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Full-Text Articles in Engineering

Emerging Need For A European Approach To Space Traffic Management, Tomas Hrozensky Feb 2019

Emerging Need For A European Approach To Space Traffic Management, Tomas Hrozensky

Space Traffic Management Conference

The intensification of space activities worldwide, together with the emergence of new actors and disruptive concepts (e.g. miniaturized satellites, mega-constellations, in-orbit operations), create new challenges to ensure the safety and security of space systems and operations as well as the long-term sustainability of space activities. Among policy responses to these challenges, the development of a new approach to space traffic management was recently brought to the forefront by the adoption of a policy directive in this domain by the United States.

A comparable STM policy has not yet been developed in Europe even though considerations for the safety, security ...


Satellite Conjunction Assessment Risk Analysis For “Dilution Region” Events: Issues And Operational Approaches, Matthew D. Hejduk Feb 2019

Satellite Conjunction Assessment Risk Analysis For “Dilution Region” Events: Issues And Operational Approaches, Matthew D. Hejduk

Space Traffic Management Conference

An important activity within Space Traffic Management is the detection and prevention of possible on-orbit collisions between space objects. The principal parameter for assessing collision likelihood is the probability of collision, which is widely accepted among conjunction assessment practitioners; but it possesses a known deficiency in that it can produce a false sense of safety when the orbital position uncertainties for the conjuncting objects are high. The probability of collision is said to be “diluted” in such a situation and to understate the possible risk; certain approaches have been recommended by researchers to provide (largely conservative) risk estimates and remediation ...


Advanced Inflatable De-Orbit Solutions For Derelict Satellites And Orbital Debris, Aman Chandra, Greg Wilburn, Jekan Thanga Feb 2019

Advanced Inflatable De-Orbit Solutions For Derelict Satellites And Orbital Debris, Aman Chandra, Greg Wilburn, Jekan Thanga

Space Traffic Management Conference

The exponential rise in small-satellites and CubeSats in Low Earth Orbit (LEO) poses important challenges for future space traffic management. At altitudes of 600 km and lower, aerodynamic drag accelerates de-orbiting of satellites. However, placement of satellites at higher altitudes required for constellations pose important challenges. The satellites will require on-board propulsion to lower their orbits to 600 km and let aerodynamic drag take-over. In this work we analyze solutions for de-orbiting satellites at altitudes of up to 3000 km. We consider a modular robotic de-orbit device that has stowed volume of a regular CubeSat. The de-orbit device would be ...


End To End Satellite Servicing And Space Debris Management, Aman Chandra, Himangshu Kalita, Roberto Furfaro, Jekan Thanga Feb 2019

End To End Satellite Servicing And Space Debris Management, Aman Chandra, Himangshu Kalita, Roberto Furfaro, Jekan Thanga

Space Traffic Management Conference

There is growing demand for satellite swarms and constellations for global positioning, remote sensing and relay communication in higher LEO orbits. This will result in many obsolete, damaged and abandoned satellites that will remain on-orbit beyond 25 years. These abandoned satellites and space debris maybe economically valuable orbital real-estate and resources that can be reused, repaired or upgraded for future use. Space traffic management is critical to repair damaged satellites, divert satellites into warehouse orbits and effectively deorbit satellites and space debris that are beyond repair and salvage. Current methods for on-orbit capture, servicing and repair require a large service ...


Space Objects Classification And Characterization Via Deep Learning And Light Curves: Applications To Space Traffic Management, Roberto Furfaro, Richard Linares, Vishnu Reddy Feb 2019

Space Objects Classification And Characterization Via Deep Learning And Light Curves: Applications To Space Traffic Management, Roberto Furfaro, Richard Linares, Vishnu Reddy

Space Traffic Management Conference

Recent advancements in deep learning (e.g. Convolutional Neural Networks (CNN), Recurrent Neural networks (RNN)) have demonstrated impressive results in many practical and theoretical fields (e.g. speech recognition, computer vision, robotics). Whereas deep learning methods are becoming ubiquitous, they have been barely explored in SSA applications, in particular with regard to object characterization for Space Traffic Management (STM).

In this paper, we report the results obtained in designing and training a set of CNNs and RNNs for Space Object (SO) classification and characterization using light-curve measurements. More specifically, we provide a comparison between deep networks trained on both physically-based ...


