Scott Jenkins, Lawrence Armi, Joseph Wasyl


We solve for optimal combinations of glide speeds and crab angles that minimize the glide slope at an arbitrary angle to the wind along a constant course heading. In this general case glide slope minimization is posed as a variational problem with both graphical and nurnerical solutions. The graphical solutions are obtained by tangent plotting of the along-course component of the glide polar for any constant crosswind component. The numerical solutions are obtained by seeded iterations with a Taylor series expansion about an analytic solution in the asymptotic limit of a small crosswind component. These solutions reveal that speeds-to-fly in severely oblique winds can actually increase with increasing tailwind component in order to avoid glide slope degradation from excessively large crab angles. Furthermore, indicated speeds-to-fly decrease with altitude in the absence of wind gradients aloft (as in absorption and insulation layers). On the other hand, if wind gradients are present aloft and obey Long's solution then indicated speeds-to-fly remain invariant with altitude. Within a lee wave field, it is shown that the glide slope between any two points is minimized by an orthogonal series of constant course glides proceeding crosswind through regions of lift and directly with or against the wind through regions of sink. The solutions were also used to compute the flattest possible glide slopes that may be achieved across the spectrum of production sailplanes under a variety of extreme conditions. It was found that larger aspect ratios and low wing loadings have an increasing advantage with increasing tailwind and diminishing crosswind component. However, this advantage is greatly diminished with increasing headwind and crosswind components. Speed-to-fly and along-course speeds segregated according to wing loading with tailwind and weak crosswind components, but varied inversely with wing thickness for oblique headwings and direct crosswinds. The practice of ballasting was shown to be advantageous for all oblique headwinds, direct crosswinds, and even in strong oblique tailwinds.


Meteorology, Aerodynamics, Design

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