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Wind-Optimal Trajectories for Multirotor eVTOL Aircraft on UAM Missions

Distributed electric propulsion powered electric vertical takeoff and landing aircraft are expected to enable urban air mobility. Low specific energy of onboard lithium-ion polymer batteries and wind conditions impose constraints on flight endurance. Therefore, from the safety and efficiency perspective, planning and flying minimum energy trajectories are important.The primary motivation for this paper is to determine if there is an operational benefit to flying wind-optimal trajectories for short flights (less than 60 miles) in the urban environment. This study employs wind-optimal trajectories for a NASA-proposed conceptual multirotor aircraft flight in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the trajectory. The optimal control problem is numerically solved using the direct method. Energy consumption and flight duration flying wind-optimal trajectories between origins and destinations in a metropolitan area are compared with energy consumption and flight duration flying on the great-circle paths between the same origin and destination pairs to determine the operational benefit of wind-optimal routing for short flights.The flight duration results for different scenarios are validated using a simulation tool designed and developed by NASA for exploring advanced air traffic management concepts. In summary,this research study suggests that for short flights in an urban environment, the wind-optimal trajectories have a very slight (insignificant) operational advantage over the great-circle trajectories in terms of energy consumption and flight duration. As expected, headwinds and tailwinds along the route of flight have a significant impact on energy consumption and flight duration.

Urban Air Mobility↗

NASA NTRS2016

Conflict Resolution for Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace with Wind Uncertainties

Air traffic in the North Atlantic oceanic airspace (NAT) experiences very strong winds caused by jet streams. Flying wind-optimal trajectories increases individual flight efficiency, which is advantageous when operating in the NAT. However, as the NAT is highly congested during peak hours, a large number of potential conflicts between flights are detected for the sets of wind-optimal trajectories. Conflict resolution performed at the strategic level of flight planning can significantly reduce the airspace congestion. However, being completed far in advance, strategic planning can only use predicted environmental conditions that may significantly differ from the real conditions experienced further by aircraft. The forecast uncertainties result in uncertainties in conflict prediction, and thus, conflict resolution becomes less efficient. This work considers wind uncertainties in order to improve the robustness of conflict resolution in the NAT. First, the influence of wind uncertainties on conflict prediction is investigated. Then, conflict resolution methods accounting for wind uncertainties are proposed.

wind uncertainties↗

NASA NTRS2022

Wind-Optimal Lateral Trajectories for a Multirotor Aircraft in Urban Air Mobility

The primary motivation for this paper is to quantify the operational benefits (energy consumption and flight duration) of flying wind-optimal lateral trajectories for short flights (less than 60 miles) anticipated in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the lateral trajectory. The optimal control problem is numerically solved using the direct collocation method. Energy consumption and flight duration flying wind-optimal lateral trajectories are compared with corresponding values obtained flying great-circle paths between the same origin and destination pairs to determine the operational benefits of wind-optimal routing for short flights. The flight duration results for different scenarios are validated using a simulation tool designed and developed at NASA for exploring advanced air traffic management concepts. This research study suggests that for short flights in an urban environment, operational benefits of the wind-optimal lateral trajectories over the corresponding great-circle trajectories in terms of energy consumption and flight duration per flight are dependent on: i) wind field’s spatial variability, ii) wind magnitude, iii) the direction of route relative to the wind field, and iv) cruise segment length. The operational benefits observed in realistic flyable wind scenarios are less than 2.5%; these could be translated to an equivalent of a maximum of 2 min of cruise flight duration savings in the urban air mobility environment. As expected, headwinds and tailwinds along the flight route most significantly impact energy consumption and flight duration.

Wind-Optimal Trajectory, Lateral Path, Urban Air M↗

NASA NTRS2016

Deconflicting Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace

North Atlantic oceanic airspace accommodates more than 1000 flights daily, and is subjected to very strong winds. Flying wind-optimal trajectories yields time and fuel savings for each individual flight. However, when taken together, these trajectories induce a large amount of potential en-route conflicts. This paper analyses the detected conflicts, figuring out conflict distribution in time and space. It further describes an optimization algorithm aimed at reducing the number of conflicts for a daily set of flights on strategic level. Several trajectory modification strategies are discussed, followed with simulation results. Finally, an algorithm improvement is presented aiming at better preserving the trajectory optimality.

wind-optimal trajectories↗

NASA NTRS2010

Aircraft Trajectory Optimization and Contrails Avoidance in the Presence of Winds

There are indications that persistent contrails can lead to adverse climate change, although the complete effect on climate forcing is still uncertain. A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectories are developed by solving a non-linear optimal control problem with path constraints. The regions of airspace favorable to persistent contrails formation are modeled as penalty areas that aircraft should avoid and are adjustable. The tradeoff between persistent contrails formation and additional fuel consumption is investigated, with and without altitude optimization, for 12 city-pairs in the continental United States. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a two percent increase in total fuel consumption can reduce the total travel times through contrail regions by more than six times. Allowing further increase in fuel consumption does not seem to result in proportionate decrease in contrail travel times.