Lasers For Communication And Coordination Control Of Spacecraft Swarms, Himangshu Kalita, Leonard Dean Vance, Vishnu Reddy, Jekan Thanga Feb 2019

Lasers For Communication And Coordination Control Of Spacecraft Swarms, Himangshu Kalita, Leonard Dean Vance, Vishnu Reddy, Jekan Thanga

Space Traffic Management Conference

Swarms of small spacecraft offer whole new capabilities in Earth observation, global positioning and communications compared to a large monolithic spacecraft. These small spacecraft can provide bigger apertures that increase gain in communication antennas, increase area coverage or effective resolution of distributed cameras and enable persistent observation of ground or space targets. However, there remain important challenges in operating large number of spacecrafts at once. Current methods would require a large number of ground operators monitor and actively control these spacecraft which poses challenges in terms of coordination and control which prevents the technology from scaled up in cost-effective manner ...


Nanosat Tracking And Identification Techniques And Technologies, Mark A. Skinner Feb 2019

Nanosat Tracking And Identification Techniques And Technologies, Mark A. Skinner

Space Traffic Management Conference

Nanosats (and CubeSats, ‘Smallsats’, etc.) are of order 10 cm in size, and are at or near the limits of what can be tracked and characterized, using existing space surveillance assets. Additionally, given the CubeSat form-factor, they are often launched in large numbers (scores), and can be virtually identical. Thus are they difficult to track and to identify.

We have identified a number of technologies that future nanosat missions could employ that would enhance the trackability and/or identification of their satellites when on-orbit. Some of these technologies require active illumination of the satellite with electromagnetic energy, either in the ...


Near Real Time Satellite Event Detection And Characterization With Remote Photoacoustic Signatures, Justin Spurbeck, Moriba K. Jah Feb 2019

Near Real Time Satellite Event Detection And Characterization With Remote Photoacoustic Signatures, Justin Spurbeck, Moriba K. Jah

Space Traffic Management Conference

Active satellites frequently maneuver to mitigate conjunctions and maintain nominal mission orbits. With an ever-growing Resident Space Object (RSO) population, the need to detect and predict any changes in active RSO trajectories has become increasingly important. There is typically a lag on the order of hours to days from time of maneuver to unmodeled dynamic event detection depending on the magnitude of the delta-v. For uncooperative objects, this detection lag poses a threat to other satellites. Implementing an active photoacoustic signature change detection methodology to detect and predict unmodeled dynamic events would reduce the overall conjunction risk and provide a ...


Astria Ontology: Open, Standards-Based, Data-Aggregated Representation Of Space Objects, Jennie Wolfgang, Kathleen Krysher, Michael Slovenski, Unmil P. Karadkar, Shiva Iyer, Moriba K. Jah Feb 2019

Astria Ontology: Open, Standards-Based, Data-Aggregated Representation Of Space Objects, Jennie Wolfgang, Kathleen Krysher, Michael Slovenski, Unmil P. Karadkar, Shiva Iyer, Moriba K. Jah

Space Traffic Management Conference

The necessity for standards-based ontologies for long-term sustainability of space operations and safety of increasing space flights has been well-established [6, 7]. Current ontologies, such as DARPA’s OrbitOutlook [5], are not publicly available, complicating efforts for their broad adoption. Most sensor data is siloed in proprietary databases [2] and provided only to authorized users, further complicating efforts to create a holistic view of resident space objects (RSOs) in order to enhance space situational awareness (SSA).

The ASTRIA project is developing an open data model with the goal of aggregating data about RSOs, parts, space weather, and governing policies in ...


Enhancing Suborbital Science Through Better Understanding Of Wind Effects, Pedro Llanos, Diane Howard Feb 2019

Enhancing Suborbital Science Through Better Understanding Of Wind Effects, Pedro Llanos, Diane Howard

Space Traffic Management Conference

This paper highlights the importance of understanding some key factors, such as winds effects, trajectory and vehicle parameters variations in order to streamline the space vehicle operations and enhance science in the upper mesosphere at about 85 km. Understanding these effects is crucial to refine current space operations and establish more robust procedures. These procedures will involve training new space operators to conduct and coordinate space operations in class E above FL600 airspace within the Air Traffic Organization (ATO).

Space vehicles such as Space Ship Two can spend up to 6 minutes in class E airspace above FL600 after launch ...


