International Transportation (68) 1 | 2016 40 Photo: Pixabay Multi-objective trajectory optimization Modern trajectory optimization afects more criteria than-fuelburn and time of light Air traic management, trajectory optimization, trajectory assessment, aviation environmental impact, contrails Today, the air traic industry is confronted with demands and goals, aiming conlicting optimization criteria. Airlines minimize fuelburn and time of light, whereas public environmental consciousness increases faster than the technical progress in the reduction of the engine emissions. Furthermore, airlines are facing an increased worldwide demand and an already limited air traic capacity. Here, the required development and assessment of optimized trajectories with multi-criteria target functions is introduced. Authors: Judith Rosenow, Stanley Förster, Martin Lindner, Hartmut Fricke T he air traic system is faced with many challenges, which are sometimes subject to strong dynamic luctuations. Beside a growing annual volume of air traic and a highly competitive and cost-driven market, there is an urgent need for environmentally sustainable transport services. Therewith, air carriers are in many ways restricted in their freedom to operate. That is why the European Commission founded the Single European Sky (SES) program to restructure the European air space with the objective of optimizing air traic to increase the eiciency of the European air traic [1]. The Single European Sky ATM Research (SESAR) program has been set up to harmonize the interests of all air traic stakeholders and develop the implementation of the SES objectives [2], which are aiming to secure a sustainable development of the European air trafic sector. Besides the triplication of capacity, the increase of safety by a factor of 10 and the decrease of air traic management costs by 50 %, the environmental compatibility of each light is to be reduced by 10 %. For these targets, air traic performance is measured and validated with the help of key performance indicators (KPI) [3], deining special target values of the performance of the air traic system. The research project MEFUL (Minimizing the emissions in operational light with guaranteed operational safety as contributing to an environmentally friendly air transport system) of the Chair of Air Transport Technology and Logistics at Technische Universität Dresden develops and applies KPIs considering cost indicators (CI), environmental performance indicators (EPI) and safety perfor- SCIENCE & RESEARCH Aviation International Transportation (68) 1 | 2016 41 Aviation SCIENCE & RESEARCH mance indicators (SPI) for an optimization of the air traic system from a single trajectory up to a complete airline network using an appropriate weighting. This weighting is realized by translating the EPIs into costs and by complying with all safety regulations. Thereby, optimal trajectories that balance the conlicting goals given by completely diferent KPIs can be identiied. Even among the EPI there are conlicting objective functions regarding an optimized trajectory. Fuel-driven emissions are minimized at high cruising altitudes (around 12 km altitude, FL 390) and a steep climb gradient, whereas nitric oxide emissions are minimized at lower cruising altitudes (around 9 km altitude, FL 290) and a shallow climb gradient lown with reduced thrust. Furthermore, the ambient atmospheric conditions are strongly inluencing the optimization. For example, the formation of condensation trails (contrails) is primarily driven by weather conditions and mostly conined to a small region in the atmosphere, which should be avoided by air traic. Here, an example of trajectory optimization under realistic weather conditions is shown considering direct operating costs, fuelburn costs and environmental costs including contrail formation. Trajectory optimization For trajectory optimization, a light performance model and a lateral pathinding algorithm are used iteratively by the simulation environment TOMATO (TOolchain for Multicriteria Aircraft Trajectory Optimization) deining the input parameters for both models and assessing the trajectories regarding the KPIs. The weather scenario used is taken from grib2 (GRIdded Binary) data, provided by the National Weather Service NOAA [4]. Figure 1 shows the iterative worklow and the interactions between input data, pathinding module and light performance model, as well as the trajectory assessment within TOMATO. The input parameters are deined by weather data, city pairs and aircraft type together with information on the airspace structure and cost charges. On this basis, the pathinding module calculates the lateral trajectory at cruising altitude, considering the global target function of the optimization (e. g. minimum costs). The calculated route, the weather data and the aircraft and engine type is used by COALA to estimate the vertical