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Advances in Aircraft and Spacecraft Science
  Volume 7, Number 1, January 2020 , pages 53-78

How airplanes fly at power-off and full-power on rectilinear trajectories
Gilles Labonté

    utomatic trajectory planning is an important task that will have to be performed by truly autonomous vehicles. The main method proposed, for unmanned airplanes to do this, consists in concatenating elementary segments of trajectories such as rectilinear, circular and helical segments. It is argued here that because these cannot be expected to all be flyable at a same constant speed, it is necessary to consider segments on which the airplane accelerates or decelerates. In order to preserve the planning advantages that result from having the speed constant, it is proposed to do all speed changes at maximum deceleration or acceleration, so that they are as brief as possible. The constraints on the load factor, the lift and the power required for the motion are derived. The equation of motion for such accelerated motions is solved numerically. New results are obtained concerning the value of the angle and the speed for which the longest distance and the longest duration glides happen, and then for which the steepest, the fastest and the most fuel economical climbs happen. The values obtained differ from those found in most airplane dynamics textbooks. Example of tables are produced that show how general speed changes can be effected efficiently; showing the time required for the changes, the horizontal distance traveled and the amount of fuel required. The results obtained apply to all internal combustion engine-propeller driven airplanes.
Key Words
    airplane accelerated trajectory; inclined rectilinear motion, airplane equation of motion; automatic trajectory planning; gliding; climbing
Gilles Labonté: Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario, Canada

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