Casey Drubin and Spencer Friske
12/11/12
Engineering 005
Team Rocket Final Project Report
Abstract: For our project we utilized MatLab to model the launch of a Titan I rocket. We
accounted for variables such as drag, gravity, thrust, and the Coriolis effect. The program
allows the user to input a certain degree of launch to predict where the rocket will land.
Overall, we struggled to achieve a fully functioning program but were successful in many
individual aspects of the code.
Introduction: We decided to model the Titan I rocket launch through MatLab that
accurately predicts the destination of the rocket given certain initial conditions. We were
motivated to complete this project because it has real world applications and is a good
review of concepts in both Engineering (MatLab) and Physics 003 (kinematics). The
project is interesting to us because it allows us to explore the area of aeronautical
engineering, a concentration of interest to both of us, while maintaining realistic
applications given our current skill set.
Background Theory: In order to grasp the concept of the rocket launch equation, it is
important understand the Coriolis effect. The Coriolis effect describes the phenomenon of
the earth spinning about its axis while the rocket is airborne. It is necessary to calculate
the Coriolis effect to understand its implications, and the calculations require the
conversion of Cartesian coordinates to spherical coordinates. The conversions can be
seen within the coding. Furthermore, it is important to realize that the force of gravity and
drag change depending on the altitude of the rocket.
Completed Project Design: In order to accurately determine the final destination of the
rocket, it was necessary to consider a variety of components. We considered the change
in gravitational force due to altitude, the change in drag force due to altitude, thrust and
the Coriolis effect. To calculate these effects, we created one overall function that called
eight individual functions. The calculations of change in gravitational force, drag force,
thrust force, the Coriolis effect, and velocity each had their respective functions. The
other functions served to convert Cartesian coordinates to spherical coordinates and vice
versa. We found the necessary equations online at Wikipedia.
Our code first utilized a for loop to iterate through one second intervals while the rocket
burns through its fuel. In each one second interval, we call all of the functions for thrust,
drag, the Coriolis effect, and gravity. We then convert all velocities to Cartesian vectors
and update the rocket’s position and velocity. We store positions and velocities in both
Cartesian- x,y,z - and spherical- r,theta, phi - coordinates.
Our code then utilizes a while loop to iterate through one-second intervals and check that
the rocket’s spherical coordinate r is greater than the radius of earth, indicating that the
rocket has not landed yet.
When the rocket does land, the longitude and latitude are returned as function outputs.
Results: While we were unable to find the final coordinates for the destination of the
rocket (results came backs as NaN), we did experience some success. We were able to
convert from spherical coordinates to Cartesian coordinates and back to spherical
coordinates with accuracy. Therefore, we succeeded in writing functions that converted
coordinates. Also, the individual functions to calculate acceleration due to gravity, thrust,
drag, and the Coriolis effect seemed successful.
Discussion: Overall the project went well as we were able to learn more about calculating
a rocket’s final destination. Additionally, we were able to hone our MatLab skills, proved
by the successful functions converting spherical coordinates to Cartesian coordinates.
Unfortunately, we were unable to get a fully functional code, but we believe that with
more time and help we would be able to create a functional code. In conclusion, the
project allowed us to learn more about the physics behind a rocket launch on Earth while
applying the skills we learned throughout the semester.