2,277 research outputs found

    Autonomous landing control of highly flexible aircraft based on Lidar preview in the presence of wind turbulence

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    This paper investigates preview-based autonomous landing control of a highly flexible flying wing model using short range Lidar wind measurements in the presence of wind turbulence. The preview control system is developed based on a reduced-order linear aeroelastic model and employs a two-loop control scheme. The outer loop employs the LADRC (linear active disturbance rejection control) and PI algorithms to track the reference landing trajectory and vertical speed, respectively, and to generate the attitude angle command. This is then used by the inner-loop using H∞ preview control to compute the control inputs to the actuators (control flaps and thrust). A landing trajectory navigation system is designed to generate real-time reference commands for the landing control system. A Lidar (light detection and ranging) simulator is developed to measure the wind disturbances at a distance in front of the aircraft, which are provided to the inner-loop H∞ preview controller as prior knowledge to improve control performance. Simulation results based on the full-order nonlinear flexible aircraft dynamic model show that the preview-based landing control system is able to land the flying wing effectively and safely, showing better control performance than the baseline landing control system (without preview) with respect to landing effectiveness and disturbance rejection. The control system’s robustness to measurement error in the Lidar system is also demonstrated

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

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    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

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

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    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

    Traffic synchronization with controlled time of arrival for cost-efficient trajectories in high-density terminal airspace

