negative, i. e., there is no divergence of the motion. Using the phugoid approximation, a criterion for the de-generation of the periodic phugoid mode into aperiodic modes is derived in form of a critical value of the lift to drag ratio [...]. In an appendix, the influence of an additional damping force (thrust control by the auto-pilot) on the character of the phugoid roots is shown.

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