THEORY OF THE FLIGHT OF AIRPLANES IN ISOTROPIC TURBULENCE - REVIEW AND EXTENSION

Recent experimental information on low-level atmospheric turbulence is first reviewed. It is suggested that the assumptions of homogeneity and isotropy customarily adopted for high altitudes are still useful in this regime, and that the integral scale is roughly equal to 9/10 of the altitude up to about 1000 ft. Next, the previously published theory of the 'power-series approximation' as applied to the vertical component of the gust is extended to include all three velocity components simultaneously. Fourteen different one- dimensional input power spectra and cross spectra are found of which only five are important. Of these five, only one is a cross-spectrum involving two different velocity components (u and v). Formulae for them are calculated and curves are presented. The 'gust derivatives' required for calculating airplane response are defined and discussed, and the most important ones are shown to be simply the negatives of classical stability derivatives. Methods of approach for calculating the remaining ones are suggested.
Presented at the AGARD Specialists' Meeting on Stability and Control, 10-14 Apr 61, held at Rhode-Saint-Genese, Belgium.