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Simulation Technology at NASA

NASA Ames Research Center is home to several high-fidelity research flight and air-traffic control simulation facilities which, together with an experienced workforce, produce high-quality research data and findings that have proven to be applicable in the real world. These assets include the Vertical Motion Simulator (VMS), Crew Vehicle Systems Research Facility (CVSRF), Future Flight Central (FFC) air traffic control tower simulator, and several air-traffic control (ATC) simulators. The VMS combines a high-fidelity simulation capability with an adaptable simulation environment, enabling customization for numerous human-in-the-loop research applications. The distinctive feature of the VMS is its unparalleled large amplitude, high-fidelity motion capability. In over 30 years of continuous operation, the VMS has contributed significantly to the body of knowledge in a range of disciplines directly benefiting several aerospace programs and flight safety, including the design and development of flight control systems for the Joint Strike Fighter, Space Shuttle Orbiter, and rotorcraft. It continues to be used for researching new vehicle configurations, vehicle control and safety, transfer-of-training, etc., by NASA, other government agencies, and Industry.The CVSRF includes two motion-based flight simulators: a Boeing 747-400 full flight simulator and the reconfigurable Advanced Concepts Flight Simulator (ACFS). These simulators are primarily used to research air-traffic management concepts and procedures, advanced navigation and avionics concepts, and cockpit human factors. FFC is a full-sized control tower simulator with a 360-degree external field-of-view display system and reconfigurable system architecture. FFC and the ATC simulators are used for testing air-traffic management automation and decision support tools and demonstrate their feasibility in a realistic environment prior to technology transfer for implementation in the National Airspace System (NAS).To support integrated simulations and flight-tests for NASA's Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) Project, NASA developed a distributed test environment incorporating Live, Virtual, Constructive, (LVC) concepts. Development of the software enabling the LVC is conducted primarily at the Distributed Simulation Research Lab (DSRL) at NASA Ames. The LVC components provide the core infrastructure supporting simulation of UAS operations by integrating live and virtual aircraft in a realistic air traffic environment. This provides the ability to conduct tests more efficiently by promoting the use of existing distributed assets. The LVC infrastructure was used in several human-in-the-loop simulations to evaluate acceptance of Detect and Avoid (DAA) advisories used by UAS pilots to maintain well clear of other virtual traffic and to negotiate maneuvers with air traffic control. It is currently being used to support testing of self-separation algorithms between unmanned and manned aircraft in live flight. Further simulations with more comprehensive air traffic scenarios mixing live and virtual aircraft is planned.In the current fiscal environment, maintaining and upgrading these high-fidelity simulation assets and retaining the skilled workforce necessary to meet future research needs is the primary non-technical challenge.

CVSRF↗

Initial Development of a Metric to Describe the Level of Safety Associated with Piloting an Aircraft with Synthetic Vision Systems (SVS) Displays

Synthetic Vision Systems (SVS) displays provide pilots with a continuous view of terrain combined with integrated guidance symbology in an effort to increase situation awareness (SA) and decrease workload during operations in Instrument Meteorological Conditions (IMC). It is hypothesized that SVS displays can replicate the safety and operational flexibility of flight in Visual Meteorological Conditions (VMC), regardless of actual out-the-window (OTW) visibility or time of day. Significant progress has been made towards evolving SVS displays as well as demonstrating their ability to increase SA compared to conventional avionics in a variety of conditions. While a substantial amount of data has been accumulated demonstrating the capabilities of SVS displays, the ability of SVS to replicate the safety and operational flexibility of VMC flight performance in all visibility conditions is unknown to any specific degree. In order to more fully quantify the relationship of flight operations in IMC with SVS displays to conventional operations conducted in VMC, a fundamental comparison to current day general aviation (GA) flight instruments was warranted. Such a comparison could begin to establish the extent to which SVS display concepts are capable of maintaining an "equivalent level of safety" with the round dials they could one day replace, for both current and future operations. A combination of subjective and objective data measures were used to quantify the relationship between selected components of safety that are associated with flying an approach. Four information display methods ranging from a "round dials" baseline through a fully integrated SVS package that includes terrain, pathway based guidance, and a strategic navigation display, were investigated in this high fidelity simulation experiment. In addition, a broad spectrum of pilots, representative of the GA population, were employed for testing in an attempt to enable greater application of the results and determine if "equivalent levels of safety" are achievable through the incorporation of SVS technology regardless of a pilot's flight experience.

