En route air traffic optimisation to reduce environmental impact

Air traffic delays due to congestion in the National Airspace System (NAS) are a source of unnecessary cost to airlines, passengers, and air transportation dependent businesses. Congestion is estimated to cost the aviation industry, passengers, and shippers approximately $10 billion per year. This cost can be further segregated into a $6 billion impact upon direct airline operating costs and a $4 billion impact upon the value of collective passenger time.

Delays also have an environmental cost. Because of congestion, aircraft are often forced to deviate from the optimal cruise altitudes and/or fuel-efficient cruise speeds for which they are designed. Such sub-optimality results in unnecessary fuel burn and gaseous emissions that may have an impact on the global environment, especially as they are being deposited into the higher reaches of the atmosphere.

The significant magnitude of air traffic delays in the summer of 2008 is an indication that the current air traffic control infrastructure is having difficulties even handling current traffic levels. Given the growth forecast in aviation over the next decade and growing fleet mix, in particular the introduction of very light jets – which cruise at the same altitude as commercial jets but have drastically different cruise speeds – there is an urgent need for air traffic control decision-support, or for automation tools to address the problem of congestion in the NAS.

Over the past three years, The Partnership for AiR Transportation Noise and Emissions Reduction (PARTNER), a U.S. Federal Aviation Administration Center of Excellence, has supported research at the Georgia Institute of Technology’s Air Transportation Laboratory, to develop and evaluate optimisation tools that can be used by en route air traffic controllers to relieve congestion. More specifically, these tools include mathematical models for determining the set of conflict-free optimal trajectories that have the minimum economic and environmental costs for en route aircraft.

The potential benefits of this approach to conflict resolution was demonstrated in computational studies, where the proposed algorithms were used to manage an entire day of traffic at a single flight level in the Cleveland Air Route Traffic Control Center, one of the most congested airspaces in the United States, and then compared to the historical traffic flow.

En route traffic optimisation algorithm

The objective of the optimisation programme that has been developed is to minimise fuel burn, and thereby the resulting costs and environmental impacts. However, the first task of any en route tactical optimisation model is to ensure safe aircraft separation. Safety requirements are considered as hard constraints that must be maintained. Once safety requirements are met, then it is possible to optimise over any cost function.

A conflict in air traffic occurs when two or more aircraft encroach the minimum required separation, as defined by the regulator. For en route traffic, aircraft are required to maintain a minimum of 5 nautical miles separation. Once a conflict is detected, it is resolved by changing the flight plan of one or more aircraft so that the minimum separation requirements are satisfied, while still allowing for conflict-free travel from entrance to exit of an airspace.

As an example, consider a set of aircraft as shown in Figure 1. Aircraft are defined by initial positions and velocities (i.e. airspeed and heading), where changes to their velocities are made to avoid conflict. Additionally, all aircraft are identified to be a particular model type with corresponding fuel burn characteristics for the given altitude. (Sample “fuel burn curves” at 33,000 ft (FL330) for three different types of aircraft are shown in Figure 2). Fuel costs are scaled such that a value of one corresponds to the minimum fuel burn level for the given aircraft type. The goal is to assign each aircraft a single instantaneous heading and speed change at a set time that provides conflict-free travel, while minimising a measure of the fuel burn costs over all the trajectories. In this regard, a static conflict resolution algorithm is resolved iteratively in time to dynamically create conflict-free trajectories for aircraft.

Given our goal of providing a framework in which fuel costs are considered in conflict resolution and aircraft routing, an appropriate cost function is defined as the sum of two nonlinear scalar functions of the airspeeds and headings of the aircraft. The first function measures the fuel burn percentage of an aircraft, while the latter accounts for the increase in distance travelled due to heading changes. Considering both parts, the overall cost function is the fuel consumption percentage increase when compared to the optimal path with no obstacles.

However, this representation results in complex nonlinear functions of the decision variables, which makes optimisation difficult to implement, especially when considering groups of aircraft. As part of the research at the ATL, tight convex linear approximations for these functions have been developed. These allow for the underlying optimisation problem to be modelled as a mixed integer linear programme, which can be solved in near-real time, allowing the optimisation model to be useable by air traffic controllers.

Case-study results

To quantify the benefits of the optimisation programme, it was implemented in a receding horizon platform for en route traffic under realistic conditions. Through a series of considerations of the fuel burn and distance travelled by each aircraft, the proposed solution is both able to route aircraft through conflict-free trajectories and able to do so in a manner that reduces the overall fuel burn of the aircraft travelling through the centre.

In the study, the estimated fuel consumption for a portion of traffic in the Cleveland centre, under standard air traffic control, is compared with an estimate of the fuel consumption when aircraft trajectories were determined using the optimisation programme detailed above. Cleveland Centre was selected for the simulation because it contains a significant portion of the en route traffic in the United States. In particular, there is significant coast to coast traffic with frequent weather disruptions. A 24-hour period of west-bound air traffic at flight level 36,000 ft over Cleveland was simulated and analysed. The day selected, Sunday, May 1, 2005, represents a nominal day in the NAS; i.e. there were no significant weather patterns or delays in the United States on that day.