Ng, Hok K.↗

NASA NTRS2010

Concepts and Challenges for Environmentally Friendly En Route Operations

A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectory is derived using Singular Perturbation Method. The regions of airspace favorable to persistent contrails formation are modeled as high-risk areas that aircraft should avoid and are adjustable. The tradeoffs between persistent contrails formation and additional travel time are investigated for wind-optimal trajectories and various contrails-avoidance trajectories at 10 different cruising altitudes for flights departing from Chicago and San Diego to New York. The additional travel times required for avoiding 100% persistent contrails formation at various flight altitudes ranged from approximately 0% to 4.3% for flights from Chicago to New York. For flights between San Diego and New York, additional traveling times vary between 1.3% and 5% depending on the cruise altitude and the percentage of contrail avoidance. Talk will present the results of aircraft fuel consumptions that are proportional to the travel time for cruising aircraft.

Sridhar, Banavar↗

NASA NTRS2011

Cross-Polar Aircraft Trajectory Optimization and Potential Climate Impact

Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flightplan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135 and 105 minutes persistent contrail formation per flight during a day with medium and high contrail formation, respectively.

Sridhar, Banavar↗

NASA NTRS2011

Cross-Polar Aircraft Trajectory Optimization and the Potential Climate Impact

Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flight plan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135 and 105 minutes persistent contrail formation per flight during a day with medium and high contrail formation, respectively.

Ng, Hok K.↗

NASA NTRS2015

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 NASA’s 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.

Ng, Hok K.↗

NASA NTRS2015

Strategic Planning of Efficient Oceanic Flights

The efficiency of oceanic flights is low due to limited navigational and communication equipment, congestion and airspace restrictions. The availability of Automated Dependent Surveillance-Broadcast (ADS-B) and other improvements provides opportunity for better strategic planning of trajectories. Transatlantic flights between US and Europe constitute one of the busiest oceanic airspace regions in the world. This paper examines the benefits of a wind-optimal trajectory concept with a strategic de-confliction component compared to the current flight planning using the North Atlantic Tracks. The methodology generates a wind-optimal route for each aircraft and a strategic reduction in the potential conflicts between aircraft by a combination of small adjustments to departure times and rerouting. The de-confliction is achieved by optimization techniques involving simulated annealing with local gradient searching. The fuel burn for the tracks in today's Organized Track System are compared with the corresponding quantities for the wind-optimized routes to evaluate the potential benefits of flying wind-optimal routes in North Atlantic Airspace. The analysis is based on air traffic between US and Europe during July 2012. The potential fuel savings depend on existing inefficiencies in current flight plans, atmospheric conditions and location of the city-pairs. The paper provides both aggregate results and detailed examination of some of the most popular city-pairs. Results show that strategic planning can improve the efficiency of flight trajectories by 3 to 5 depending on city-pairs and aircraft type. This translates into a potential fuel savings in the range of (420-970) kg per flight for a Boeing 767-300, the most widely used aircraft between the city-pairs in this study.

oceanic operations↗

NASA NTRS2016

Strategic Design of Long-Haul and Oceanic Aircraft Trajectories in Aviation Operations

Long-Haul Aircraft consume most of their fuel during the cruise phase of flight. The inefficiency in cruise flights compared to efficient routes varies is around 3 to 4. The efficiency of oceanic flights is low due to limited navigational and communication equipment, congestion and airspace restrictions. The availability of Automated Dependent Surveillance-Broadcast (ADS-B) and other improvements provides opportunity for better strategic planning of trajectories. Transatlantic flights between US and Europe constitute one of the busiest oceanic airspace regions in the world. This talk examines the benefits of a wind-optimal trajectory concept with a strategic de-confliction component compared to the current flight planning using the North Atlantic Tracks. The analysis is based on air traffic between US and Europe during July 2012. The potential fuel savings are in the range of (420-970) kg per flight for a Boeing 767-300, the most widely used aircraft between the city-pairs in this study. The talk also describes a global simulation of aviation operations combining flight plans and real air traffic data with historical commercial city-pair aircraft type and schedule data and global atmospheric data. The resulting capability extends the simulation and optimization functions of NASAs Future Air Traffic Management Concept Evaluation Tool (FACET) to global scale. This new capability is used to characterize the evolution of global air traffic, analyze fuel savings and seasonal variations in the long-haul wind-optimal traffic patterns in six major regions of the world.

strategic trajectory design↗

NASA NTRS2014

Annualized TASAR Benefits for Virgin America Operations

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Virgin America. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that about 25,000 gallons of fuel and about 2,500 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Virgin America in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Virgin America TASAR requests peaked at two to four requests per hour per sector in high-altitude Oakland and Salt Lake City center sectors east of San Francisco.