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    The growth in air traffic has led to a continuously growing environmental sensitivity in aviation, encouraging the research into methods for achieving a greener air transportation. In this context, continuous descent operations (CDOs) allow aircraft to follow an optimum flight path that delivers major environmental and economic benefits, giving as a result engine-idle descents from the cruise altitude to right before landing that reduce fuel consumption, pollutant emissions and noise nuisance. However, this type of operations suffers from a well-known drawback: the loss of predictability from the air traffic control (ATC) point of view in terms of overfly times at the different waypoints of the route. In consequence, ATC requires large separation buffers, thus reducing the capacity of the airport. Previous works investigating this issue showed that the ability to meet a controlled time of arrival (CTA) at a metering fix could enable CDOs while simultaneously maintaining airport throughput. In this context, more research is needed focusing on how modern arrival managers (AMANs)—and extended arrival managers (E-AMANs)—could provide support to select the appropriate CTA. ATC would be in charge to provide the CTA to the pilot, who would then use four-dimensional (4D) flight management system (FMS) trajectory management capabilities to satisfy it. A key transformation to achieve a more efficient aircraft scheduling is the use of new air traffic management (ATM) paradigms, such as the trajectory based operations (TBO) concept. This concept aims at completely removing open-loop vectoring and strategic constraints on the trajectories by efficiently implementing a 4D trajectory negotiation process to synchronize airborne and ground equipment with the aim of maximizing both flight efficiency and throughput. The main objective of this PhD thesis is to develop methods to efficiently schedule arrival aircraft in terminal airspace, together with concepts of operations compliant with the TBO concept. The simulated arrival trajectories generated for all the experiments conducted in this PhD thesis, to the maximum possible extent, are considered to be energy-neutral CDOs, seeking to reduce the overall environmental impact of aircraft operations in the ATM system. Ultimately, the objective of this PhD is to achieve a more efficient arrival management of traffic, in which higher levels of predictability and similar levels of capacity are achieved, while the safety of the operations is kept. The designed experiments consider a TBO environment, involving a high synchronization between all the involved actors of the ATM system. Higher levels of automation and information sharing are expected, together with a modernization of both current ATC ground-support tools and aircraft FMSs to comply with the new TBO paradigm.L’increment de tràfic aeri ha portat a una major sensibilitat mediambiental en l’aviació, motivant la recerca en mètodes per aconseguir un transport aeri més ecològic. En aquest context, les operacions de descens continu (CDOs) permeten a les aeronaus seguir una trajectòria que aporta grans beneficis econòmics i ambientals, donant com a resultat descensos amb els motors al ralentí des de l’altitud de creuer fins just abans d’aterrar. Aquestes trajectòries redueixen el consum de combustible, les emissions contaminants i el soroll generat per les aeronaus. No obstant això, aquest tipus d’operacions té un gran desavantatge: la pèrdua de predictibilitat des del punt de vista del controlador aeri (ATC) en termes de temps de pas als diferents punts de la ruta. Com a conseqüència, l’ATC necessita assignar una major separació entre les aeronaus, la qual cosa comporta una reducció en la capacitat de l’aeroport. Estudis previs investigant aquest problema han demostrat que la capacitat de complir amb un temps controlat d’arribada (CTA) a un punt de la ruta (utilitzat per seqüenciar les aeronaus) podria habilitar les CDOs tot mantenint la capacitat de l’aeroport. En aquest context, es necessita investigar més en com els gestors d’arribades (AMANs) i els gestors d’arribades ampliats (E-AMANs) podrien donar suport en la selecció de la CTA més adequada. L’ATC seria l’encarregat d’enviar la CTA al pilot, el qual, per tal de complir amb la CTA, faria servir la capacitat de gestió de trajectòries d’un sistema de gestió de vol (FMS) de quatre dimensions (4D). Una transformació clau per aconseguir una gestió més eficient del tràfic d’arribada és l’ús de nous paradigmes de gestió del tràfic aeri (ATM), com per exemple el concepte d’operacions basades en trajectòries (TBO). Aquest concepte té com a objectiu eliminar completament de les trajectòries la vectorització en “bucle obert” i les restriccions estratègiques. Per aconseguir-ho, es proposa implementar de manera eficient una negociació de la trajectòria 4D, amb l’objectiu de sincronitzar l’equipament de terra amb el de l’aeronau, maximitzant d’aquesta manera l’eficiència dels vols i la capacitat del sistema. El principal objectiu d’aquest doctorat és desenvolupar mètodes per gestionar aeronaus de manera eficient en espai aeri terminal, juntament amb conceptes d’operacions que compleixin amb el concepte de TBO. Les trajectòries d’arribada simulades per tots els experiments definits en aquesta tesi doctoral, en la mesura que s’ha pogut, són CDOs d’energia neutral. D’aquesta manera, la idea és reduir el màxim possible l’impacte mediambiental de les operacions aèries al sistema ATM. En definitiva, l’objectiu d’aquest doctorat és aconseguir una gestió del tràfic d’arribada més eficient, obtenint una major predictibilitat i capacitat, i assegurant que la seguretat de les operacions es manté. Els experiments dissenyats consideren una situació on el concepte de TBO és present, el que comporta una sincronització elevada entre tots els actors implicats en el sistema ATM. Així mateix, s’esperen nivells majors d’automatització i de compartició d’informació, juntament amb una modernització de les eines de suport en terra a l’ATC i dels FMSs de les aeronaus, tot