On trajectory optimisation for the reduction of fuel burn and emissions

Abstract

The air transport industry presently depends entirely on fossil fuels and primarily on gas turbine technology for propulsive means. This implies that every flight contributes to the usage of a finite energy resource, to the emission of green-house gases and secondary emissions (mainly nitrous oxides), and also to noise pollution. However, the matter of environmental impact is being addressed through several initiatives which are being undertaken to reduce the use and dependency of air transport on fossil fuel resources. These initiatives include, but are not limited to, the use of alternative sources of fuels, improvements in aerodynamics, reduction in structural weight, improvements in engine technologies and operation of the vehicle. The latter is of particular interest since, while all other factors contribute significantly towards the general aims, environmental considerations are only complete when the way the vehicle is operated is taken into account, as this also significantly affects the impact on the environment. Traditionally, in operation, fuel efficiency has been achieved through flying at high altitudes where lower air densities allow aircraft to fly faster. While this sufficed in the past, currently there is a drive towards the development of techniques and technologies that enable the aircraft to fly more efficiently with minimal impact on operational procedures. In particular, the focus is on flying the most efficient routing, operating the most fuel efficient speed, and operating the most fuel efficient altitude. The industry has to date predominantly addressed these areas through the introduction of the Cost Index (Cl) function, the execution of Continuous Descent Approaches (CDAs), and by reducing the track miles of arrival and approach routes. Whilst these initiatives are important and significant steps towards flying truly optimal flight profiles, by identifying operational limitations, the gap between what they can achieve and the theoretical optimal can be narrowed further through additional development. A major limitation of the Cl and CDA concepts is the sensitivity of the optimal flight profile to dynamic (tactical) conditions such as unexpected variations in weather (winds, temperature, turbulence, etc), and ATC constraints (unplanned tactical traffic separation requirements). These can have a very significant impact on the optimal four-dimensional (4D) path an aircraft should follow. Over the course of a long flight, conditions can change significantly, and the predeparture flight plan, which might incorporate Cl and CDA concepts, may no longer be valid. This often results in re-planning being far from selecting the optimal profile for the new operating conditions and constraints. This is generally because re-planning will tend to focus on satisfying the new constraints in the simplest of manners, and tools for identifying the optimal modifications in the 4D trajectory are not used, or are not available. Availability and use of such tools, therefore, would enable more efficient flights to be flown following tactical replanning, which in practice can mitigate a major obstacle in achieving more efficient flights. Optimal flight path replanning tools can conceptually be deployed in two operational environments, namely airborne or on the ground. In the former, such tools would be used by the flight crew in their replanning tasks and would typically reside either within the FJVIS or the Electronic Flight Bag (EFB). In the latter solution, they could equip airline operations centres or air traffic control. This research addresses the above considerations by focusing on the development of aircraft trajectory algorithms that are suited both for strategic and for tactical use. In the former, a collection of algorithms that employ pseudospectral techniques and non-linear programming was developed. These algorithms, collectively named TRAOPT, are intended for strategic use, to be used to generate better pre-flight plans. Since pseudospectral techniques are inherently single-objective, a novel scalarisation method referred to as the adaptive bi-section e-constraint method was developed to add bi-objective optimisation capability. The potential benefit of using TRAOPT for strategic flight planning was quantified through the optimisation of a set of recorded trajectories, namely, a climb, and a descent, both incorporating a cruise phase. Through this exercise it was deduced that by maintaining the same flight time of a typical climb or descent, while optimising the speed-altitude schedule, fuel gains in the range of 50 kg to 90 kg could be achieved. This is also equivalent to a reduction of around 150 kg to 300 kg in CO2 emissions. With flight time flexibility, further gains could be achieved. In the latter, the research focussed on simplifying the computationally intensive algorithms in TRAOPT to pave the way for their deployment in FMSs for better online tactical flight re-planning. This led to the development of the fast optimal trajectory generator, FOTG. The fast algorithms were developed through the analysis of a substantial number of trajectory optimisation problems solved using TRAOPT. The analysis of the solutions led to the derivation of distinctive optimal flight strategies which were exploited to develop a set of deterministic algorithms, that do not rely on optimisation theory, which are able to generate optimal trajectories with comparable accuracy to that obtained by TRAOPT, in a fraction of the computational time and complexity. Moreover, since the algorithms are deterministic, and therefore guarantee an optimal solution in a quantified number of computational steps, FOTG does not suffer from certification issues.