Rocket Motion
Table of Contents ABSTRACT 2 1.0 INTRODUCTION 2 2.0 THEORY 3 3.0 PROCEDURE 4 4.0 RESULTS 4 5.0 DISCUSSIONS 9 6.0 CONCLUSIONS 10 7.0 APPENDIX 11
ABSTRACT
Motion of the rocket is simulated using two numerical analysis methods. From the simulation different parameters such as altitude, velocity, acceleration and range for initial fuel flows were calculated.
Two numerical methods, Euler’s integration and 4th order Runge-Kutta integration are used for calculating different parameters for the vertically launched rocket. The efficiency and the accuracy of the methods were compared. It was found out that the 4th order Runge-Kutta is more efficient than Euler’s integration method for the given time step.
Also for the rocket given the optimal initial fuel mass flow rate for attaining the highest altitude is found to be 35.5 Kg/S which gives an altitude of 1362594 m. 1.0 INTRODUCTION
Rockets are important part of space travelling. But rockets are also in many other important applications. The basic understanding of the physics behind rocket motion is easier to understand as it obeys Newton’s laws of motion. But this understanding is not enough to design and test a rocket as there are other critical parameters that must be taken into account.
It is critical to know the trends in the rocket parameters such as its velocity, distance travelled and acceleration in order to design rocket for its appropriate application. For this simulating the motion of the rocket and analysing the data measured is one of the efficient ways.
In this report two numerical methods, Euler’s integration and 4th order Runge-Kutta integration are used for calculating different parameters for a vertically launched rocket. This report also discusses the trends in behaviour of some of the parameters measured and in particular the efficiency and accuracy of the both methods.
2.0 THEORY
Figure x: Forces acting on Rocket
From Figure X
ABSTRACT
Motion of the rocket is simulated using two numerical analysis methods. From the simulation different parameters such as altitude, velocity, acceleration and range for initial fuel flows were calculated.
Two numerical methods, Euler’s integration and 4th order Runge-Kutta integration are used for calculating different parameters for the vertically launched rocket. The efficiency and the accuracy of the methods were compared. It was found out that the 4th order Runge-Kutta is more efficient than Euler’s integration method for the given time step.
Also for the rocket given the optimal initial fuel mass flow rate for attaining the highest altitude is found to be 35.5 Kg/S which gives an altitude of 1362594 m. 1.0 INTRODUCTION
Rockets are important part of space travelling. But rockets are also in many other important applications. The basic understanding of the physics behind rocket motion is easier to understand as it obeys Newton’s laws of motion. But this understanding is not enough to design and test a rocket as there are other critical parameters that must be taken into account.
It is critical to know the trends in the rocket parameters such as its velocity, distance travelled and acceleration in order to design rocket for its appropriate application. For this simulating the motion of the rocket and analysing the data measured is one of the efficient ways.
In this report two numerical methods, Euler’s integration and 4th order Runge-Kutta integration are used for calculating different parameters for a vertically launched rocket. This report also discusses the trends in behaviour of some of the parameters measured and in particular the efficiency and accuracy of the both methods.
2.0 THEORY
Figure x: Forces acting on Rocket
From Figure X