amb l’objectiu de complir amb el nou paradigma de TBO.El incremento de tráfico aéreo ha llevado a una mayor sensibilidad medioambiental en la aviación, motivando la investigación de métodos para conseguir un transporte aéreo más ecológico. En este contexto, las operaciones de descenso continuo (CDOs) permiten a las aeronaves seguir una trayectoria que aporta grandes beneficios económicos y ambientales, dando como resultado descensos con los motores al ralentí desde la altitud de crucero hasta justo antes de aterrizar. Estas trayectorias reducen el consumo de combustible, las emisiones contaminantes y el ruido generado por las aeronaves. No obstante, este tipo de operaciones tiene una gran desventaja: la pérdida de predictibilidad desde el punto de vista del controlador aéreo (ATC) en términos de tiempos de paso en los diferentes puntos de la ruta. Como consecuencia, el ATC necesita asignar una mayor separación entre las aeronaves, lo cual comporta una reducción en la capacidad del aeropuerto. Estudios previos investigando este problema han demostrado que la capacidad de cumplir con un tiempo controlado de llegada (CTA) en un punto de la ruta (utilizado para secuenciar las aeronaves) podría habilitar las CDOs manteniendo al mismo tiempo la capacidad del aeropuerto. En este contexto, es necesario investigar más en cómo los gestores de llegadas (AMANs)—y los gestores de llegadas extendidos (E-AMANs)—podrían dar soporte en la selección de la CTA más adecuada. El ATC sería el encargado de enviar la CTA al piloto, el cual, para cumplir con la CTA, usaría la capacidad de gestión de trayectorias de un sistema de gestión de vuelo (FMS) de cuatro dimensiones (4D). Una transformación clave para conseguir una gestión más eficiente del tráfico de llegada es el uso de nuevos paradigmas de gestión del tráfico aéreo (ATM), como por ejemplo el concepto de operaciones basadas en trayectorias (TBO). Este concepto tiene como objetivo eliminar completamente de las trayectorias la vectorización en “bucle abierto” y las restricciones estratégicas. Para conseguirlo, se propone implementar de manera eficiente una negociación de la trayectoria 4D, con el objetivo de sincronizar el equipamiento de tierra con el de la aeronave, maximizando de esta manera la eficiencia de los vuelos y la capacidad del sistema. El principal objetivo de este doctorado es desarrollar métodos para gestionar aeronaves de manera eficiente en espacio aéreo terminal, junto con conceptos de operaciones que cumplan con el concepto de TBO. Las trayectorias de llegada simuladas para todos los experimentos definidos en esta tesis doctoral, en la medida de lo posible, son CDOs de energía neutra. De esta manera, la idea es reducir lo máximo posible el impacto medioambiental de las operaciones aéreas en el sistema ATM. En definitiva, el objetivo de este doctorado es conseguir una gestión del tráfico de llegada más eficiente, obteniendo una mayor predictibilidad y capacidad, y asegurando que la seguridad de las operaciones se mantiene. Los experimentos diseñados consideran una situación xxi donde el concepto de TBO está presente, lo que comporta una sincronización elevada entre todos los actores implicados en el sistema ATM. Asimismo, se esperan mayores niveles de automatización y de compartición de información, junto con una modernización de las herramientas de soporte en tierra al ATC y de los FMSs de las aeronaves, todo con el objetivo de cumplir con el nuevo paradigma de TBO. Primero de todo, se define un marco para la optimización de trayectorias utilizado para generar las trayectorias simuladas para los experimentos definidos en esta tesis doctoral. A continuación, se evalúan los beneficios de volar CDOs de energía neutra comparándolas con trayectorias reales obtenidas de datos de vuelo históricos. Se comparan dos fuentes de datos, concluyendo cuál es la más adecuada para estudios de eficiencia en espacio aéreo terminal. Las CDOs de energía neutra son el tipo preferido de trayectorias desde un punto de vista medioambiental pero, dependiendo de la cantidad de tráfico, podría ser imposible para el ATC asignar una CTA que pueda ser cumplida por las aeronaves mientras vuelan la ruta de llegada publicada. En esta tesis doctoral, se comparan dos estrategias con el objetivo de cumplir con la CTA asignada: volar CDOs de energía neutra por rutas más largas/cortas o volar descensos con el motor accionado por la ruta publicada. Para ambas estrategias, se analiza la sensibilidad del consumo de combustible a diferentes parámetros, como la altitud inicial de crucero o la velocidad del viento. Finalmente, en esta tesis doctoral se analizan dos estrategias para gestionar de manera eficiente el tráfico de llegada en espacio aéreo terminal. Primero, se utiliza una estrategia provisional a medio camino entre la negociación completa de trayectorias 4D y la vectorización en “bucle abierto”: se propone una metodología para gestionar de manera eficaz tráfico de llegada donde las aeronaves vuelan CDOs de energía neutra en un procedimiento de navegación de área (RNAV) conocido como trombón. A continuación, se propone una nueva metodología para generar rutas de llegada dinámicas que se adaptan automáticamente a la demanda actual de tráfico. De igual manera, se aplican CDOs de energía neutra a todo el tráfico de llegada. Hay diferentes factores a considerar que podrían limitar los beneficios de las soluciones propuestas. La cantidad y distribución del tráfico de llegada tiene un gran efecto sobre los resultados obtenidos, limitando en algunos casos una gestión eficiente de las aeronaves de llegada. Además, algunas de las soluciones propuestas comportan elevadas cargas computacionales que podrían limitar su aplicación operacional, motivando mayor investigación en el futuro con el fin de optimizar los modelos y metodologías utilizados. Finalmente, permitir a algunos aviones volar descensos con el motor accionado podría facilitar la gestión de las aeronaves de llegada en los experimentos que se centran en el procedimiento de trombón y en la generación de rutas de llegada dinámicas.Postprint (published version

