Optimizing Aircraft Trajectories with Multiple Cruise Altitudes in the Presence of Winds

This study develops a trajectory optimization algorithm for approximately minimizing aircraft travel time and fuel burn by combining a method for computing minimum-time routes in winds on multiple horizontal planes, and an aircraft fuel burn model for generating fuel-optimal vertical profiles. It is applied to assess the potential benefits of flying user-preferred routes for commercial cargo flights operating between Anchorage, Alaska and major airports in Asia and the contiguous United States. Flying wind optimal trajectories with a fuel-optimal vertical profile reduces average fuel burn of international flights cruising at a single altitude by 1-3 percent. The potential fuel savings of performing en-route step climbs are not significant for many shorter domestic cargo flights that have only one step climb. Wind-optimal trajectories reduce fuel burn and travel time relative to the flight plan route by up to 3 percent for the domestic cargo flights. However, for trans-oceanic traffic, the fuel burn savings could be as much as 10 percent. The actual savings in operations will vary from the simulation results due to differences in the aircraft models and user defined cost indices. In general, the savings are proportional to trip length, and depend on the en-route wind conditions and aircraft types

Assessing fuel burn inefficiencies in oceanic airspace

Increasing the efficiency of aircraft operations offers a shorter term solution to decreasing aircraft fuel burn than fleet replacement. By estimating the current airspace inefficiency, we can get an idea of the upper limit of savings. Oceanic airspace presents a unique opportunity for savings due to increased separation differences vs. overland flight. We assess fuel burn inefficiency by comparing estimated fuel burn for real world flights with the estimated optimal fuel burn. For computing fuel burn, we use the Base of Aircraft Data (BADA) with corrections based on research by Yoder (2005). Our fuel burn results show general agreement with Yoder’s results. Optimal operation depends on flying 4-D trajectories that use the least amount of fuel. We decompose optimal 4-D trajectories into vertical and horizontal components and analyze the inefficiencies of each separately. We use the concept of Specific Ground Range [Jensen, 2011], to find optimal altitudes and speeds. We combine the optimal altitudes and speeds with an aircraft proximity algorithm to find pairs of aircraft in a vertical blocking situations. To find the fuel optimal horizontal track in a wind field, we use methods from the field of Optimal Control. The original problem formulation can be transformed into a Two Point Boundary Value problem which we solve using MATLAB’s bvp4c function. From our set of flights, we hypothesized a scenario where aircraft stack in such a way that they cannot climb to their optimal altitudes because of separations standards. Using aircraft positions we find when aircraft were within separation standards and were blocked from climbing or descending to their optimal altitude. We split our inefficiency results into a blocked and non-blocked set to see if blocking had an effect on mean inefficiency. Our set of flights consisted of real world flights that flew through WATRS and CEP airspace regions during the month of April 2016. Using the optimal altitude for actual flight Mach profiles, we compute a mean inefficiency of 4.75% in WATRS and 4.50% in CEP, both of which are roughly 2 to 2.5 percentage points higher than studies using proprietary performance models and data. BADA overestimates optimal altitudes, leading to an overestimate in inefficiency. Inefficiency due to off-optimal speed for WATRS is 2.18% vs. 1.86% in CEP. Blocking events result in a 2.59 percentage point increase in mean inefficiency due to off-optimal altitude in WATRS flights, and a 1.21 percentage point increase in mean inefficiency due to off-optimal altitude in CEP flights. Using wind-optimal horizontal tracks gave a 1.24% mean inefficiency in WATRS, and a 0.41% mean inefficiency in CEP. The results indicate that, in total, flights through WATRS and CEP have approximately the same inefficiency due to off-optimal altitudes, but that blocking effects are more prevalent in WATRS. In addition, flights through WATRS are farther from their wind-optimal horizontal tracks than flights in CEP

Wind optimal flight trajectories to minimise fuel consumption within a 3 dimensional flight network

This paper assesses the potential fuel savings benefits that can be gained from wind optimal flight trajectories. This question is posed on a 3 dimensional fixed flight network consisting of discrete waypoints which is representative of the size of Europe. The optimisation implements Dijkstra's shortest path algorithm to compute the minimum fuel burn route through a network and compares this to the fuel burn for the shortest distance route. Particular effort is applied to testing the repeatability and robustness of the results. This is achieved through a sensitive analysis based on a number of identified model parameters relating to the setup of the flight network. The results of this study show fuel savings between 1.0%-10.3%, and suggest that the benefits of wind optimal flight trajectories are significant

