ESDU 04024:2010

INTRODUCTION

This Item presents an introduction to rigid aeroplane response
to gusts and atmospheric turbulence, together with the design
criteria required to satisfy airworthiness requirements for both
types of disturbance. The Item includes the vertical response of an
aeroplane to a simple discrete sharp-edged gust, extension of this
approach to accommodate the delays due to the build-up of lift and
incidence and the further extension to a two degree-of-freedom
model to provide lift and pitch response. Aeroplane response to
atmospheric turbulence is provided through the relation between the
frequency response function of an aeroplane and the methods of the
power spectral density of a random variable.

The basic equations for the lift and normal acceleration on an
aeroplane due to the simple sharp-edged gust, that is assumed
instantaneously to change the velocity and angle of incidence of
the aeroplane, are developed. The equations are extended to
overcome the restrictive nature of an infinite gust gradient by
introducing a gust alleviation factor that also accommodates for
the lag effects of the build-up of lift in response to gust entry
and sudden changes of incidence. The analysis is further extended
to cover two degree-of-freedom motion in pitch and plunge. The gust
design criteria for the purposes of satisfying airworthiness
requirements are presented.

Continuous atmospheric turbulence is assumed to be a stationary
random process and so the results of power-spectral analysis,
dependant upon a scale length and an intensity or standard
deviation of the turbulence, can be applied to the analysis of gust
loads on aeroplanes. The general relationship for linear systems
between the power spectrum of a random input variable and an output
response are used to relate the spectrum of aeroplane loads to the
spectrum of atmospheric gust velocity. For the case of aeroplane
output loads having a normal or Gaussian distribution, as the
standard deviation is used to describe the probability distribution
of aeroplane loads. In order to assess the probability of the
highest peak within a time interval or the number of peaks expected
in a time interval, frequency of exceedance data methods provide an
alternative to cumulative probability methods. Airworthiness
requirements for aeroplanes subject to continuous turbulence are
described using the power spectral method and the frequency of
exceedance method.

The methods presented provide a fairly simplistic approximation
to realistic atmospheric disturbances, both for discrete gusts and
for turbulence, however they do provide a satisfactory means by
which representative aeroplane loading can be estimated and
certification satisfied.

Appendix A presents a brief review of random variable theory
introducing a description of the Fourier series and integral,
introduction of the power-spectral density function and its
relationship to the properties of stationary random processes
including the mean, standard deviation and auto-correlation
function.

The relatively new statistical discrete gust method, which is a
way to describe the more extreme gusts in a spectrum, is outlined
in Appendix B. This method, which does not form part of the
airworthiness requirements, caters for gusts within the high
frequency range of the spectrum, involves aeroplane responses in
the time domain and uses sequences or families of discrete vertical
gusts to formulate the probability of occurrence of a given
sequence of gusts.