• 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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• 제10권5호
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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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• 제5권5호
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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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• 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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• 제4권3호
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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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• 제3권4호
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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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• 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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.156.2-156
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• 2001

Hypersonic civil airplanes are recently heated up again in USA and Japan, but there are several difficulties when we obtain its optimal trajectories. In this paper, we formulated the trajectory optimization problem as an optimal control problem and solved it by the direct shooting method with the Genetic Algorithm, GA. The result shows it is effective to use this method for the trajectory optimization of the hypersonic flight.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2004년도 제22회 춘계학술대회논문집
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• pp.742-748
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• 2004

In this paper are presented TSTO system analysis including some controlled variables on the engine operation such as a fuel flow rate and a pressure ratio of compressor, as well as variables on the trajectory. TSTO studied here is accelerated up to Mach 6 by a fly-back booster powered by air breathing engines. Three different types of engine cycle were treated for propulsion system of the booster, such as a turbo ramjet, a precooled turbojet and an EXpander cycle Air Turbo Ramjet (ATREX). The history of the controlled variables on the engine operation was optimized by Sequential Quadratic Programming (SQP) to accomplish the minimum fuel consumption. The trajectory was also optimized simultaneously. The results showed that the turbo ramjet gave the best fuel consumption. The optimal trajectory was almost the same except in the transonic range and just before reaching to Mach 6. The history of the pressure ratio of compressor considerably depended on the engine type. It is concluded that simultaneous optimization for engine control and trajectory is effective especially for a high-speed airplane propelled by turbojets like the TSTO booster.

• 한국항공우주학회지
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• 제39권3호
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• pp.254-260
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• 2011

원격측정링크는 항공기의 움직임에 따라 안테나 이득과 편파가 실시간으로 변화하는 동적 통신링크이다. 본 논문에서는 항공기의 비행궤적, 자세, 3차원 안테나 패턴을 사용하여 실시간 탑재안테나 이득과 송수신 안테나의 편파 부정합을 계산하였다. 그리고 다중경로 환경을 2-Ray 둥근지구 반사지형으로 모델링하고, 항공기에서 송신한 RF 신호를 빔폭이 좁은 안테나로 수신할 때 수신신호세기를 예측하였다. 또한 비행시험을 실시하고 측정값과 예측값을 비교하여 잘 일치함을 확인하였다.