Some aspects of aircraft response to atmospheric turbulence

Aspects of the requirements for and the calculation of design loads due to atmospheric disturbances are discussed. Special attention has been paid to the relation between discrete gusts and continuous turbulence. It is recommended that a worst case gust model, as described in this report, be further developed.

Worst case gust shapes for atmospheric turbulence with known spectrum

A worst case gust shape has been derived for turbulence or gust patches, assuming only that the average spectrum of such patches is known. The maximum value of the response can be calculated quite easily. The result differs from the PSD-method. Some examples of worst case inputs and outputs are given, also for nonlinear systems.

The deterministic power-spectral-density-method for nonlinear systems

The Deterministic Power-Spectral-Density method can be derived from the Design Envelope Analysis of the continuous P.S.D.-method. It provides a method to determine a deterministic function that gives a maximum response equal to the P.S.D.-design load for linear systems. The P.S.D.-design load is undefined for nonlinear systems. In this report a ...

The deterministic power-spectral-density-method for linear systems

The Deterministic Power-Spectral-Density-method has been derived directly from the continuous P.S.D.-method. It can be regarded as a "translation" from the frequency domain to the space or time domain. The critical gust profile, giving maximum response, is obtained directly. The D.P.S.D.-method gives the same results as the continuous P.S.D.-...

The response of aircraft to two-dimensional vertical turbulence

Equations for the response of an aircraft to two-dimensional vertical atmospheric turbulence have been derived, both for an aircraft regarded as a continuous system and for an aircraft split up into a number of panels. These equations have been applied to an aircraft model with two degrees of freedom of the size of the Fokker 100, respectively....

Atmospheric turbulence spectra and correlation functions

The derivation of one- two- and three-dimensional spectra and correlation functions for isotropic (atmospheric) turbulence and the mutual relations have been collected from various sources. Aircraft loads usually are determined using a one-dimensional turbulence description. In some cases a two- or even three-dimensional description might be...

Definition of P.S.D.-design loads for nonlinear aircraft

The Power Spectral Density (P.S.D.)-method is used to define design loads due to atmospheric turbulence. The design loads are calculated using linear transfer functions. These methods can not be used if the equations describing the behaviour of the aircraft are nonlinear. One method to define design loads for a nonlinear aircraft is by means of...

The generation of a random process with a spectrum with fractional power

A method is described to generate a random Gaussian process with a power spectrum with fractional power, for example the von Karman spectrum for atmospheric turbulence. The method uses digital filtering of a white noise process and it is based on the use of fractional derivatives. An algorithm to generate the process is presented.

Statistical properties of atmospheric turbulence relevant to the calculation of airplane loads

Measured time histories of atmospheric turbulence have been analysed. Distribution functions and exceedance curves of the turbulence and its derivative are presented. The load exceedance curves of various mathematical airplane models due to these turbulence patches have been calculated. Deviations of the properties of these patches from the...

Review and comparison of discrete and continuous gust methods for the determination of airplane design loads

Historical reviews of the discrete gust and the continious gust concept, in relation to the present requirements, are given in this report. A comparison is made between the discrete gust method and the power spectral density method on the basis of simple airplane models. No direct relation between the two methods exists. The main cause of the...

The determination of gustloads on nonlinear aircraft using a Power Spectral Density approach

Design loads for nonlinear aircraft, i.e. aircraft with gust alleviation system or yaw dampler, cannot be established with the Power Spectral Density method. The only method available is by means of computer simvilation. Methods to approximate load exceedance curves of nonlinear aircraft are proposed in this report. For the derivation of the...

Aircraft design loads due to non-stationary atmospheric turbulence patches

In this report it is assumed that atmospheric turbulence appears in patches and that within the patches the turbulence can be described.as a modulated Gaussian process. The patch lengths have a certain probability density function. Load exceedance curves and design loads for various aircraft models for this turbulence model are compared with...

A non-stationary model for atmospheric turbulence patches, for the prediction of aircraft design loads

In this report a model for atmospheric turbulence is proposed. It is assumed that atmospheric turbulence appears in patches and that within the patches the turbulence can be described as a modulated Gaussian process. Statistical properties of this model and of atmospheric turbulence are compared. Using data from various sources a probability...

Equations for the response of an airplane to non-stationary atmospheric turbulence patches

In this report a method is described to calculate the load exceedance curve for a linear system having a finite, modulated Gaussian process as input. The derivation is based on the use of ensemble averages, defined as the expected values at a certain point of time. The equations can be used for any airplane-transfer function for which the Power...

Comparison between the statistical discrete gust method and the power spectral density method

The Power Spectral Density method and the Statistical Discrete Gust Method to calculate aircraft design loads due to atmospheric turbulence are compared qualitatively and quantitatively on the basis of the load exceedance curves for certain aircraft models. It is shown that both methods are related to each other, giving the same results for...