Bartolone, Anthony P.↗

Global Precipitation Measurement (GPM) Safety Inhibit Timeline Tool

The Global Precipitation Measurement (GPM) Observatory is a joint mission under the partnership by National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA), Japan. The NASA Goddard Space Flight Center (GSFC) has the lead management responsibility for NASA on GPM. The GPM program will measure precipitation on a global basis with sufficient quality, Earth coverage, and sampling to improve prediction of the Earth's climate, weather, and specific components of the global water cycle. As part of the development process, NASA built the spacecraft (built in-house at GSFC) and provided one instrument (GPM Microwave Imager (GMI) developed by Ball Aerospace) JAXA provided the launch vehicle (H2-A by MHI) and provided one instrument (Dual-Frequency Precipitation Radar (DPR) developed by NTSpace). Each instrument developer provided a safety assessment which was incorporated into the NASA GPM Safety Hazard Assessment. Inhibit design was reviewed for hazardous subsystems which included the High Gain Antenna System (HGAS) deployment, solar array deployment, transmitter turn on, propulsion system release, GMI deployment, and DPR radar turn on. The safety inhibits for these listed hazards are controlled by software. GPM developed a "pathfinder" approach for reviewing software that controls the electrical inhibits. This is one of the first GSFC in-house programs that extensively used software controls. The GPM safety team developed a methodology to document software safety as part of the standard hazard report. As part of this process a new tool "safety inhibit time line" was created for management of inhibits and their controls during spacecraft buildup and testing during 1& Tat GSFC and at the Range in Japan. In addition to understanding inhibits and controls during 1& T the tool allows the safety analyst to better communicate with others the changes in inhibit states with each phase of hardware and software testing. The tool was very useful for communicating compliance with safety requirements especially when working with a foreign partner.

Dion, Shirley↗

Lithium-Ion Electrolytes Containing Phosphorous-Based, Flame-Retardant Additives

Future NASA missions aimed at exploring Mars, the Moon, and the outer planets require rechargeable batteries that can operate over a wide temperature range (-60 to +60 C) to satisfy the requirements of various applications. In addition, many of these applications will require improved safety, due to their use by humans. Currently, the state-of-the-art lithium-ion (Li-ion) system has been demonstrated to operate over a wide range of temperatures (-40 to +40 C); however, abuse conditions can often lead to cell rupture and fire. The nature of the electrolyte can greatly affect the propensity of the cell/battery to catch fire, given the flammability of the organic solvents used within. Li-ion electrolytes have been developed that contain a flame-retardant additive in conjunction with fluorinated co-solvents to provide a safe system with a wide operating temperature range. Previous work incorporated fluorinated esters into multi-component electrolyte formulations, which were demonstrated to cover a temperature range from 60 to +60 C. This work was described in Fluoroester Co-Solvents for Low-Temperature Li+ Cells (NPO-44626), NASA Tech Briefs, Vol. 33, No. 9 (September 2009), p. 37; and Optimized Li-Ion Electrolytes Con tain ing Fluorinated Ester Co-Solvents (NPO-45824), NASA Tech Briefs, Vol. 34, No. 3 (March 2010), p. 48. Other previous work improved the safety characteristics of the electrolytes by adding flame-retardant additives such as triphenyl phosphate (TPhPh), tri-butyl phosphate (TBuPh), triethyl phosphate (TEtPh), and bis(2,2,2-trifluoroethyl) methyl phosphonate (TFMPo). The current work involves further investigation of other types of flame-retardant additives, including tris(2,2,2-trifluoroethyl) phosphate, tris(2,2,2-trifluoroethyl) phosphite, triphenylphosphite, diethyl ethylphosphonate, and diethyl phenylphosphonate added to an electrolyte composition intended for wide operating temperatures. In general, many of the formulations investigated in this study displayed good performance over a wide temperature range, good cycle life characteristics, and are expected to have improved safety characteristics, such as low flammability. Of the electrolytes studied, 1.0 M LiPF6 in EC+EMC+DEP (20:75:5 v/v %) and 1.0 M LiPF6 in EC+EMC+DPP (20:75:5 v/v %) displayed the best operation at low temperatures, whereas the electrolyte containing triphenylphosphite displayed the best cycle life performance compared to the baseline solution. It is anticipated that further improvements can be made to the life characteristics with the incorporation of a SET promoters (such as VC, vinylene carbonate), which will likely inhibit the decomposition of the flame-retardant additives.

