A ring-vortex downburst model for flight simulations

Abstract

A mathematical model of a downburst for real-time flight simulations of takeoffs and landings in low-altitude severe wind shears due to downbursts or microbursts was developed. The downburst mature stage was idealized to resemble the circulatory wind-flow patterns noted in meteorological downburst data from the Joint Airport Weather Studies (JAWS) Project. The idealization produced a three-dimensio nal axisymmetric circulatory flowfield similar to that around a horizontal smoke ring or ring vortex at an appropriate height above the ground. The flowfield around a ring vortex has a stream function expressed in Sir Horace Lamb's classical textbook Hydrodynamics in terms of the complete elliptic integrals combination of [F(k)—E(k)]; which is approximated herein by the expression: [0.788fc2/(0.25 + 0.75Vl - A:2)], in the limited range of 0<£ 2 <1 for the modulus k = (r2 —rl)/(r2-rl}^ where rl and r2 denote the least and greatest distances, respectively, of the point P from the ring vortex. Digital differentiations of the downburst stream function at the airplane center of gravity yield both the WZ downdraft and the WR radial wind velocity component. The latter is then resolved into the two horizontal components WX and WY for wind speeds along and across the runway, respectively. Occupying 383 words of memory and having an average real-time execution time of 1.3 ms on a Harris H800 digital computer, the present ring-vortex downburst model provides economical simulation of severe wind-shear flow patterns that closely resemble some of the flow patterns noted in meteorological data from the JAWS Project.