Dynamic modelling and experimental investigation of the downrange of a water rocket

 

Physik  |  Technik

 

Yelyzaveta Doroshenko, 2005 | Basel, BS

 

Water rockets are small-scale rocket prototypes powered by the pressurized air forcing the water out of the rocket. Rapid air expansion during the launch tube phase followed by the dynamic pressure and mass variation during the thrust as well as the complex aerodynamic profile are the main factors that substantially complicate the modelling of the rocket’s motion. In this study, the downrange of a water rocket is investigated based on the initial pressure and the launch angle. A dynamic model of a rocket’s motion, dependent on the initial parameters, is developed by implementing Euler’s method in Excel. In addition, the drag coefficient is determined empirically by performing the drop test. The experiment at various initial pressures and launch angles is conducted and the qualitative analysis of the numerical and the empirical range is performed. There is evidence that the range will increase nonlinearly with the increase of the initial pressure while the optimal range will be achieved with the launch angles lower than 45 degrees. Despite the relatively precise simulation of the trajectory and the range prediction, the feasible explanation for the data deviation is presented. The findings can be used for the optimization of rocket’s prototypes and research.

Introduction

This study investigates and analyses the dependence of the water rocket’s downrange on the initial launch conditions, such as the initial pressure and the launch angle.

Methods

This research paper implements Euler’s method to simulate the rocket’s motion in Excel. The drag coefficient is determined empirically by conducting the drop test. The nose cone, fins and the fin brackets models are created in Shapr3D and 3D-printed in PLA. Each experiment is conducted 3 times for various initial pressures, ranging from 3,5 to 5,5 bars, and launch angles, ranging from 30 to 60 degrees. The rocket’s motion is manually tracked in the Tracker App. The numerical and the empirical range and trajectory data are combined into graphs for the further analysis. The model’s precision is evaluated in Excel by performing error and statistical analyses.

Results

Both empirical and numerical data revealed a significant non-linear increase in the range with the increase of the initial pressure, reaching its peak of (100±0,01) m and of (84±0,01) m with (5,5±0,01) bars initial pressure from the empirical and the numerical datasets respectively. The maximal empirical range value of (107±0,01) m was recorded at 42 degrees launch angle and the maximal numerical range value of (84,63±0,01) m was recorded at 40 degrees angle. After the range reaches its peak, the further increase in launch angles is followed by the range decrease. In both empirical and numerical datasets the launch angle contributes to the range, though a considerably more substantial impact of the angle on the range is observed from the empirical findings. A relatively significant difference in the numerical and empirical range values, with the average percentage error being 9,11% and 8,71% in case of the pressure and launch angle variation respectively, is observed.

Discussion

The empirical results predominantly confirmed the expected dependence of the downrange on both the initial pressure and the launch angle, revealing similar trends. The dynamic water thrust profile is modelled to accurately predict the water flow behaviour. However, the model tends to underestimate the range at various launch angles, leading to greater deviations at higher pressures. Feasible explanations for the deflections include the neglection of the air thrust and water losses in the model, and inaccuracies in the drag coefficient calculation. The attachment of the GPS to the rocket and the accelerometer use may increase the empirical precision. Yet, the model may be deemed sufficiently accurate, providing reasonable range values.

Conclusions

This work has explored the dependence of the rocket’s downrange on the initial pressure and the launch angle. The dynamic model of the rocket’s motion, applying Euler’s method in Excel, is developed to predict the rocket’s range and the trajectory. The drag coefficient is determined. The empirical and numerical findings are analysed and interpreted, and possible explanations for the data deviations are presented. Yet, the question to what extent the neglection of the air thrust and water losses in the model may have contributed to the sporadic range underestimation is debatable. Thus, the enhancements in the model and instrument accuracy are necessary for further research.

 

 

Würdigung durch den Experten

Maximilian Kirchhoff

Yelyzaveta hat mit hohem Engagement iterativ die fundamentalen Aspekte der Raketentechnik analysiert, experimentiert, korreliert und verbessert, und die komplexen physikalischen Zusammenhänge auf systematische und verständliche Weise vorgeführt – ein wichtiger Schritt um weiteren Forschern das aktuelle Thema der Raketentechnik schnell näher zu bringen und die erarbeiteten Grundlagen weiterzuentwickeln und zu verbessern !

Prädikat:

sehr gut

 

 

 

Gymnasium am Münsterplatz, Basel
Lehrer: Mads Macholm