Smart, Marshall C.↗

Space station crew safety: Human factors interaction model

A model of the various human factors issues and interactions that might affect crew safety is developed. The first step addressed systematically the central question: How is this space station different from all other spacecraft? A wide range of possible issue was identified and researched. Five major topics of human factors issues that interacted with crew safety resulted: Protocols, Critical Habitability, Work Related Issues, Crew Incapacitation and Personal Choice. Second, an interaction model was developed that would show some degree of cause and effect between objective environmental or operational conditions and the creation of potential safety hazards. The intermediary steps between these two extremes of causality were the effects on human performance and the results of degraded performance. The model contains three milestones: stressor, human performance (degraded) and safety hazard threshold. Between these milestones are two countermeasure intervention points. The first opportunity for intervention is the countermeasure against stress. If this countermeasure fails, performance degrades. The second opportunity for intervention is the countermeasure against error. If this second countermeasure fails, the threshold of a potential safety hazard may be crossed.

Cohen, M. M.↗

Space Station crew safety - Human factors model

A model of the various human factors issues and interactions that might affect crew safety is developed. The first step addressed systematically the central question: How is this Space Station different from all other spacecraft? A wide range of possible issue was identified and researched. Five major topics of human factors issues that interacted with crew safety resulted: Protocols, Critical Habitability, Work Related Issues, Crew Incapacitation and Personal Choice. Second, an interaction model was developed that would show some degree of cause and effect between objective environmental or operational conditions and the creation of potential safety hazards. The intermediary steps between these two extremes of causality were the effects on human performance and the results of degraded performance. The model contains three milestones: stressor, human performance (degraded) and safety hazard threshold. Between these milestones are two countermeasure intervention points. The first opportunity for intervention is the countermeasure against stress. If this countermeasure fails, performance degrades. The second opportunity for intervention is the countermeasure against error. If this second countermeasure fails, the threshold of a potential safety hazard may be crossed.

Cohen, M. M.↗

The Grid Density Dependence of the Unsteady Pressures of the J-2X Turbines

The J-2X engine was originally designed for the upper stage of the cancelled Crew Launch Vehicle. Although the Crew Launch Vehicle was cancelled the J-2X engine, which is currently undergoing hot-fire testing, may be used on future programs. The J-2X engine is a direct descendent of the J-2 engine which powered the upper stage during the Apollo program. Many changes including a thrust increase from 230K to 294K lbf have been implemented in this engine. As part of the design requirements, the turbine blades must meet minimum high cycle fatigue factors of safety for various vibrational modes that have resonant frequencies in the engine's operating range. The unsteady blade loading is calculated directly from CFD simulations. A grid density study was performed to understand the sensitivity of the spatial loading and the magnitude of the on blade loading due to changes in grid density. Given that the unsteady blade loading has a first order effect on the high cycle fatigue factors of safety, it is important to understand the level of convergence when applying the unsteady loads. The convergence of the unsteady pressures of several grid densities will be presented for various frequencies in the engine's operating range.

Schmauch, Preston B.↗

Crowdsourcing for Innovative Personal Protection Technology

Personal protective equipment (PPE) plays a vital role in safeguarding workers from workplace hazards and minimizing exposure to harmful substances or conditions. To meet the changing needs and challenges faced by workers in various industries, PPE is continuously evolving. As new technologies emerge, advances in materials, design, and functionality contribute to PPE improvements. By incorporating personal protective technology (PPT) into traditional PPE, worker safety and well-being can be further enhanced. Crowdsourcing can harness a wide range of perspectives and expertise to identify novel technologies, materials, designs, or applications that can revolutionize PPE and improve worker protection. Partnering with the National Aeronautics and Space Administration (NASA) Center for Center of Excellence for Collaborative Innovation (CoECI), the National Institute for Occupational Safety and Health (NIOSH) National Personal Protection Technology Laboratory (NPPTL) launched three crowdsourcing challenges. These challenges aimed to promote innovation in several PPE areas: protective clothing, counterfeit respirators, and respirator fit. Preliminary results produced promising technologies and approaches promoting improved awareness, comfort, adaptability, and effectiveness against workplace hazards.

