From Cork to Coasting: A Multi-Stage ODE Model of Water-Rocket Flight

Authors

• Viktoria Savatorova, Central Connecticut State UniversityFollow
• Patryk Kustra, Central Connecticut State University
• Ethan Dyer, Central Connecticut State University
• Connor Carlson, Central Connecticut State University
• Aleksei Talonov, University of Nevada Las Vegas

Publication Date

6-18-2026

Keywords

Mathematical modeling, differential equations, water rockets, numerical simulation, parameter sensitivity, model validation

Disciplines

Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Water rockets provide an affordable and engaging context for exploring applications of differential equations. Motivated by outreach activities conducted with undergraduate students, we develop a four-stage mathematical model of vertical water-rocket flight that is suitable for use in an ODE or mathematical modeling course. The model includes the cork-release phase, water-thrust propulsion, air-thrust propulsion with compressible and potentially choked flow, and the final ballistic stage with quadratic drag. While retaining key physical features, the model can be formulated as a system of ordinary differential equations that can be integrated numerically using tools familiar to students. We compare model predictions with collected experimental data and incorporate parameter sensitivity analysis for key quantities such as initial pressure, water fill fraction, and drag coefficient. To support classroom adoption, we provide MATLAB code, suggested experiments, and pedagogical notes. The resulting module offers a complete mathematical modeling project that guides students from physical assumptions through differential equations, numerical simulation, and comparison with experimental data.

Recommended Citation

Savatorova, Viktoria; Kustra, Patryk; Dyer, Ethan; Carlson, Connor; and Talonov, Aleksei (2026) "From Cork to Coasting: A Multi-Stage ODE Model of Water-Rocket Flight," CODEE Journal: Vol. 20: Iss. 2, Article 6.
Available at: https://scholarship.claremont.edu/codee/vol20/iss2/6

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