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Reducing emissions using aircraft trajectory optimization
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Flight Dynamics. (Flight Dynamics)
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Flight Dynamics. (Flight Dynamics)ORCID iD: 0000-0003-2391-641X
(English)In: Aerospace Science and Technology, ISSN 1270-9638, E-ISSN 1626-3219Article in journal (Other academic) Submitted
Abstract [en]

Optimal aircraft trajectories reducing engine emissions are computed using numerical optimization. The emissions from the jet engine are modeled as functions of the aircraft altitude, airspeed and throttle setting. Combining the emission models with a performance model of the aircraft, the optimization problem is formulated with the objective of reducing emissions for a given distance flight. The resulting problem, involving a system of differential and algebraic equations, is discretized using collocation and the optimization problem is solved using sequential quadratic programming. Different objectives are investigated, such as minimizing the total emissions of carbon dioxide, carbon monoxide, oxides of nitrogen and hydrocarbons during a flight. Methods from life cycle impact assessment are used to weigh the different emissions to an index and several different indices are used and compared. A model of the Boeing 737-600 is used to illustrate the developed optimization method. The results show that the trajectories differ significantly depending on the chosen objective. Using a combination of objectives at different altitudes may give the most appropriate problem formulation.

Keyword [en]
Trajectory optimization, Boeing fuel flow method, Emissions index
National Category
Vehicle Engineering
URN: urn:nbn:se:kth:diva-10955OAI: diva2:233073
QS 20120327Available from: 2009-08-27 Created: 2009-08-27 Last updated: 2012-03-27Bibliographically approved
In thesis
1. On improving efficiency of flight using optimization
Open this publication in new window or tab >>On improving efficiency of flight using optimization
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, optimization is used to improve the performance of aircraft. The focus is on operating current generation aircraft more efficiently rather than designing new aircraft. Drag minimization and aircraft trajectory optimization is used to increase efficiency. Optimization methods are implemented and evaluated on different problem formulations.

The first part of the thesis presents a drag minimization strategy using multiple control surfaces distributed across the span of an elastic wing. Aeroelasticity is exploited to reduce drag for a wide range of flight conditions. A method to minimize drag during a long distance flight is developed and tested in a wind tunnel environment. The method is based on continuously changing the control surface deflections to obtain a more beneficial load distribution from a drag point of view for the current flight condition. In a second study, the method is extended to include the angle of attack as a variable together with the control surface deflections in the drag minimization algorithm. Extensive wind tunnel testing demonstrates the possibility to reduce drag significantly with the presented method for a wide range of flight conditions.

The second topic in the thesis is optimizing the aircraft trajectory. The emissions from the aircraft engine are modeled as smooth functions suitable for optimization using published certification data. These emissions are combined in different environmental indices and used as objective functions in the aircraft trajectory optimization problem. The optimization problem is formulated by discretizing the trajectory in time. The resulting large scale nonlinear optimization problem is solved using a sequential quadratic programming method. The trajectory optimization problem is first studied using a model of the Boeing 737 and the results show that the optimal trajectory depends significantly on the definition of the environmental objective function. A method to treat restricted airspace is also presented and evaluated using a model of the Swedish Air Force trainer SK60. The results show that the method for imposing airspace constraints on the flight path works well, especially when the initial point for the optimization is feasible.


Place, publisher, year, edition, pages
Stockholm: KTH, 2009. 37 p.
Trita-AVE, ISSN 1651-7660 ; 2009:45
National Category
Vehicle Engineering
urn:nbn:se:kth:diva-10958 (URN)
Public defence
2009-09-22, F3, KTH, Lindstedtsvägen 26, Stockholm, 10:15 (English)
QC 20100720Available from: 2009-09-04 Created: 2009-08-27 Last updated: 2010-07-20Bibliographically approved

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