Image Analysis of the Dynamics of Reusable Launch Vehicle
Authors: Martin Ainsley , Stay Gavin , Lingel Abigail , Fontes Douglas 
Published: January 2025

Abstract
The advent of reusable rocket technology represents a pivotal shift towards sustainability and efficiency in space exploration. Among these advancements, SpaceX’s Falcon 9 First Stage stands out, known for its ability to launch into orbit and return to Earth for repeated flights. This development has lowered cost barriers to space exploration, thereby sparking an era of unprecedented scientific discovery, commercial partnerships, and innovation. Flight control of reusable rockets in terms of their kinetics from re-entry to landing is essential to promote a safe and efficient rocket return. In this sense, understanding the detailed dynamic characteristics of the flight helps us to identify the required maneuvers for a safe landing and critical phases regarding the kinetics. In this study, our goal is to reconstruct the trajectory of SpaceX’s Falcon 9 First Stage using only telemetry data from the January 2nd, 2024 launch. We also estimate the engine flow rates required for maintaining the trajectory. This research uniquely contributes to the accessibility of aerospace engagement by providing a detailed empirical analysis using real-time, publicly available data.
Our methodological approach involved extracting time, speed, and altitude data from the publicly streamed launch video. We reconstructed the booster’s telemetry from stage separation to landing by applying fundamental kinematics equations and graphical analysis. Newton’s Second Law, Newton’s Law of Gravitation, and the drag equation were then utilized to calculate the net forces acting on the booster throughout its trajectory. Considering the booster’s geometry and the varying atmospheric conditions, we isolated engine forces from drag and gravitational forces, enabling the determination of engine flow rates.
Our findings intricately map the journey of SpaceX’s Falcon 9 First Stage through detailed velocity and acceleration graphs that illustrate the inherent complexity of reusable rocket technology. These results match both theoretical predictions and the observed timing of burns in the launch video, validating the precision of our trajectory reconstruction. The derived engine flow rates indicate low fuel consumption, with only 8.6% of the total launch fuel mass being expended on the return journey. This efficiency is crucial for maintaining reduced costs associated with reusable rocket technology, making it an effective pathway for future space exploration.
This study provides a detailed empirical analysis of the Falcon 9 First Stage, enriching both academic and practical understanding of its operational dynamics. A comprehensive literature review indicates that trajectory validation and engine flowrate extrapolation from live-streamed telemetry data are relatively unexplored, as related papers utilize extensive computational models or in-depth flight data provided directly by SpaceX. By analytically applying publicly accessible validating telemetry data, this paper facilitates broader engagement with space missions without the need for extensive infrastructure. This methodology provides unique educational and research opportunities by allowing researchers, enthusiastics, and the public to connect with space flights as they happen. Additionally, it provides a way for media to use real-time data and graphs to further engage their audience. As the industry moves toward more maintainable and cost-effective practices, the lessons learned from the Falcon 9 First Stage’s development and operation will undoubtedly inform future innovations in aerospace technology.