trajectory considering the given cruising altitude. Additionally, COALA quantiies engine emissions. Using the KPIs, TOMATO calculates the length of time of contrail formation as well as all cost components and evaluates the trajectory. During the next iteration, TOMATO adjusts the input parameters for the pathinding module and for COALA to iteratively converge to an optimal trajectory. Trajectory calculation The vertical trajectory optimization is done by an aircraft performance model COALA (COmpromized Aircraft performance model with Limited Accuracy) for an Airbus A320 aircraft with two CFM56-5A3 engines (111.2 kN, each) based on the integration of the dynamic equation as a result of light mechanics allowing for the loss of aircraft mass due to fuel low. Take-of is realized with 100 % thrust, which is reduced after three minutes and followed by a continuous climb operation (cco). The target true air speed at cruising altitude is derived from an extremum estimation of the speciic range under consideration of the diferent boundary conditions (i.e. diferences in temperature and density gradient). For descent, continuous descent operations (cdo) with idle thrust and a true air speed for a maximum lift/ drag angle during gliding light are calculated as proposed by Kaiser [5] and Scheiderer [6]. The target functions of true air speed for the diferent light phases are used as controlled variable by using a proportional plus integral plus derivative controller (PID controller). Maximum thrust during cruise and climb, the drag coeicient and the fuel low are calculated using BADA by EUROCONTROL [7]. The trajectories correspond to recommended light proiles (see ICAO [8]) with a climb gradient of 1,000 feet per nautical mile and a descent gradient in the range of 300 feet per nautical mile. Unsteady light attitudes are considered during take-of and climb and are optimized with respect to minimum forces of acceleration in the vertical and horizontal direction. Conditions of contrail formation Condensation trails are ice particles that develop at light level from condensed water vapor emitted by the aircraft [9]. The water condenses on soot particles that are also emitted by the aircraft. For contrail formation, the ambient atmosphere has to be cold enough to counterbalance the exhaust heat, which works against condensation. The threshold temperature can be derived from the Schmidt-Appelman criterion [10], [11]. Under these conditions, contrails will live for about 100 s until the complete evaporation of the ice particles [9]. However, in an ice-supersaturated ambient atmosphere (ISS) (that means a relative humidity with respect to ice more than 100 %, which is possible due to missing activated ice nuclei at light level), contrails will form into longlived artiicial cirrus clouds, which are also called persistent contrails [12]. In the Earth atmosphere energy budget, contrails act like a barrier [13], [14]. They scatter incoming shortwave solar radiation back to the sky and they absorb and re-emit outgoing longwave terrestrial radiation back to the Earth’s surface. The contribution of a contrail on this extinction of radiation is called radiative forcing (RF) and measured in watts per square meter [19]. Trajectory assessment The developed optimization objectives can be grouped into two categories. 1) direct operating and delay costs, and 2) environ- › TOMATO Simulation Environment Path finding module COALA performance model Output Total costs: Fuel costs Operating and delay costs External environmental costs Input City pairs Input Weather data Optimized trajectory: Time, Latitude, Longitude Input Airspace structure and restricted areas Cost charges and parameters RH % Input Aircraft and engine performance data Emissions parameter KPI Assessment Figure 1: Workflow of trajectory optimization and assessment with TOMATO International Transportation (68) 1 | 2016 42 SCIENCE & RESEARCH Aviation mental costs due to the environmental impact of engine emissions. Furthermore, costs due to contrail formation will be discussed. The direct operating costs (DOC), i.e. fuelburn, staf and maintenance costs, are used for trajectory optimization since they are clearly linked to a single light event. Fuel costs make up the biggest share of DOC components, accounting for 25 to 30 % of DOC. Currently, the price of jet fuel is comparatively low and set to EUR 0.39 per kilogram following the average of IATA fuel price monitor for the year 2016 [15]. Staing costs are time-dependent and also a major constituent of DOC. For each light crew member, costs of EUR 1.6 per minute, and for each cabin crew member EUR 0.7 per minute are assumed based on surveys [16]. Maintenance, insurance and aircraft depreciation costs are also timedependent and investigated in some studies [16] [17], which are used here to calculate a cost rate depending on aircraft passenger capacity. To factor in the