crowdsourcing↗

Designing for Advanced Aerial Mobility: Human-Autonomy Teaming and In-Time System-Wide Safety Assurance

The continued growth of aviation shall require new innovative technologies and operational concepts to meet the ever-increasing demands on air transportation. The NASA Advanced Air Mobility (AAM) project focuses on emerging aviation markets, such as Urban Air Mobility (UAM). UAM is defined as “...a safe and efficient system for air passenger and cargo transportation within an urban area. It is inclusive of small package delivery and other urban unmanned aerial system services and supports a mix of onboard/ground-piloted and increasingly autonomous operations” ([1]). The AAM project emphasizes technology development and validating system-level concepts and solutions in coordination with other NASA Aeronautics Research Mission Directorate (ARMD) projects to enable UAM metro- and micro-plex vertiport and airspace concepts of operations. The NASA AAM research portfolio includes the concepts of Remote Supervisor-in-Command (RSC) and Fleet and Airspace Manager (FAM) as possible human roles for consumer fleet providers. NASA research in RSC is focused on development of guidelines and standards for remote pilots/operators passively and actively controlling a large fleet of autonomous aircraft. For FAM, flight and ground system concepts and technologies to enable high density homogeneous operations at increased scale from vertiport(s), and coordination with other humans in the systems (e.g., UAM urban airspace manager, Air Traffic Control) are key research areas. The envisioned UAM operations are posited to require autonomous systems to enable functions ranging from fleet and resource management to vehicle control. Although automation has become increasingly sophisticated and ubiquitous in civil aviation, autonomy represents a significant evolution in automation, which has generally been limited in functional scope and capability. As autonomy takes on increasing responsibilities, humans and machines will be required to work together in new and different ways [2], rather than traditional design approaches focused on how machines (i.e., autonomy) can do the work of people. The emerging field of human-autonomy teaming (HAT) represents a comprehensive and prioritized research-driven approach to enable the success of future emerging aviation market applications through capabilities and principles that facilitate humans and machine working and thinking better together. The NASA Transformational Tools and Technologies (TTT) Autonomous System (AS) Sub-project was created to assist with the transition into higher levels of autonomy to enable new modes of air transportation, such as UAM. TTT-AS has identified HAT as a key research need to enable UAM while maintaining today’s ultra-safe aviation system safety levels. The latter challenge has been taken up by the NASA System-Wide Safety (SWS) Project, which recognizes that aviation safety, as it evolves, shall require new ways of thinking about safety to include integration of a wide-range of existing and new safety systems and practices, enhanced tools and technologies, increased access to data and data fusion, improved data analysis capabilities, enhanced in-time risk monitoring and detection, hazard prioritization and mitigation, safety assurance decision-support, and in-time integrated system analytics [3].The operational concept of UAM represents a variety of work that has been termed, “work-as-imagined” to characterize the idea that how people think that work is done and how work is actually done are often not the same [4]. To ensure design success and system safety, looking at “work-as-done” provides a comparative approach toward UAM concept and technology design through examination of corresponding analogs found today in aviation (e.g., on-demand operations) and other transportation domains (e.g., port operations). The paper shall discuss various alternative applications with specific focus on airline operation center (AOC) operations, and unmanned aerial system (UAS) command-and-control to inform scaled-versions of FAM and RSC, respectively, and with consideration of the national airspace system contextual environment. The tenets and principles of the HAT field and current NASA research efforts under the TTT-AS sub-project shall also be described. Finally, the SWS sub-project efforts to develop In-Time System-Wide Safety Assurance (ISSA) and In-Time Safety Management Systems (IASMS) are discussed in terms of how “in-time” safety assurance may be conceptualized for the on-demand mobility air taxi “work-as-imagined” operational concept [5]. As part of this effort, concepts from the emerging field of resilience engineering, are being studied. Traditional approaches to aviation safety have focused on what can go wrong and how to prevent it. Another approach to thinking about system safety should reflect not only “avoiding things that go wrong” (protective safety) but also “ensuring that things go right” (productive safety), that enables a system to exhibit the resilient performance [6] necessary for the success of the future aviation system emerging concepts of operations. The paper shall describe efforts focused on how productive safety and resilience may enable a more complete approach to system safety thinking and design of ISSA and IASMS for UAM. Future directions and research needs shall also be discussed.

resilience↗

Development of small radioisotope heaters.

