IN high‐speed level flight in the compressibility region an entirely new factor makes its appearance, viz: small variations of atmospheric density and speed of sound with height. This factor affects dynamic stability due to continuous changes of height during longitudinal disturbances; there is no effect in lateral disturbances. The affects are very small in low‐speed flight but they increase steadily with Mach number. The short‐period oscillations are not affected but the corrections to phugoid motion become appreciable in high subcritical flight, larger in supercritical (transonic) range, and very important in supersonic flight. The effects of compressibility are of paramount significance but they should be considered in conjunction with varying height effects. Another result of the investigation is the appearance of a new mode of disturbance, due to the stability quartic being converted into a quintic. The fifth (real) root is often small, it may vary in sign according to aerodynamic properties of the aircraft and characteristics of the power unit. The new mode is a subsidence or a divergence, and it determines height stability or instability, hence it may show to what extent an aircraft is able to keep constant altitude over long stretches of time.
Neumark, S. (1950), "Longitudinal Stability, Speed and Height: An Examination of Dynamic Longitudinal Stability in Level Flight, Including the Effects of Compressibility and changes in Atmospheric Phenomena with Height", Aircraft Engineering and Aerospace Technology, Vol. 22 No. 11, pp. 323-334. https://doi.org/10.1108/eb031964
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