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Advances in Aircraft and Spacecraft Science
  Volume 4, Number 4, July 2017 , pages 371-399

The feasible constant speed helical trajectories for propeller driven airplanes
Gilles Labonté

    The motion of propeller driven airplanes, flying at constant speed on ascending or descending helical trajectories is analyzed. The dynamical abilities of the airplane are shown to result in restrictions on the ranges of the geometrical parameters of the helical path. The physical quantities taken into account are the variation of air density with altitude, the airplane mass change due to fuel consumption, its load factor, its lift coefficient, and the thrust its engine can produce. Formulas are provided for determining all the airplane dynamical parameters on the trajectory. A procedure is proposed for the construction of tables from which the flyability of trajectories at a given angle of inclination and radius can be read, with the corresponding minimum and maximum speeds allowed, the final altitude reached and the amount of fuel burned. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and the C-130 Hercules.
Key Words
    airplane helical trajectory; banked turn; airplane equation of motion; circular arc connection; automatic trajectory planning
Gilles Labonté: Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada

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