Human-In-The-Loop Landing Flare Flight Test Simulation Of The Spaceliner Orbiter, Frank Morlang Feb 2019

Human-In-The-Loop Landing Flare Flight Test Simulation Of The Spaceliner Orbiter, Frank Morlang

Space Traffic Management Conference

Against the background that all future air traffic participants are requested to act as System Wide Information Management (SWIM) communicating sub-systems by the future Single European Sky Air Traffic Management Research (SESAR) SWIM 'Intranet for ATM' concept, facing the challenge of integration of space traffic in the current Air Traffic Management (ATM) needs SWIM compliance of future commercial space transportation (CST) vehicles having “landing like an aircraft at an airport” characteristics. In order to evaluate future spacecraft cockpit procedures in a transition context from Aircraft Access to SWIM (AAtS) to Spacecraft Access to SWIM in a network wide airspace management ...


Framework For Evaluating Traffic Management Services In Higher Airspace, Jennifer Gentry, Debra Moch-Mooney, Anuja Mahashabde Feb 2019

Framework For Evaluating Traffic Management Services In Higher Airspace, Jennifer Gentry, Debra Moch-Mooney, Anuja Mahashabde

Space Traffic Management Conference

Flying faster, farther, longer and higher has always captured the public’s imagination. Yet there is a vast realm of airspace that remains unexplored, save for a handful of scientific and national security missions. It is a realm rife with extremes, where flights can reach multi-Mach speeds or stay aloft for months as they slowly circumnavigate the globe. It is a realm that lies high above the clouds, at the edge of space.

Recent breakthroughs in technology, fueled by a globalized economy and society’s appetite for information, have set the stage for routine commercial operations in this new realm ...


A Statistical Approach For Commercial Space Vehicle Integration Into The National Airspace System, Christopher Hays, Daniel Chu, Pedro Llanos Feb 2019

A Statistical Approach For Commercial Space Vehicle Integration Into The National Airspace System, Christopher Hays, Daniel Chu, Pedro Llanos

Space Traffic Management Conference

This paper explores commercial space vehicle (CSV) suborbital flight trajectories in the temporal and spatial domains for CSV integration into the National Airspace System. The research data was collected via the Suborbital Space Flight Simulator (SSFS) housed in the College of Aviation at Embry-Riddle Aeronautical University - Daytona Beach campus, and analyzed using an original MATLAB data analytics tool. This study primarily focuses on statistical trends observed in previously simulated flights supported by three Project PoSSUM (Polar Suborbital Science in the Upper Mesosphere) campaigns comprised of 34 flights and 19 control flights, and to identify relevant milestones in the CSV flight ...


Assessment Of The Impact Of Air Launch Operations On Air Traffic In Europe, Sven Kaltenhaeuser, Tanja Luchkova, Niklas Klay, Rui Bin Randy Ang Feb 2019

Assessment Of The Impact Of Air Launch Operations On Air Traffic In Europe, Sven Kaltenhaeuser, Tanja Luchkova, Niklas Klay, Rui Bin Randy Ang

Space Traffic Management Conference

The development in commercial space transportation is strongly driven by a growing demand for payload capacities and cost efficient access to space. Accordingly, there is also a demand for further launch opportunities in the European region. Factors such as short waiting times for launches, rapid response capabilities, proximity of production sites to the launch site and independence from established and highly utilized launch systems are increasingly playing a role. Air launches are discussed as a way to meet this demand. They also offer the particular advantage of relatively low requirements on infrastructure and location of the spaceport compared to conventional ...


Space Launch And Reentry Operations Collaborative Decision Making (Cdm) Concept, Catherine N. Bolczak, Diane E. Boone, Bill Lash, Constance E. Morgan Feb 2019

Space Launch And Reentry Operations Collaborative Decision Making (Cdm) Concept, Catherine N. Bolczak, Diane E. Boone, Bill Lash, Constance E. Morgan

Space Traffic Management Conference

The Federal Aviation Administration’s Air Traffic Organization manages the National Airspace System (NAS) for all users. Demand for this airspace is growing as space launch and reentry (L/R) operations increase in number, vehicle and mission types, and locations. Collaborative Decision Making (CDM) is a well-established practice for resolving airspace demand issues among multiple NAS users as it considers multiple stakeholders’ perspectives to make informed decisions. The MITRE Corporation is conducting research on how CDM principles can be applied to L/R operations and has developed an initial Space CDM concept. Our paper describes this concept, including high-level operational ...


