• Advances in aircraft and spacecraft science
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• v.10 no.5
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• pp.473-494
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• 2023

This article introduces a formalism for the analysis of airplane trajectories on which the motion is determined by specifying the power of the engines. It explains a procedure to solve the equations of motion to obtain the value of the relevant flight parameters. It then enumerates the constraints that the dynamical abilities of the airplane impose on the amount of fuel used, the speed, the load factor, the lift coefficient, the positivity and upper boundedness of the power available. Examples of analysis are provided to illustrate the method proposed, with rectilinear and circular trajectories. Two very different types of airplanes are used in the examples: a Silver Fox-like small UAV and a common Cessna 182 Skylane.

• 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.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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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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• v.5 no.5
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• pp.551-579
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• 2018

This work is concerned with the motion of propeller driven airplanes, flying at constant velocity on ascending or descending rectilinear trajectories. Its purpose is to provide important features of rectilinear flights that are required for airplane trajectory planning but that cannot be found already published. It presents a method for calculating the amount of fuel used, the restrictions on the trajectory parameters, as inclination and speed, which result from the load factor, the lift coefficient, the positivity and upper boundedness of the power available. It presents a complete discussion of both ascending and descending flights, including gliding. Some original remarks are made about the parameters of gliding. It shows how to construct tables of parameters allowing to identify rapidly flyable trajectories. Sample calculations are shown for the Cessna 182 and a Silver Fox like unmanned aerial vehicle.

• Advances in aircraft and spacecraft science
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• v.4 no.4
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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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• 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.2 no.4
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• pp.367-389
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• 2015

Simple solutions are obtained for the fuel required by internal combustion engine airplanes on trajectories with a constant rate of climb or descent. Three modes of flight are considered: constant speed, constant Mach number and constant angle of attack. Starting from the exact solutions of the equations of motion for the modes of motion considered, approximate solutions are obtained that are much easier to compute while still being quite precise. Simpler formulas are derived for the weight of fuel, speed, altitude, horizontal distance, time to climb, and power required. These formulas represent a new important contribution since they are fundamental for the analysis of aircraft dynamics and thus have direct applications for the analysis of aircraft performances and mission planning.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.10a
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• pp.196-201
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• 2001

Very Large Floating Structures have been planned for effective utilization of ocean space in recent years. The VLFS usually has a control tower to guide airplane securely. This paper present an effective method for calculating the wave induced hydroelastic responses of VLFS considering the effect of control tower-shapes. The source and dipole distribution method is used to calculate the hydrodynamic loads and equation of motion is derived by considering the static and dynamic coupling effects from different segments of the plate. The rigidity matrix for VLFS is formulated by finite element method using a plate theory. The calculated results for VLFS with a control tower are compared with those for VLFS without a control tower.