A design study was conducted to (1) determine potential applications of small (1 to 50 watt) radioisotope heaters in manned spacecraft thermal control and life support systems and (2) develop designs for an optimum group of heaters to fulfill a maximum number of applications with mission times from 14 days to 5 years. Thirty-seven potential application areas were identified requiring up to 300 heaters ranging in size from less than 1 to over 100 watts. Safety and design criteria were selected and reference heater designs developed. Optimization analysis indicated that two heater sizes, 10- and 50-w, and two fuels, promethia and plutonia, would most efficiently meet the majority of identified applications.

Smith, T. H.↗

Safety of spacecraft lightweight pressure vessels

With the advent of the age of flight and specifically space flight, a major effort was devoted to the development of lightweight metallic flight hardware. The paper deals with metallic pressure vessels designed to hold liquids or gases under pressure and with the methods for assuring safety through elimination of failures. The consequences of discontinuity stress failures range from leakage, bursting, and detrimental deformation to catastrophic failure, or literally, an explosion of the vessel. Controls, system design, protective devices and tests are discussed.

Bolger, P. H.↗

Evaluation of advanced high rate Li-SOCl2 cells

Under NASA sponsorship, JPL is developing advanced, high rate Li-SOCl2 cells for future space missions. As part of this effort, Li-SOCl2 cells of various designs were examined for performance and safety. The cells differed from one another in several aspects, such as: nature of carbon cathode, catalysts, cell configuration, case polarity, and safety devices. Performance evaluation included constant-current discharge over a range of currents and temperatures. Abuse-testing consisted of shortcircuiting, charging, and over-discharge. Energy densities greater than 300 Wh/Kg at the C/2 rate were found for some designs. A cell design featuring a high-surface-area carbon cathode was found to deliver nearly 500 Wh/Kg at moderate discharge rates. Temperature influenced the performance significantly.

Deligiannis, F.↗

Reliability Model Generator for fault-tolerant systems

This paper discusses an analysis tool, the Reliability Model Generator, that reasons from structural and functional system design specifications to generate a reliability model for the system under investigation. The resultant model defines a system state space sufficient to characterize the effects of single and multiple component failures. This model may then be examined by the analyst or used as input to an existing reliability evaluation tool, the Semi-Markov Unreliability Range Evaluator (SURE), to compute numeric bounds for system reliability (i.e., safety, mission success, availability, etc.). In defining the input to the Reliability Model Generator, a separation of the component function from structural specification is proposed to allow easy modification for analysis of alternative architectures. A hierarchical system description paradigm promotes multiple abstractions, thereby enabling analysis at all phases of the design process. The work described in this paper has been supported under NASA contract NAS1-10899, Integrated Airframe/Propulsion Control System Architecture (IAPSA II). IAPSA II promotes a system engineering methodology and supporting analytical tools to evaluate flight control architecture configuration alternatives during early phases of the design cycle when the cost and schedule impact of design revisions is minimal. Emphasis is placed on traceability to ensure that the requirements drive the resulting design.

Catherine M McCann↗

Advanced rechargeable sodium batteries with novel cathodes

Various high energy density rechargeable batteries are being considered for future space applications. Of these, the sodium-sulfur battery is one of the leading candidates. The primary advantage is the high energy density (760 Wh/kg theoretical). Energy densities in excess of 180 Wh/kg were realized in practical batteries. Other technological advantages include its chemical simplicity, absence of self-discharge, and long cycle life possibility. More recently, other high temperature sodium batteries have come into the spotlight. These systems can be described as follow: Na/Beta Double Prime-Al2O3/NaAlCl4/Metal Dichloride Sodium/metal dichloride systems are colloquially known as the zebra system and are currently being developed for traction and load leveling applications. The sodium-metal dichloride systems appear to offer many of the same advantages of the Na/S system, especially in terms of energy density and chemical simplicity. The metal dichloride systems offer increased safety and good resistance to overcharge and operate over a wide range of temperatures from 150 to 400 C with less corrosion problems.