Strategies In Developing An Aviation & Aerospace Skill Ecosystem For The State Of Telangana, India – Case Study Of Task -Telangana Academy For Skill And Knowledge, Kim Chua, Sujiv Nair, M.P Ganesh Dr. Jan 2019

Strategies In Developing An Aviation & Aerospace Skill Ecosystem For The State Of Telangana, India – Case Study Of Task -Telangana Academy For Skill And Knowledge, Kim Chua, Sujiv Nair, M.P Ganesh Dr.

International Journal of Aviation, Aeronautics, and Aerospace

The aviation & aerospace sector in India has been expanding and growing through partnerships and new research facilities, thereby encouraging more players to invest and optimize the manufacturing process. Improving green and fuel-efficient technologies have contributed to a steady rise in fuelling the demand for aerospace engineers.

The state of Telangana is fast emerging as a new aviation cluster with some of the country’s best-qualified engineers and technicians. The potential of the aerospace industry is immense as it continuously requires skilled technicians and engineers. Considering the precision of skill required, it is imperative that rigorous training be imparted to all ...


Ultrafine Aluminium: Quench Collection Of Agglomerates, Tejasvi K, Y Pydi Setty, Vemana Venkateswara Rao Jan 2019

Ultrafine Aluminium: Quench Collection Of Agglomerates, Tejasvi K, Y Pydi Setty, Vemana Venkateswara Rao

International Journal of Aviation, Aeronautics, and Aerospace

Combustion of aluminized solid propellants exhibits phenomena associated with accumulation, agglomeration, ignition, and combustion of ultra-fine aluminium particles. In this study, agglomeration phenomenon of ultra-fine aluminium in solid propellant combustion is investigated using quench collection experimental technique over the pressure ranges from 2MPa to 8MPa. The ultra-fine aluminium powder synthesized by Radio Frequency Induction Plasma technique having harmonic mean size of 438nm is used for agglomeration study. The quenching distance is varied from 5mm to 71mm from the propellant burning surface to estimate the effect on agglomerate size. The morphology and chemical compositions of the collected products were then studied ...


3d Textile Preforms And Composites For Aircraft Strcutures: A Review, Abbasali Saboktakin Jan 2019

3d Textile Preforms And Composites For Aircraft Strcutures: A Review, Abbasali Saboktakin

International Journal of Aviation, Aeronautics, and Aerospace

Over the last decades, the development of 3D textile composites has been driven the structures developed to overcome disadvantages of 2D laminates such as the needs of reducing fabrication cost, increasing through-thickness mechanical properties, and improving impact damage tolerance. 3D woven, stitched, knitted and braided preforms have been used as composites reinforcement for these types of composites. In this paper, advantages and disadvantages of each of them have been comprehensively discussed. The fabric architects and their specification in particular stitched preforms and their deformation mode for aerospace applications have been reviewed. Exact insight into various types of damage in textile ...


Low Level Turbulence Detection For Airports, Anthony O' Connor, Derek Kearney Jan 2019

Low Level Turbulence Detection For Airports, Anthony O' Connor, Derek Kearney

International Journal of Aviation, Aeronautics, and Aerospace

Abstract—— Low level wind shear and turbulence present a serious safety risk to aircraft during the approach, landing and take-off phases. Despite many advances in on-board and ground based warning systems. Wind shear remains a formidable force that coupled with a microburst can overpower any aircraft. Aviation reports have concluded that pilots need to have improved information in relation to tailwinds, wind shear and wind variations on approach and during the landing phases. Low level wind shear continues to cause disruption, delays and contribute to aircraft crashes. As recently as 2016, two Boeing aircraft crashed while attempting a Go-around manoeuver ...


