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Advances in Aircraft and Spacecraft Science
  Volume 4, Number 3, May 2017 , pages 237-267

Low thrust inclined circular trajectories for airplanes
Gilles Labonté

    Automatic trajectory re-planning is an integral part of unmanned aerial vehicle mission planning. In order to be able to perform this task, it is necessary to dispose of formulas or tables to assess the flyability of various typical flight segments. Notwithstanding their importance, there exist such data only for some particularly simple segments such as rectilinear and circular sub-trajectories. This article presents an analysis of a new, very efficient, way for an airplane to fly on an inclined circular trajectory. When it flies this way, the only thrust required is that which cancels the drag. It is shown that, then, much more inclined trajectories are possible than when they fly at constant speed. The corresponding equations of motion are solved exactly for the position, the speed, the load factor, the bank angle, the lift coefficient and the thrust and power required for the motion. The results obtained apply to both types of airplanes: those with internal combustion engines and propellers, and those with jet engines. Conditions on the trajectory parameters are derived, which guarantee its flyability according to the dynamical properties of a given airplane. An analytical procedure is described that ensures that all these conditions are satisfied, and which can serve for producing tables from which the trajectory flyability can be read. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and an F-16 jet airplane.
Key Words
    automatic trajectory planning; airplane circular trajectory; inclined circular trajectories; inclined pendulum trajectories; Dubins 3D trajectories
Gilles Labonté: Department of Mathematics and Computer Science and Department of Electrical Engineering and Computer Engineering, Royal Military College of Canada, Kingston, Ontario, Canada

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