Fuel Benefit from Optimal Trajectory Assignment on the North Atlantic Tracks

The North Atlantic Tracks represent one of the highest density international traffic regions in the world. Due to the lack of high-resolution radar coverage over this region, the tracks are subject to more restrictive operational constraints than flights over the continental U.S. Recent initiatives to increase surveillance over the North Atlantic has motivated studies on the total benefit potential for increased surveillance over the tracks. One of the benefits of increased surveillance is increased accessibility of optimal altitude and speed operations over the track system. For a sample of 4033 flights over 12 days from 2014-2015, a fuel burn analysis was performed that calculates the fuel burn from optimal altitude, optimal speed and optimal track trajectories over the North Atlantic Tracks. These results were compared with calculated as-flown fuel burn in order to determine the benefit potential from optimal trajectories. Operation at optimal altitude and speed increased this benefit to 2.83% reduction potential in average fuel burn. Operation at optimal altitude alone, however, reduces the benefit potential to 1.24% reduction in average fuel burn. Optimal track assignment allows for a 3.20% reduction in average fuel burn. For the sample data, 45.1% of flights were unable to access their optimal altitude and speed due to separation requirements. Reduced separation up to 5 nautical miles can decrease the number of conflicts to 14.0%. Reducing the separation requirements both longitudinally and laterally can allow for increased accessibility of optimal altitudes, speeds and track configurations. Pilot decision support tools that increase awareness of aircraft fuel performance by integrating optimal altitude and speed configurations can also reduce aircraft fuel burn. The utility of such a tool is evaluated through a survey on pilot-decision making.This work was funded by the US Federal Aviation Administration (FAA) Office of Environment and Energy as a part of ASCENT Project 15 under Air Force Contract FA8721-05-C-0002. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the FAA or other ASCENT Sponsors

Three-Dimensional Trajectory Design for Reducing Climate Impact of Trans-Atlantic Flights

The impact of aircraft emissions and contrails on the environment adds an additional aspect to aircraft trajectory optimization. This study developed a three-dimensional trajectory optimization algorithm for trans-Atlantic flights in cruise to generate aircraft trajectories that minimize environmental impacts due to CO2 emissions and contrails in the presence of winds. The climate-optimal trajectory is developed using dynamic programming that adjusts a wind-optimal aircraft heading while determining the optimal locations, altitudes and times for en-route step climbs. Flying wind-optimal routes minimize aircraft travel time, fuel burn and associated emissions during cruise while adjusting aircraft heading and en-route step climbs at the optimal locations and times minimize climate impact of contrails. This capability integrates an air traffic management simulation with aircraft fuel burn and emissions models, contrail formation and dispersion models, simplified climate response models, and a common climate metric. A study was conducted to evaluate the potential cost and benefits of flying climate-optimal routes in North Atlantic Airspace and their impacts to the Organized Track System design based on the trans-Atlantic air traffic during a day, July 12, 2012. Results show eastbound flights achieved a larger environmental benefit with less additional fuel burn than westbound flights that operated in strong headwinds that caused more additional fuel burn and aircraft emissions to avoid traversing contrails favorable regions

Computational Approaches to Simulation and Optimization of Global Aircraft Trajectories

This study examines three possible approaches to improving the speed in generating wind-optimal routes for air traffic at the national or global level. They are: (a) using the resources of a supercomputer, (b) running the computations on multiple commercially available computers and (c) implementing those same algorithms into NASAs Future ATM Concepts Evaluation Tool (FACET) and compares those to a standard implementation run on a single CPU. Wind-optimal aircraft trajectories are computed using global air traffic schedules. The run time and wait time on the supercomputer for trajectory optimization using various numbers of CPUs ranging from 80 to 10,240 units are compared with the total computational time for running the same computation on a single desktop computer and on multiple commercially available computers for potential computational enhancement through parallel processing on the computer clusters. This study also re-implements the trajectory optimization algorithm for further reduction of computational time through algorithm modifications and integrates that with FACET to facilitate the use of the new features which calculate time-optimal routes between worldwide airport pairs in a wind field for use with existing FACET applications. The implementations of trajectory optimization algorithms use MATLAB, Python, and Java programming languages. The performance evaluations are done by comparing their computational efficiencies and based on the potential application of optimized trajectories. The paper shows that in the absence of special privileges on a supercomputer, a cluster of commercially available computers provides a good option for computing wind-optimal trajectories for national and global air traffic system studies

Benefits Analysis of Wind-Optimal Operations For Trans-Atlantic Flights

North Atlantic Tracks are trans-Atlantic routes across the busiest oceanic airspace in the world. This study analyzes and compares current flight-plan routes to wind-optimal routes for trans-Atlantic flights in terms of aircraft fuel burn, emissions and the associated climate impact. The historical flight track data recorded by EUROCONTROL's Central Flow Management Unit is merged with data from FAA's Enhanced Traffic Management System to provide an accurate flight movement database containing the highest available flight path resolution in both systems. The combined database is adopted for airspace simulation integrated with aircraft fuel burn and emissions models, contrail models, simplified climate response models, and a common climate metric to assess the climate impact of flight routes within the Organized Track System (OTS). The fuel burn and emissions for the tracks in the OTS are compared with the corresponding quantities for the wind-optimized routes to evaluate the potential environmental benefits of flying wind-optimal routes in North Atlantic Airspace. The potential fuel savings and reduction in emissions depend on existing inefficiencies in current flight plans, atmospheric conditions and location of the city-pairs. The potential benefits are scaled by comparing them with actual flight tests that have been conducted since 2010 between a few city-pairs in the transatlantic and trans-pacific region to improve fuel consumption and reduce the environmental impact of aviation

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance vary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are: (1) determining what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major u.s. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort-topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimality with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider unmodelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance x,ary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are (1) determining, what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major U.S. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimility with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider un-modelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented

Climate related air traffic management. Final report. Assessing the role of air traffic management in reducing environmental impacts of aviation

Climate related air traffic management. Final report. Assessing the role of air traffic management in reducing environmental impacts of aviatio