• Advances in aircraft and spacecraft science
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• 제5권1호
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• pp.73-105
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• 2018

A particular type of constant speed helical trajectory, with variable ascension rate, is proposed. Such trajectories are candidates of choice as motion primitives in automatic airplane trajectory planning; they can also be used by airplanes taking off or landing in limited space. The equations of motion for airplanes flying on such trajectories are exactly solvable. Their solution is presented, together with an analysis of the restrictions imposed on the geometrical parameters of the helical paths by the dynamical abilities of an airplane. The physical quantities taken into account are the airplane load factor, its lift coefficient, and the thrust its engines can produce. Formulas are provided for determining all the parameters of trajectories that would be flyable by a particular airplane, the final altitude reached, and the duration of the trajectory. It is shown how to construct speed interval tables, which would appreciably reduce the calculations to be done on board the airplane. Trajectories are characterized by their angle of inclination, their radius, and the rate of change of their inclination. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and the F-16 Fighting Falcon.

• Advances in aircraft and spacecraft science
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• 제4권4호
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• pp.371-399
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• 2017

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.

• Advances in aircraft and spacecraft science
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• 제7권1호
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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.