Distefano, S.↗

Calibrating Airplane Instrumentation To Measure Winds

Elaborate combination of techniques used to calibrate wind-measuring instrumentation aboard F104 airplane. Obtains wind profiles more rapidly. Airplane equipped with standard NACA research nose boom, including pressure probes and flow vanes yielding data on static and total pressures, angle of attack, and angle of sideslip. Has ring-laser-gyroscope inertial reference unit, giving linear and angular velocities, linear acceleration, and orientation of airplane. Body-mounted total-temperature sensor also used. Improved method of calibration devised to determine whether winds aloft at and shortly after time of measurement allow safe launch of Space Shuttle. Proves beneficial in other safety- or research-oriented applications in which wind velocities over range of altitudes must be determined in nearly real time.

Haering, Edward A., Jr.↗

John F. Kennedy Space Center's Technology Development and Application 2006-2007 Report

Topics covered include: Reversible Chemochromic Hydrogen Detectors; Determining Trajectory of Triboelectrically Charged Particles, Using Discrete Element Modeling; Using Indium Tin Oxide To Mitigate Dust on Viewing Ports; High-Performance Polyimide Powder Coatings; Controlled-Release Microcapsules for Smart Coatings for Corrosion Applications; Aerocoat 7 Replacement Coatings; Photocatalytic Coatings for Exploration and Spaceport Design; New Materials for the Repair of Polyimide Electrical Wire Insulation; Commodity-Free Calibration; Novel Ice Mitigation Methods; Crack Offset Measurement With the Projected Laser Target Device; New Materials for Structural Composites and Protective Coatings; Fire Chemistry Testing of Spray-On Foam Insulation (SOFI); Using Aerogel-Based Insulation Material To Prevent Foam Loss on the Liquid-Hydrogen Intertank; Particle Ejection and Levitation Technology (PELT); Electrostatic Characterization of Lunar Dust; Numerical Analysis of Rocket Exhaust Cratering; RESOLVE Projects: Lunar Water Resource Demonstration and Regolith Volatile Characterization; Tribocharging Lunar Soil for Electrostatic Beneficiation; Numerically Modeling the Erosion of Lunar Soil by Rocket Exhaust Plumes; Trajectory Model of Lunar Dust Particles; Using Lunar Module Shadows To Scale the Effects of Rocket Exhaust Plumes; Predicting the Acoustic Environment Induced by the Launch of the Ares I Vehicle; Measuring Ultrasonic Acoustic Velocity in a Thin Sheet of Graphite Epoxy Composite; Hail Size Distribution Mapping; Launch Pad 39 Hail Monitor Array System; Autonomous Flight Safety System - Phase III; The Photogrammetry Cube; Bird Vision System; Automating Range Surveillance Through Radio Interferometry and Field Strength Mapping Techniques; Next-Generation Telemetry Workstation; GPS Metric Tracking Unit; and Space-Based Range.

Source record↗

Modeling of the Mode S tracking system in support of aircraft safety research

This report collects, documents, and models data relating the expected accuracies of tracking variables to be obtained from the FAA's Mode S Secondary Surveillance Radar system. The data include measured range and azimuth to the tracked aircraft plus the encoded altitude transmitted via the Mode S data link. A brief summary is made of the Mode S system status and its potential applications for aircraft safety improvement including accident analysis. FAA flight test results are presented demonstrating Mode S range and azimuth accuracy and error characteristics and comparing Mode S to the current ATCRBS radar tracking system. Data are also presented that describe the expected accuracy and error characteristics of encoded altitude. These data are used to formulate mathematical error models of the Mode S variables and encoded altitude. A brief analytical assessment is made of the real-time tracking accuracy available from using Mode S and how it could be improved with down-linked velocity.

Sorensen, J. A.↗

A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.

Maddalon, Jeffrey M.↗