costs for air traic control, charges of en-route and terminal navigation services, the principles of EURO- CONTROL are applied. Both service charges are calculated similarly and for each local charging zone an individual rate or a European average of EUR 50.61 is used. Airport handling and dispatching fees, representing a 15 % share of DOC, as well as indirect operating costs have no inluence on trajectory optimization and are not considered in this study. In case of a delayed aircraft, the timedependent cost factors are signiicantly higher (e.g. compensation for misconnected passengers). In such a case the airline may decide to incur higher speed and fuel costs to reduce delay costs. For each delay minute, additional costs of EUR 2.34 for pilots and EUR 1.02 for cabin crew members are assumed and the maintenance rate for cost calculation is increased by 30 %. On average, soft and hard costs for delayed passengers of EUR 0.2 per delayed minute and passenger are assumed, as long as delay is less than 15 min [16]. Per kilogram of kerosene burned, an aircraft engine emits on average 3160 g carbon dioxide CO 2 , 1240 g water vapor H 2 O, 14 g nitric oxides NO x , 0.025 g soot [18]. Each of these emission types and the contrails contribute to global warming and are quantiied within a speciic EPI. The impact of an EPI on global warming is assessed by the Global Warming Potential (GWP) [18], a measure of the relative efect of the greenhouse gas impact compared to the impact of CO 2 . As global climate analyses [18] have shown, 10 % [20] of the total number of lights in 2005 contributed to global warming due to contrail formation as much as 21 % of the total aviation CO 2 emissions in the same year. This means for MEFUL: Contrails are expensive and must be considered carefully. The CO 2 -equivalent emissions can be converted into costs using the Emission Trading System (ETS), which is a powerful tool for translating the environmental impact of emissions into cost functions and thus into objective functions within the trajectory optimization. Using the ETS, companies purchase tradable emission allowances, also called EU Allowance (EUA). One emission allowance corresponds to one ton of emitted CO 2 and the current price per EUA is at approximately EUR 6.50. A continuous reduction in the number of EUAs per company and an expected growing demand for air transport would result in a 10 times higher value of the certiicates. For this reason, in MEFUL the price is set to EUR 65 per EUA for the year 2050. Application The weather scenario for this study has been taken from February 27, 2016, 12 a.m. with a resolution of 1 degree. On this day, a few ISS appeared in the atmosphere at cruising altitude, increasing with height. Two of them were located along the windoptimal path from Prague (LKPR) to Tunis (DTTA), approximately 240 km and 800 km after take-of (compare Figure 2 and blue regions therein). There, contrail formation will take place. Furthermore, wind speed and wind direction are shown in figure 2. Several lateral routes at diferent cruising altitudes had been calculated by COALA and Cost component Case 1 Case 2 Case 3 Case 4 Case 5 DOC [EUR] 17757 17786 17897 17942 19189 Environ. costs [EUR] 3940 3464 2842 2857 3866 Contrail costs [EUR] 1142 656 0 0 543 Total costs [EUR] 22841 21907 20739 20799 23599 Table 1: Results of the trajectory optimization 200 300 400 500 600 700 800 900 1000 0 200 400 600 800 1000 1200 1400 1600 Pressure [hPa] (reversed) Distance [km] case 1 case 2 case 3 case 4 Figure 2: Lateral trajectories in the given weather scenario. Wind speed and direction are indicated by arrows. ISS are shown by blue grid points. Case 5 is shown in red.. Figure 3: Lateral trajectory optimization (Case 2 to 4) to avoid contrail formation. Case 3 causes minimum total costs. International Transportation (68) 1 | 2016 43 Aviation SCIENCE & RESEARCH assessed by TOMATO to ind out the trajectory with minimum costs. The number of possible trajectories is large, but may be conlated into ive cases, which are discussed in the following and shown in igure 2 and igure 3. Case 1 (orange) corresponds to the base scenario: the aircraft is lying along its fuel-minimum trajectory (250 hPa, FL 340) considering wind speed and direction right through the ISS inducing a contrail. In Cases 2 to 4, the vertical trajectory is adjusted (compare igure 3) and in Case 5 the lateral trajectory is varied (as shown in igure 2). Table 1 summarizes the costs of the diferent trajectories. In Case 2 (green), the irst contrail can be avoided by lying below the ISS (FL 290), but in the second ISS the contrail is induced. In Case 3 (purple), both contrails are avoided by lying below both ISSs (FL 290 and FL 300). Although step climbs are expensive, the beneit of contrail avoidance exceeds the additional DOC. In Case 4 (blue), contrails are avoided as in Case 3, but after descending below the