# The "optimal-range-velocity-polar" : a new theoretical tool for the optimization of sailplane flight trajectories

## Abstract

On a cross-country flight a sailplane pilot may optimize his average cross-country speed by adjusting his instantaneous horizontal velocity (and therewith his instantaneous vertical velocity) so that he flies faster through regions with downward moving air and slower through regions with upward moving air. For the exact solution of this optimization problem in case of a given arbitrary vertical atmospheric velocity distribution along the course a simple new tool is introduced in this paper in the form of the definition of an "optimal-range-velocity-polar" or, short, ORV-polar. This ORV-polar is the plot which provides the optimal average vertical velocity of the sailplane over the range as a function of its average horizontal velocity. In the paper the shape, the properties, the construction and the use of the ORV-polar are discussed. In particular it is shown that the optimal velocity histories which correspond to the individual points of the ORV-polar are each dependent on only one quantity, the so called "McCready-ring setting". As a result these optimal velocity histories may be generated in practice in a relatively easy way with aids and/or instruments currently in use by the sailplane pilots. For theoretical purposes the ORV-polar concept facilitates the understanding of known theoretical results, such as the rule that (not taking into account the possibility of an early landing by lack of height) the optimal velocity history over the total range is completely determined by the largest possible net rate of climb encountered along the course. Also, the concept of the ORV-polar makes it easy to understand that flying S-curves, as proposed by some authors, when optimal, is never the only optimal strategy. For practical purposes the ORV-concept makes it feasible to determine the exact optimal McCready-ring-setting for any range with any vertical atmospheric velocity distribution. For the special case of a square-wave thermal model the optimal McCready-ring-setting may even be determined by a simple graphical method which requires no more information that the velocity polar (i.e. the regular relationship between the horizontal and vertical velocity) of the sailplane. As such this particular optimal McCready-ring-setting can be determined by any sailplane pilot without the aid of a computer. As an example of this last use of the ORV-polar concept the paper also presents the optimal McCready-ring-settings for a variety of square-wave-thermal-model values for a particular sailplane type (LS-3) representative for the modern racing-class of sailplanes.
Original language English Eindhoven Technische Hogeschool Eindhoven 42 Published - 1977

### Publication series

Name Memorandum COSOR 7728 0926-4493

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