    An Approach to Analyze Tradeoffs for Aerospace System Design and Operation

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    There are important tradeoffs that need to be considered for the design and operation of aerospace systems. In addition to tradeoffs, there may also be multiple stakeholders of interest to the system and each may have different preferences as to the balance amongst the tradeoffs under consideration. A tradeoff hyperspace is created when there are three or more tradeoff dimensions and this increases the challenge associated with resolving the hyperspace in order to determine the best design and operation of a system. The corresponding objectives of this research are to develop a framework to analyze tradeoff hyperspaces and to account for the preferences of multiple stakeholders in this framework.This work was supported by the National Aeronautics and Space Administration (NASA) under grant NRA- #NNX10AN92A (NASA Ames). The authors are grateful to Dr. Neil Y. Chen and Dr. Banavar Sridhar in the Aviation Systems Division at NASA Ames for their valuable guidance and feedback in managing this project

    4-dimensional trajectory generation algorithms for RPAS mission management systems

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    This paper presents the algorithms enabling real-time 4-Dimensional Flight Trajectory (4DT) functionalities in Next Generation Mission Management Systems (NG-MMS), which are the core element of future Remotely Piloted Aircraft Systems (RPAS) avionics. In particular, the algorithms are employed for multi-objective optimisation of 4DT intents in various operational scenarios spanning from online strategic to tactical and emergency tasks. The adopted formulation of the multi-objective 4DT optimisation problem includes a number of environmental objectives and operational constraints. In particular, this paper describes the algorithm for planning of 4DT based on a multi-objective optimisation approach and the generalised expression of the cost function adopted for penalties associated with specific airspace volumes, accounting for weather, condensation trails and noise models

    Aeronautical Engineering: A special bibliography with indexes, supplement 51

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    This bibliography lists 206 reports, articles, and other documents introduced into the NASA Scientific and Technical Information System in November 1974

    Computer aiding for low-altitude helicopter flight

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    A computer-aiding concept for low-altitude helicopter flight was developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generated algorithm based on dynamic programming, and a head-up display (HUD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor symbol. The trajectory-generation algorithm uses knowledge of the global mission requirements, a digital terrain map, aircraft performance capabilities, and advanced navigation information to determine a trajectory between mission waypoints that minimizes threat exposure by seeking valleys. The pilot evaluation was conducted at NASA Ames Research Center's Sim Lab facility in both the fixed-base Interchangeable Cab (ICAB) simulator and the moving-base Vertical Motion Simulator (VMS) by pilots representing NASA, the U.S. Army, and the U.S. Air Force. The pilots manually tracked the trajectory generated by the algorithm utilizing the HUD symbology. They were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world