second ISS, the aircraft cruises at the lower altitude (FL 300) to avoid an additional vertical movement. However, lying at non-ideal altitude is more expensive than the additional climb phase. In Case 5 (red in igure 2), the trajectory is laterally modiied at cruising altitude (250 hPa, FL 340) to reduce contrail formation (compare igure 2. However, the resulting costs are out of scale). Conclusion Under the given atmospheric conditions, lateral adjustment (Case 5) is not an economical alternative, because the costs for additional trip fuel and trip time by far exceed the savings achieved by contrail avoidance (i. e. excessively long detour). Hence, vertical adjustments to the trajectory are recommended because of low increase in DOC. The beneit of additional climb phases to the previous altitudes depends on the remaining distance. Trajectory optimization considering the environmental impact poses a challenge for the air traic management, because the input parameters (e.g. weather data) are time-variant and diicult to predict. In the absence of ISS, minimum environmental costs are expected for trajectories with minimum fuel costs. If contrail formation is expected, potentially long detours for lateral adjustments will be often out of the question, whereas non-optimal cruising altitudes and steps are acceptable. ■ REFERENCES [1] SES, “Verordnung (eg) Nr. 549/ 2004 des europäischen Parlaments und des Rates vom 10. März 2004 zur Festlegung des Rahmens für die Schafung eines einheitlichen Luftraums,” Rahmenverordnung, 2004. [2] Generaldirektion Energie Europäische Kommision, “SESAR Modernisierung des Flugverkehrsmanagements in Europa,” 2008. [3] SESAR. Consortium, “Roadmap to a Single European Transport Area - Towards a competitive and resource eicient transport system,” EC COM, Bd. 144 inal, 2011. [4] http: / / nomads.ncep.noaa.gov/ 20.02.2016. [5] M. Kaiser, Optimierung von Trajektorien strahlgetriebenerVerkehrslugzeuge bei konkurrierenden SESAR Zielfunktionen mittels Entwicklung eines hochpräzisen Flugleistungsmodells, Dresden: PhD Thesis, Technische Universität Dresden, 2015. [6] J. Scheiderer, Angewandte Flugleistung, Springer-Verlag Berlin Heidelberg, 2008. [7] EUROCONTROL, (BADA) Base of Aircraft Data; 4, User Manual Family, 2012. [8] ICAO, Continuous Climb Operations (CCO) Manual, Doc 9993 AN/ 495. [9] U. Schumann, “Formation, properties and climatic efect of contrails,” in: C.R. Physique, pp. 549-565, 2005. [10] H. Appleman, “The formation of exhaust condensation trails by jet aircraft,” in: Bull. Amer. Meteor. Soc., pp. 14-20, 1953. [11] E. Schmidt, „Die Entstehung von Eisnebel aus den Auspufgasen von Flugzeugmotoren,“ in: Schriften der Deutschen Akademie für Luftfahrtforschung”, Verlag R. Oldenburg, Münschen/ Berlin, pp. 1-15, 1941. [12] R. Sussmann und K. Gierens, “Diferences in early contrail evolution of two-engine versus four-engine aircraft: Lidar measurements and numerical simulations”, in: J. Geophysical Research, pp. 4899-4911, 2001. [13] G. Myhre, D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura und H. Zhang, “Anthropogenic and Natural Radiative Forcing”, in: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, 2013. [14] R. Meerkötter, U. Schumann, D. Minnis, D.R. Doelling, T. Nakajima und Y. Tsushima, “Radiative forcing by contrails,” in: J. Geophysical Research 17, p. 1080-1094, 1999. [15] http: / / www.iata.org/ publications/ economics/ fuel-monitor/ Pages/ price-analysis.aspx, 08.04.2016. [16] University of Westminster, “European Airline delay cost reference values, Final Report,” 2011, London. [17] G. Cros, “FY2013 Maintenance Cost Preliminary Analysis,” 10th IATA Maintenance Cost Conference, 2014. [18] D. Lee, G. Pitari, V. Grewe, K. Gierens, J.E. Penner, A. Petzold und M.J. Prather, “Transport impacts on atmosphere and climate: Aviation,” in: Atmospheric Environment, p. 4678-4734, 2010. [19] J. Rosenow, M. Kaiser und H. Fricke, “Modeling contrail life cycles based on highly precise light proile data of modern aircraft,” in: International Conference on Research in Airport Transportation (ICRAT), Berkeley, 2012. [20] P. Spichtinger, “Eisübersättigte Regionen,” in: PhD thesis, Weßling, Institut für Physik der Atmosphäre, Deutsches Zentrum für Luft- und Raumfahrt (DLR) e.V., 2004. Martin Lindner, Dipl.-Ing. Institute of Logistics and Aviation, TU Dresden (DE) martin_lindner@tu-dresden.de Hartmut Fricke, Prof. Dr.-Ing. habil. Institute of Logistics and Aviation, TU Dresden (DE) fricke@ifl.tu-dresden.de Stanley Förster, Dipl.-Inf. Institute of Logistics and Aviation, TU Dresden (DE) stanley.forster@tu-dresden.de Judith Rosenow, Dipl.-Hydrol. Institute of Logistics and Aviation, TU Dresden (DE) judith.rosenow@tu-dresden.de Your editorial contact: Eberhard Buhl, Managing Editor, Mail: eberhard.buhl@trialog.de Your advertising contact: Hellfried Zippan, Media Sales, Mail: hellfried.zippan@trialog.de Let’s keep in touch …