The traffic flow into the centre throughout the day is shown in Figure 3. Peak periods of traffic are between 14-24 hours. During this time period, a maximum of 22 aircraft are observed at FL36 within the centre. For the most part, heavy traffic yields between 14-20 aircraft at the flight level at any given time.

The aircraft represented include a broad spectrum of models: wide body, narrow body, regional and business class jets. As shown in Figure 4, narrow body aircraft represent the largest portion of aircraft, followed by regional jets. The diversity of aircraft demonstrates the need to consider fuel burn curves for each model of aircraft, especially when one considers that each aircraft’s optimal operating air speed varies from one aircraft to another. Hence, conflict resolution algorithms that assume equal airspeed for all aircraft will incur significant fuel consumption because aircraft will not be able to operate at their optimal air speed. Additionally, use of the fuel burn curves provides a quantifiable measure for the optimisation that may not be consistent between aircraft. For example, consideration of only speed deviations from the optimal speed in the cost, might lead to unfair solutions. An aircraft flying at 10 knots faster than its optimal speed may increase its fuel burn by 5%, while another aircraft would only increase its fuel burn 1%. Sample fuel curves are provided in Figure 2 on page 39 for three types of aircraft.

The simulation modelling attempts to make a fair comparison between the two fuel consumption estimates. The process first requires that Enhanced Traffic Management System (ETMS) data flight trajectories are filtered, to extract en route data over the Cleveland centre at FL36. Fuel consumption curves for each aircraft were generated by making use of the Base of Aircraft Data (BADA). While the models used for each aircraft and associated parameters are not exact, they represent the standard in estimating fuel consumption of airplanes. Furthermore, in terms of the sensitivity of the model, because the programme works to minimise deviations from a direct routing, the solutions approach a shortest path solution, which always produce the most fuel efficient path.

Simulations were performed on the flights described above, and comparisons of fuel consumptions were made between the observed trajectories and the trajectories suggested by the solutions of the algorithm.

The savings that can be achieved by the implementation of the proposed algorithm are summarised in Figure 5. In the two histograms provided, the reduction in distance travelled with respect to the observed trajectories is displayed both in terms of nautical miles and percentages. It is important to note that the trajectories suggested by the algorithm are always at least as good as the observed trajectories, with an average saving of around nine nautical miles. Furthermore, as shown in Figure 6 on page 41, the average speed suggested by the solution of the algorithm is always near-optimal. Hence, almost all aircraft travel at their optimal airspeeds through the use of the algorithm, making potential savings clear.

In Figure 7 on page 41, it is shown that if historical observed speeds are to deviate from the optimal speeds, then the savings from the algorithm will increase significantly. If all aircraft decrease their speed 10% or 15% below optimal, then the lower bound on the system savings is 3.37% and 6.13%, respectively. In fact, the results demonstrate that the fuel system saving is at least 1.4%, under the assumption that all aircraft in the observed data travel their routes at fuel optimal speeds. For aircraft that completely traverse the centre at distances greater than 350NM – representing 24% of all flights – the lower bound on the fuel savings is 2.1%. It can be safely assumed that fuel savings are probably greater than these bounds.

A scatter plot of individual aircraft is shown in Figure 8, relating the total distance travelled to the savings achieved by the proposed algorithm. As expected, the effectiveness of the algorithm increases significantly with the travel distance. Finally, Figure 9 contains two plots comparing the historical observed trajectories of sample aircraft with the corresponding trajectories in the solution. In some cases, especially when the flight distances are short, the solutions are similar to the observed values, while at other times significant savings are observed.

Overall, it is shown that the developed mathematical model and solution algorithm results in efficient conflict resolution procedures, which minimise the fuel burn and imply reduced environmental impact due to en route air traffic. Moreover, such optimal solutions can be obtained in near-real time, enabling the implementation of the developed procedures even for very high volumes of traffic.

En Route Traffic Optimisation to Reduce Environmental Impact is Project 5 of the Partnership for AiR Transportation Noise and Emissions Reduction. PARTNER is an aviation cooperative research organisation, and an FAA/NASA/Transport Canada-sponsored Centre of Excellence. PARTNER fosters breakthrough technological, operational, policy, and workforce advances for the betterment of mobility, economy, national security, and the environment. The organisation’s operational headquarters is at the Massachusetts Institute of Technology. For more information on PARTNER and all of its projects, visit www.partner.aero.

Figure 1: Aircraft are defined by initial positions and velocities

Figure 2: Sample fuel curves for aircraft at FL330

Figure 3: Traffic flow into Cleveland Centre throughout May 1, 2005

Figure 4: Traffic flow into Cleveland Centre by aircraft type

Figure 5: Histograms for absolute and % reduction in NM travelled

Figure 6: Histograms for absolute and % difference in average speed from optimal speed

Figure 7: Percent fuel savings from the algorithm will increase significantly if observed speeds in the historical data are to deviate from the optimal speeds

Figure 8: Scatter plot showing the relationship between distance saving and distance travelled

Figure 9: Sample observed and suggested conflict-free trajectories - straighter lines represent the suggested trajectories