    Optical Properties of Condensation Trails

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    Persistent condensation trails are clouds, induced by the exhaust of an aircraft engine in a cold and ice-supersaturated environment. These artificial ice clouds can both cool and heat the atmosphere by scattering solar radiation and absorbing terrestrial radiation, respectively. The influence of condensation trails on the Earth-atmosphere energy balance and therewith the answer to the question of the dominating process had been mostly approximated on a global scale by treating the condensation trail as plane parallel layer with constant optical properties. Individual condensation trails and the influence of the solar angle had been analyzed, always using a course spatial grid and never under consideration of the aircraft performance, generating the condensation trail. For a trajectory optimization, highly precise results of the impact of condensation trails on the radiation budget and the influence of the aircraft performance on this impact is needed, so that future air traffic may consider the main factors of flight performance on the environmental impact of condensation trails. That’s why, a model is developed in this thesis to continuously estimate the scattering and absorption properties and their dependence on the aircraft performance.:1 Introduction 3 1.1 Motivation 3 1.2 State of the art 5 1.3 Approach 6 2 Theoretical background 9 2.1 The Earth’s atmosphere 9 2.1.1 The mean vertical structure of the atmosphere 12 2.1.2 Standard atmospheres 14 2.2 Radiation 15 2.2.1 Nature of radiation 15 2.2.2 Important metrics describing radiation 17 2.2.3 Relevant spectra and principles of radiation 19 2.2.4 Solar radiation 20 2.2.5 Terrestrial radiation 21 2.2.6 Radiative transfer and extinction 22 2.2.7 Radiative transfer equation 30 2.2.8 Energy budget of the Earth-atmosphere system 32 2.3 Thermodynamics 33 2.3.1 Atmospheric stability 33 2.3.2 Turbulence 36 2.3.3 Conditions of contrail formation 41 3 Development of a radiative forcing model 45 3.1 Model atmosphere 45 3.2 Flight performance model 46 3.3 Atmospheric radiative transfer model 49 3.3.1 Two Stream Approximation 51 3.3.2 Discrete ordinate radiative transfer solver 52 3.3.3 Methods to calculate broadband radiances and irradiances 53 3.4 Contrail life cycle model 57 3.4.1 Dissipation regime 58 3.4.2 Diffusion regime 63 3.5 Contrail radiative forcing model 74 3.5.1 Consideration of multiple scattering using a Monte Carlo simulation 74 3.5.2 Geometry of the Monte Carlo simulation 75 3.5.3 Interpretation of Beer’s law 76 3.5.4 Procedure of the Monte Carlo simulation 79 3.5.5 The extinguished power per unit length contrail 87 3.5.6 Scattering and absorption efficiencies Qs, Qa and asymmetry parameters gHG 89 3.5.7 Calibration of the Monte Carlo simulation 94 4 Calculations 99 4.1 Contrail properties 99 4.1.1 Conditions of contrail formation 100 4.1.2 Initial dimensions at the end of the dissipation regime 101 4.1.3 Microphysical properties during the diffusion regime 103 4.2 Radiative transport up to the contrail 105 4.2.1 Solar direct and diffuse radiance 106 4.2.2 Terrestrial irradiance 107 4.3 Scattering and absorption properties of radiation within the contrail 109 4.3.1 Monte Carlo simulation for solar radiation 109 4.3.2 Monte Carlo simulation for terrestrial irradiances 112 4.3.3 Relevance of multiple scattering 116 4.4 Radiative extinction 116 4.4.1 Solar zenith and azimuthal angle 118 4.4.2 Flightpath 120 4.4.3 Contrail evolution 122 4.4.4 Turbulence 126 4.4.5 Wavelength specific extinction 129 4.5 Terrestrial energy forcing of a contrail 133 4.6 Verification 135 5 Conclusion and outlook 141 5.1 Conclusion 141 5.2 Outlook 144 List of Figures 147 List of Tables 151 Abbreviations and Symbols 153 Glossary 161 Bibliography 169 Acknowledgements 183Langlebige Kondensstreifen sind Eiswolken, welche durch Kondensation von Wasserdampf