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National Advisory Committee for Aeronautics, Report - A Study of the Application of Power Spectral Methods of Generalized Harmonic Analysis to Gust Loads on Airplanes

The applicability of some results from the theory of general—
ized harmonic analysis (or power-spectral analysis) to the
analysis of gust loads on airplanes in continuous rough air is
examined. The general relations for linear systems between
power spectrums of a random input disturbance and an output
response are used to relate the spectrum of airplane load in
rough air to the spectrum qf atmospheric gust velocity. The
power spectrum of loads is shown to provide a measure of the
load intensity in terms of the standard deviation (root mean
square) of the load distribution for an airplane in flight through
continuous rough air. For the case of a load output having a
normal distribution, which appears from experimental evidence
to apply to homogeneous rough air, the standard deviation is
shown to describe the probability distribution of loads or the
proportion of total time that the load has given values. Thus,
for an airplane in flight through homogeneous rough air, the
probability distribution of loads may be determined from a
power-spectral analysis.

In order to illustrate the application of power-spectral
analysis to gust-load analysis and to obtain an insight into the
relations between loads and airplane gust-response character—
istics, two selected series of calculations are presented. In the
first series, the standard deviations of loads in continuous rough
air described by an assumed power spectrum are calculated for
systematic variations in the frequency and damping character—
istics of the airplane response to a step—gust input. The results
obtained indicate that the loads in rough air are particularly
sensitive to variations in the damping characteristics of the
oscillatory response to a step gust and largely independent of
variations in the frequency. In the second application, the
standard deviation of loads is calculated for selected variations
of each of several airplane geometric and aerodynamic param—
eters of an idealized and stable transport~type airplane. The
standard deviations obtained are compared with results derived
by conventional techniques of using the calculated peak response
to an idealized and representative discrete gust. The resutts
indicate that for stable configurations both methods of analysis
yield results that are consistent to a first approximation.