# A Discrete Gust Model for Use in the Design of Wind Energy Conversion Systems

Walter Frost The University of Tennessee Space Institute, Tullahoma 37388

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Robert E. Turner NASA/Marshall Space Flight Center, AL

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## Abstract

Discrete gust models, although idealizations of actual atmospheric conditions, are useful for engineering design. For fatigue design, these models must be representative of the conditions a structure or vehicle will experience on a continuous basis throughout its lifetime. The definition of a discrete gust must, therefore, include magnitude, time of rise and decay, and rate of occurrence.

A discrete gust model is described. The model incorporates the number-of-crossings theory. An expression for the number of times per unit time the wind exceeds a specific value is derived as a function of mean wind speed and the standard deviation of turbulence. A technique for determining the cut-off frequency which represents the upper limit of integration used to estimate the standard deviation of wind fluctuation accelerations is described. Utilizing this definition of cut-off frequency, comparison of prediction and experiment is carried out.

The number of times the wind speed exceeds a certain value over a yearly period is then estimated by integrating the product of the number-of-crossings joint probability times the Weibull distribution. A mathematical filter to isolate those disturbances in the atmosphere of a characteristic size, for example, those which would completely engulf a rotor, is developed based on vertical and lateral coherence functions. The resulting model is expressed in a convenient engineering design format.

## Abstract

Discrete gust models, although idealizations of actual atmospheric conditions, are useful for engineering design. For fatigue design, these models must be representative of the conditions a structure or vehicle will experience on a continuous basis throughout its lifetime. The definition of a discrete gust must, therefore, include magnitude, time of rise and decay, and rate of occurrence.

A discrete gust model is described. The model incorporates the number-of-crossings theory. An expression for the number of times per unit time the wind exceeds a specific value is derived as a function of mean wind speed and the standard deviation of turbulence. A technique for determining the cut-off frequency which represents the upper limit of integration used to estimate the standard deviation of wind fluctuation accelerations is described. Utilizing this definition of cut-off frequency, comparison of prediction and experiment is carried out.

The number of times the wind speed exceeds a certain value over a yearly period is then estimated by integrating the product of the number-of-crossings joint probability times the Weibull distribution. A mathematical filter to isolate those disturbances in the atmosphere of a characteristic size, for example, those which would completely engulf a rotor, is developed based on vertical and lateral coherence functions. The resulting model is expressed in a convenient engineering design format.

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