OPTIMAL-RANGE-VELOCITY-POLAR: A NEW THEORETICAL TOOL FOR THE OPTIMIZATION OF SAILPLANE FLIGHT TRAJECTORIES

Abstract

0n a cross-country flight a sailplane pilot may optimize his average cross-country speed by adjusting his instantaneous horizontal velocity (and thereby his instantaneous vertical velocity) so that he flies faster thru regions with downward moving air and slower thru 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, 0RV-polar. This ORV-polar is the plot which provides the optimal average vertical velocity of the sailplane over the course as a function of its average horizontal velocity.The shape, the properties, the construction and the use of the 0RV-polar are discussed in this paper. In particular it is shown that the optimal velocity histories which correspond to the individual points of the 0RV-polar are each dependent on only one quantity, the so called "MacCready-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 (ignoring 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 MacCready-ring-setting for any course with any vertical atmospheric velocity distribution. For the special case of a square wave thermal model, the optimal MacCready-ring setting may be determined by a simple graphical method which requires no more information than the velocity polar (i.e., the regular relationship between the horizontal and vertical velocity) of the sailplane. As such, this particular optimal MacCready-ring-setting can be determined by any sailplane pilot without the aid of a computer. As an example of this last use of the 0RV-polar concept. The paper also presents the optimal MacCready-ring-settings for a variety of square-wave thermal-model values for a particular sailplane type (LS-3) representative of modern racing-class sailplanes.