Source record↗

NASA NTRS2015

Annualized TASAR Benefit Estimate for Virgin America Operations

Henderson, Jeffrey↗

NASA NTRS2014

Traffic Aware Strategic Aircrew Requests (TASAR)

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Alaska Airlines. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that between 8,000 and 12,000 gallons of fuel and 900 to 1,300 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Alaska Airlines in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Alaska TASAR requests peaked at four to eight requests per hour in high-altitude Seattle center sectors south of Seattle-Tacoma airport..

Wing, David J.↗

NASA NTRS2015

Annualized TASAR Benefit Estimate for Alaska Airlines Operations

The Traffic Aware Strategic Aircrew Request (TASAR) concept offers onboard automation for the purpose of advising the pilot of traffic compatible trajectory changes that would be beneficial to the flight. A fast-time simulation study was conducted to assess the benefits of TASAR to Alaska Airlines. The simulation compares historical trajectories without TASAR to trajectories developed with TASAR and evaluated by controllers against their objectives. It was estimated that between 8,000 and 12,000 gallons of fuel and 900 to 1,300 minutes could be saved annually per aircraft. These savings were applied fleet-wide to produce an estimated annual cost savings to Alaska Airlines in excess of $5 million due to fuel, maintenance, and depreciation cost savings. Switching to a more wind-optimal trajectory was found to be the use case that generated the highest benefits out of the three TASAR use cases analyzed. Alaska TASAR requests peaked at four to eight requests per hour in high-altitude Seattle center sectors south of Seattle-Tacoma airport.

Henderson, Jeffrey↗

NASA NTRS2016

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 feasible approach for national and global air traffic system studies.

global air traffic optimization↗

NASA NTRS2021

Small UAV Flight Planning in Urban Environments

This work proposes a fast algorithm for generating obstacle-free and wind-efficient flight paths at a constant above-ground-level altitude in urban environments because a fast flight path planning algorithm is an essential function or service needed for enabling small unmanned aerial vehicle (sUAV) to operate in urban environments within Class G airspace. The proposed method first converts the 3D path planning problem to a 2D problem by constructing an obstacle map at a given above-ground-level altitude. A quad-tree decomposition is then used to build a search space in terms of obstacle occupancy and wind difference. The wind cost of traveling through each cell is defined based on energy consumption under various wind conditions. A repulsive potential is also adopted to make sure that the flight plans stay away from obstacles. The Theta* search algorithm, a variant of A* algorithm, is applied to mitigate the path angle change constraints introduced by grid-based graphs. With the Theta* and postsmoothing techniques, an obstacle-free, wind efficient, and constant above-ground-level flight plan can be quickly generated for sUAV operations in urban environments while meeting the lateral path angle constraints. The results showed that the path planning algorithm is efficient and can be finished within several seconds. With a proper choice of wind coefficient, the proposed path planning algorithm outperforms the multiple-shooting trajectory optimization method even in an obstacle-free environment. With the flexibility of incorporating other geo-related costs and computation efficiency, the proposed algorithm shows the potential for real-time flight path planning in complex urban environments.

Path planning↗

NASA NTRS2019

Using Wind Observations from Nearby Aircraft to Update the Optimal Descent Trajectory in Real-Time

The ability to meet a controlled time of arrival during a continuous descent operation will enable environmentally friendly and fuel efficient descent operations while simultaneously maintaining airport throughput. However, if the wind forecast used to compute the initial trajectory plan is not accurate enough, the guidance system will need to correct time deviations from the plan during the execution of the descent. Previous work proposed an on-board guidance strategy based on model predictive control, which repeatedly updates the trajectory plan in real-time from the current aircraft state and for the remainder of the descent. However, the wind conditions downstream, at altitudes not explored yet, were difficult to predict due to the lack of data. This paper shows the potential benefits of using wind observations, broadcast by nearby aircraft, to reconstruct the wind profile downstream. The wind profile in the trajectory optimization problem is modeled as a spline, which control points are updated to fit the observations before re-planning the trajectory. Results from simulations using realistic wind data show that the performance of model predictive control significantly improves when including up-to-date wind observations, in terms of time and energy errors at the metering fix and fuel consumption.

Dalmau, Ramon↗