Great Circle Guidance for Long-Range Bank to Turn Vehicles

—This paper presents a mathematical framework for Great Circle Guidance (GCG) applied to Bank-to-Turn (BTT) air vehicles operating over long distances, where flat-earth assumptions are no longer valid. By leveraging great circles-geodesics on a spherical Earth, as navigation paths between waypoints, the developed approach accounts for Earth curvature and introduces definitions for course angles, cross-track, and down-track errors. The work formalizes six theorems that establish the foundation of great circle tracking and transitions, including a guidance law designed specifically for BTT vehicles. This law is shown to convergence onto the desired path. Joshua Matthews is a Principal Systems Engineer and Tech Lead at Applied Systems Engineering Incorporated (ASEI) with nearly two decades of industry experience. He holds both a B.S. degree (2003) and an M.S. degree (2006) in Electrical and Computer Engineering from Brigham Young University (BYU) were he studied adaptive control of fixed wing Micro Air Vehicles (MAVs) with the MAGICC Lab. Upon graduating, Joshua worked at Raytheon as a Guidance, Navigation, and Control (GNC) Engineer, earning the Excellence in Engineering and Technology Award from Raytheon and eventually becoming a Lead Systems Engineer. His professional interests include the autonomous control of air vehicles, systems engineering, and Model Based Systems Engineering (MBSE). Dr. Ahmed Abdelmawgoud, an accomplished expert in advanced missile guidance algorithms, hypersonic technology, and multi-agent control systems, has built a distinguished career in the defense and aerospace industry. He earned his B.S.M.E., M.S., and Ph.D. in electrical engineering from the University of Texas at San Antonio. His early work included contributions to cooperative unmanned systems research followed by a notable tenure at Southwest Research Institute, where he led and contributed to large-scale robotic projects and served as a key team member in designing the world’s largest commercial robot. Since joining Raytheon in 2019, Dr. Abdelmawgoud has advanced through roles in senior and principal systems engineering to his current position as Senior Manager of Systems Engineering. In this capacity, he manages hypersonic performance for a major product, collaborates across multiple missile programs, leads engineering teams, reviews and develops innovative concepts for internal investment, and teaches on-site courses in missile guidance, robotics, and related topics while mentoring emerging engineers. Dr. Abdelmawgoud’s leadership and technical excellence have earned him extensive recognition, including selection to the Arizona Daily Star’s 40 Under 40 list, along with multiple awards for innovation, collaboration, and advanced technology contributions across 2022–2025. His achievements span developing a novel guidance technique and strengthening Raytheon’s innovation community. Since 2020, he has also served as an adjunct professor in the University of Arizona’s Department of Aerospace and Mechanical Engineering, where he has developed and taught multiple engineering courses. Committed to service and mentorship, he volunteers within the local community and remains dedicated to advancing hypersonic technologies and developing the next generation of aerospace engineers.