Computational Study Of Flow Interactions Over A Close Coupled Canard-Wing On Fighter, Setyawan Bekti Wibowo, Sutrisno Sutrisno, Tri Agung Rohmat Jan 2019

Computational Study Of Flow Interactions Over A Close Coupled Canard-Wing On Fighter, Setyawan Bekti Wibowo, Sutrisno Sutrisno, Tri Agung Rohmat

International Journal of Aviation, Aeronautics, and Aerospace

There have been many attempts to improve the flying performance of a fighter. By modifying the flow that occurs along the fuselage is expected to improve the performance of the aircraft. One of the indicators of combat aircraft performance is the ability to perform maneuver movement. Adding a canard as forewing on the fighter wing configuration is considered capable of raising the ability in maneuver movement. The use of canard-delta pairs will affect the performance and aerodynamic characteristics of the plane. Wings and canards with delta configuration will make the rolled-up vortex as a lifting force producer on the aircraft ...


Speech Interfaces And Pilot Performance: A Meta-Analysis, Kenneth A. Ward Jan 2019

Speech Interfaces And Pilot Performance: A Meta-Analysis, Kenneth A. Ward

International Journal of Aviation, Aeronautics, and Aerospace

As the aviation industry modernizes, new technology and interfaces must support growing aircraft complexity without increasing pilot workload. Natural language processing presents just such a simple and intuitive interface, yet the performance implications for use by pilots remain unknown. A meta-analysis was conducted to understand performance effects of using speech and voice interfaces in a series of pilot task analogs. The inclusion criteria selected studies that involved participants performing a demanding primary task, such as driving, while interacting with a vehicle system to enter numbers, dial radios, or enter a navigation destination. Compared to manual system interfaces, voice interfaces reduced ...


Mro Cybersecurity Swot, Danita Baghdasarin Jan 2019

Mro Cybersecurity Swot, Danita Baghdasarin

International Journal of Aviation, Aeronautics, and Aerospace

This article intended to identify gaps in the safety management system (SMS) framework when it comes to dealing with cyber risks and hazards in the maintenance, repair, and overhaul (MRO) industry. Cybersecurity is currently a concern of the aviation industry, but organizations in the MRO industry do not seem to be aware of any specific risks and hazards and therefore are not prepared to handle them. Concerns are largely around the increasing reach of aviation and the digital transformation of infrastructure, but the body of knowledge does not go into any greater detail. As a result, it is hard to ...


Urban Flow And Small Unmanned Aerial System Operations In The Built Environment, Kevin A. Adkins Jan 2019

Urban Flow And Small Unmanned Aerial System Operations In The Built Environment, Kevin A. Adkins

International Journal of Aviation, Aeronautics, and Aerospace

The Federal Aviation Administration (FAA) has put forth a set of regulations (Part 107) that govern small unmanned aerial system (sUAS) operations. These regulations restrict unmanned aircraft (UA) from flying over people and their operation to within visual line of sight (VLOS). However, as new applications for unmanned aerial systems (UAS) are discovered, their capabilities improve, and regulations evolve, there is an increasing desire to undertake urban operations, such as urban air mobility, package delivery, infrastructure inspection, and surveillance. This built environment poses new weather hazards that include enhanced wind shear and turbulence. The smaller physical dimensions, lower mass and ...


Shape-Stabilization Of Pcm/Hdpe Composites With 3d-Printing Applications For Battery Thermal Management, Thomas Benjamin Freeman Dec 2018

Shape-Stabilization Of Pcm/Hdpe Composites With 3d-Printing Applications For Battery Thermal Management, Thomas Benjamin Freeman

Dissertations and Theses

Phase-change materials (PCMs) are a useful alternative to more traditional methods of thermal management of Li-ion batteries in electric or hybrid-electric vehicles. PCMs are materials which absorb large amounts of latent heat and undergo solid-to-liquid phase change at near-constant temperature. The goal of this thesis is to experimentally investigate the thermal properties of a novel shape-stabilized PCM/HDPE composite extruded filament. The extruded filament can then be used in a 3D printer for custom PCM/HDPE shapes. These custom PCM/HDPE shapes can be used to help reduce weight, energy consumption, and complexity of the thermal management of the ESS ...


Design Of An Attitude Control System For A Spacecraft With Propellant Slosh Dynamics, Nolan Coulter Dec 2018

Design Of An Attitude Control System For A Spacecraft With Propellant Slosh Dynamics, Nolan Coulter

Dissertations and Theses

The presence of propellant slosh dynamics in a spacecraft system during a maneuver leads to attitude control system (ACS) performance degradation resulting in attitude tracking errors and instability. As spacecraft missions become more complex and involve longer durations, a substantial propellant mass is required to achieve the mission objectives and perform orbital maneuvers. When the propellant tanks are only partially filled, the liquid fuel moves inside the tanks with translational and rotational accelerations generating the slosh dynamics. This research effort performs a comparative study with different optimal control techniques and a novel application of a model reference artificial immune system ...


