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.