Numerical Simulation of the Effects of Initial Air Pressure and Water Volume on the Performance of a Water Rocket Using the Fourth Order Runge Kutta (RK4) Method

Water rockets provide a simple yet effective physics experiment integrating mechanics, fluid dynamics, and kinematics. Their performance is influenced by initial air pressure and water volume fraction, which can be quantitatively analyzed using numerical simulation. This study investigates the effects of varying pressure (300–500 kPa) and water volume fraction (f = 0.10–0.60) on thrust profiles and maximum altitude, with analysis covering four distinct phases. The method involves formulating nonlinear differential models for each phase, followed by numerical simulations using the fourth order Runge Kutta (RK4) method with an optimized time step (Δt = 0.001 s) to ensure convergence and computational efficiency. Results show that higher pressures increase peak thrust and maximum altitude, but shorten the duration of water thrust. An optimal water volume fraction of f ≈ 0.20–0.30 provides a balance between thrust intensity and duration to achieve maximum altitude. Further experiments with variations in bottle structure and aerodynamic parameters are recommended.