an Rußpartikeln in einer eisübersättigten Atmosphäre entstehen. Der Wasserdampf entstammt einerseits aus dem Triebwerkabgas und andererseits aus der Atmosphäre. Kondensstreifen können die Atmosphäre durch Rückstreuung solarer Strahlung kühlen und durch Rückstreuung und Absorption terrestrischer Strahlung erwärmen. Der Einfluss von Kondensstreifen auf den Wärmehaushalt der Atmosphäre und damit die Antwort auf die Frage nach dem dominierenden Effekt wurde bisher zumeist auf globaler Ebene ermittelt, wobei der Kondensstreifen als planparallele Schicht mit konstanten optischen Eigenschaften angenähert wurde. Individuelle Kondensstreifen und der Einfluss des Sonnenstandes wurden bisher nur mithilfe eines groben Rasters betrachtet und niemals unter Berücksichtigung der Flugleistung des Luftfahrzeuges, welches den Kondensstreifen generiert hat. Für eine Trajektorienoptimierung sind jedoch präzise Berechnungen des Strahlungseinflusses und eine gewissenhafte Berücksichtigung der Flugleistung notwendig. Nur so kann der zukünftige Luftverkehr die Haupteinflussfaktoren der Flugeigenschaften auf den Strahlungseinfluss der Kondensstreifen berücksichtigen. Aus diesem Grund wurde in dieser Arbeit ein Modell entwickelt, welches die Eigenschaften des Strahlungstransfers durch den Kondensstreifen kontinuierlich bestimmt und die aus der Flugleistung resultierenden Parameter berücksichtigt.:1 Introduction 3 1.1 Motivation 3 1.2 State of the art 5 1.3 Approach 6 2 Theoretical background 9 2.1 The Earth’s atmosphere 9 2.1.1 The mean vertical structure of the atmosphere 12 2.1.2 Standard atmospheres 14 2.2 Radiation 15 2.2.1 Nature of radiation 15 2.2.2 Important metrics describing radiation 17 2.2.3 Relevant spectra and principles of radiation 19 2.2.4 Solar radiation 20 2.2.5 Terrestrial radiation 21 2.2.6 Radiative transfer and extinction 22 2.2.7 Radiative transfer equation 30 2.2.8 Energy budget of the Earth-atmosphere system 32 2.3 Thermodynamics 33 2.3.1 Atmospheric stability 33 2.3.2 Turbulence 36 2.3.3 Conditions of contrail formation 41 3 Development of a radiative forcing model 45 3.1 Model atmosphere 45 3.2 Flight performance model 46 3.3 Atmospheric radiative transfer model 49 3.3.1 Two Stream Approximation 51 3.3.2 Discrete ordinate radiative transfer solver 52 3.3.3 Methods to calculate broadband radiances and irradiances 53 3.4 Contrail life cycle model 57 3.4.1 Dissipation regime 58 3.4.2 Diffusion regime 63 3.5 Contrail radiative forcing model 74 3.5.1 Consideration of multiple scattering using a Monte Carlo simulation 74 3.5.2 Geometry of the Monte Carlo simulation 75 3.5.3 Interpretation of Beer’s law 76 3.5.4 Procedure of the Monte Carlo simulation 79 3.5.5 The extinguished power per unit length contrail 87 3.5.6 Scattering and absorption efficiencies Qs, Qa and asymmetry parameters gHG 89 3.5.7 Calibration of the Monte Carlo simulation 94 4 Calculations 99 4.1 Contrail properties 99 4.1.1 Conditions of contrail formation 100 4.1.2 Initial dimensions at the end of the dissipation regime 101 4.1.3 Microphysical properties during the diffusion regime 103 4.2 Radiative transport up to the contrail 105 4.2.1 Solar direct and diffuse radiance 106 4.2.2 Terrestrial irradiance 107 4.3 Scattering and absorption properties of radiation within the contrail 109 4.3.1 Monte Carlo simulation for solar radiation 109 4.3.2 Monte Carlo simulation for terrestrial irradiances 112 4.3.3 Relevance of multiple scattering 116 4.4 Radiative extinction 116 4.4.1 Solar zenith and azimuthal angle 118 4.4.2 Flightpath 120 4.4.3 Contrail evolution 122 4.4.4 Turbulence 126 4.4.5 Wavelength specific extinction 129 4.5 Terrestrial energy forcing of a contrail 133 4.6 Verification 135 5 Conclusion and outlook 141 5.1 Conclusion 141 5.2 Outlook 144 List of Figures 147 List of Tables 151 Abbreviations and Symbols 153 Glossary 161 Bibliography 169 Acknowledgements 18
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