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National Advisory Committee for Aeronautics, Technical Notes - Estimates of Probability Distribution of Root Mean Square Gust Velocity of Atmospheric Turbulence from Operational Gust Load Data by Random Process Theory

Under the assumption that the operational gust or gust—load his-
tory of an airplane is a Gaussian random.process with a single param—
eter, the root-mean—square value, relations are derived between the
probability distribution of the rootdmean-square acceleration and the
associated number of peak accelerations above given values. These rela-
tions are then used in the analysis of available operational gust-load.
data in the form of peak counts to derive estimates of the probability
distributions of root-mean—square acceleration. These probability
distributions are then transformed on the basis of airplane—gust-response
theory in order to derive the associated probability distribution of
root-mean—square gust velocity. The application of these results to
the calculation of load histories is also considered briefly.

During the last few years, advances have been made in the analysis
of airplane behavior in rough air through the application of the tech-
niques of generalized harmonic analysis (refs. 1 to 7). The application
of these techniques is based upon the representation of atmospheric tur-
bulence as a continuous random disturbance characterized by power—
Spectral-density functions and certain prdbability distributions. The
power spectrum of the turbulence is then used along with the airplane
response characteristics to determine the power spectra and other sta—
tistical characteristics of the airplane loads or motions in rough air.
The application of this approach to the problem of calculating load
histories for operational flight requires detailed.information on the
Spectrum of turbulence in the atmosphere. The information required may
be considered of two types: detailed.information on the spectrum of
turbulence and its variations, and information on the probability of
encountering the various spectra.