• Advances in aircraft and spacecraft science
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• v.4 no.3
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• pp.237-267
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• 2017

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.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.399-425
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• 2016

The dynamical requirements are obtained for airplanes to travel on inclined circular trajectories. Formulas are provided for determining the load factor, the bank angle, the lift coefficient and the thrust or power required for the motion. The dynamical properties of the airplane are taken into account, for both, airplanes with internal combustion engines and propellers, and airplanes with jet engines. A procedure is presented for the construction of tables from which the flyability of trajectories at a given angle of inclination can be read, together with the corresponding minimum and maximum radii allowed. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and a F-16 jet airplane.

• Advances in aircraft and spacecraft science
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• v.7 no.1
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• pp.53-78
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• 2020

Automatic 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.