FLYING QUALITIES OF PILOTED AIRCRAFT - CAFE Foundation

MIL–STD–1797AAPPENDIX AThe two most common ways of describing gust correlation are the Dryden and von Karman power spectraldensity forms. As mentioned earlier, the significant aspect of a choice between the two lies in the engineeringconvenience versus the physical correctness. However, the correctness advantage of the von Karman form isnot an issue unless the significant spectral content is centered in the microscale range about one decade ormore above the integral scale break frequency.d. Dimensionality of gust fieldA gust field can be described using various orders of dimensionality. The simplest is a one–dimensional–fieldmodel that involves just the three orthogonal velocity components taken at a single point (usually the aircraftcenter of gravity). The Taylor hypothesis 17/ (frozen field) can be applied, however, in order to approximategust gradients with respect to the x–axis of the aircraft without increasing dimensionality. A two–dimensionalfield model used to define a gust field in the aircraft x–y plane can be modified for the size of the aircraft relativeto gust scales. (A large aircraft relative to the gust scale attenuates gust gradient spectral power at highfrequencies.) A two–dimensional field can lead to greatly increased mathematical complexity over that of aone–dimensional field (AGARD Rpt 372) but some turbulence models simply define one–dimensionaluniform velocity components and then add two–dimensional forms for gust gradients that contain aircraft sizeeffects (Stanford Univ. SUDAAR No. 489). A third dimension can be introduced in the form of analtitude–dependent wind shear (e.g., FAA–RD–79–84 and NASA–CR–152064).e. StationarityA random gust is stationary if, for a collection of gust samples, the corresponding probability and correlationproperties describe any additional gust sample that may be taken. Thus stationarity implies an atmosphericdisturbance having an invariant mean, variance, and correlation length (or time) along the flight path. There isno restriction on whether the probability distribution is Gaussian or not.An alternative means of introducing patchiness or intermittency is to create a nonstationary turbulence fieldthrough direct modulation of intensity (AIAA Paper 80–0763). Thus the basic noise source can remainGaussian.Practical implementation considerationsThe application of atmospheric disturbance models can involve a number of practical implementationproblems—many associated with digital computer programming. One role of this Handbook is to assist inanswering some of the common implementation questions and to point out pitfalls frequently encountered.Some examples include:Digital implementation of continuous spectral forms.Correct scaling of random noise sources.Evaluation of need for gradient components.Implementation of gust gradients, gust time derivatives, and gust transport lags.Table LV illustrates some of the practical implementation matters.17/ The Taylor hypothesis (J. Atmos. Sciences, Vol 20) assumes a gust field frozen in space such that time andspace dependencies along the relative wind are directly related by the airspeed.671