WIND SHEAR AND HYPERBOLIC DISTRIBUTIONS (Research Note)

A data set on wind shear, consisting of 24 frequency distributions of changes in headwind speed experienced by aircraft during landing phase. is modelled parsimoniously by means of the hyperbolic distribution. Large wind shears meeting aircraft during landing and take-off constitute a major problem for air traffic and may lead to fatal accidents. The nature and the frequenc- ies of occurrence of the various kinds of these wind shears have been discussed inter alia by Payne and Cox (1969), Jones (1976), Haynes (1980), Woodfield and Woods (1983), and Kanji (1985). The present report contains an analysis, by means of the hyperbolic distribution, of part of a basic data set on distributions of wind shear which has been established by the Aeronautical Research Council and the Royal Aircraft Establishment in collaboration with British Airways. A detailed discussion of the data is given in Woodfield and Woods (1983). In total, the data comprise the records of more than 9,000 landings. As will be shown, the hyperbolic distribution allows a well-fitting and parsimonious reduction of the data. The resulting model may be useful for flight control, risk evaluation and flight simulation. Note in this connection that it is the tails, rather than the central parts, of the distributions that are of main interest in the present context. The hyperbolic distributions have been used on two previous occasions (Barndorff-Nielsen, 1979, 1986) to describe a quite different type of acceleration in turbulent wind fields. For other kinds of applications, in particular to particle size distributions, and for the theory of hyperbolic distributions, see Bagnold and Barndorff-Nielsen (1980), Barndorff-Nielsen