A Remote Observatory For Geocoronal Hydrogen Emissions, Margaret A. Gallant Dec 2018

A Remote Observatory For Geocoronal Hydrogen Emissions, Margaret A. Gallant

Dissertations and Theses

The Investigating Near Space Interaction Regions (INSpIRe) observatory is an adapt- able research facility that is designed to use Fabry-Perot interferometer (FPI) to study the faint Balmer series emissions of the terrestrial upper thermosphere and exosphere, collectively known as the geocorona. This instrumentation is designed to be deployable to a clear-air site, necessitating remote operations of the entire observatory, including control and monitoring. The facility currently employs a siderostat to allow for pointing at sky targets, a pressure-tuned dual-etalon FPI to allow for high spectral resolution (R_80,000) measurements, and several charge-coupled device (CCD) imagers for guiding and collecting data ...


Design And Implementation Of Intelligent Guidance Algorithms For Uav Mission Protection, Karina Rivera Dec 2018

Design And Implementation Of Intelligent Guidance Algorithms For Uav Mission Protection, Karina Rivera

Dissertations and Theses

In recent years, the interest of investigating intelligent systems for Unmanned Aerial Vehicles (UAVs) have increased in popularity due to their large range of capabilities such as on-line obstacle avoidance, autonomy, search and rescue, fast prototyping and integration in the National Air Space (NAS). Many research efforts currently focus on system robustness against uncertainties but do not consider the probability of readjusting tasks based on the remaining resources to successfully complete the mission. In this thesis, an intelligent algorithm approach is proposed along with decision-making capabilities to enhance UAVs post-failure performance. This intelligent algorithm integrates a set of path planning ...


A Numerical And Experimental Evaluation Of The Turbulent Heat Flux In A Heated Jet In Crossflow, Michael R. Borghi Jr. Nov 2018

A Numerical And Experimental Evaluation Of The Turbulent Heat Flux In A Heated Jet In Crossflow, Michael R. Borghi Jr.

Dissertations and Theses

The injection of fully-developed turbulent heated air from a tube into a cooler turbulent duct flow is examined, as an analogy to film cooled turbine blades. Scale Resolving Simulations (SRS) are used to examine the flow numerically. A Detached Eddy Simulation (DES) methodology is examined but found to be ineffective at correctly capturing the physics of the flow. A Large Eddy Simulation (LES) numerical model is developed and applied in which tube and duct turbulence inflow effects are emulated using a divergence-free synthetic eddy method (SEM). The LES sensitivity to the synthetic inflow turbulence is examined with a series of ...


Variable Fidelity Studies In Wake Vortex Evolution, Safety, And Control, Petr Kazarin Nov 2018

Variable Fidelity Studies In Wake Vortex Evolution, Safety, And Control, Petr Kazarin

Dissertations and Theses

The purpose of this research is to develop a variable-fidelity approach for addressing the safety of unmanned aerial system (UAS) operations in the national aerospace system (NAS). This task is implemented on the basis of safety investigation toolkit for analysis and reporting wake vortex safety system (SITAR WVSS) code, which is a dynamic low-fidelity model addressing generation, evolution, and interaction of the leader-aircraft wake vortex with the follower-aircraft lifting surfaces.

The first part of the dissertation deals with the generation, evolution, and interaction of the wake vortices produced by an aircraft. In particular, it presents the results of the vortex ...


Direct Adaptive Control For A Trajectory Tracking Uav, Nirmit Prabhakar Nov 2018

Direct Adaptive Control For A Trajectory Tracking Uav, Nirmit Prabhakar

Dissertations and Theses

This research focuses on the theoretical development and analysis of a direct adaptive control algorithm to enable a fixed-wing UAV to track reference trajectories while in the presence of persistent external disturbances. A typical application of this work is autonomous flight through urban environments, where reference trajectories would be provided by a path planning algorithm and the vehicle would be subjected to significant wind gust disturbances. Full 6-DOF nonlinear and linear UAV simulation models are developed and used to study the performance of the direct adaptive control system for various scenarios. A stability proof is developed to prove convergence of ...