Project Director

Elliott, Trevor S.

Department Examiner

Margraves, Charles H.; McDonald, Gary


Dept. of Mechanical Engineering


University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)


In this paper, the mathematical modelling of a rocket with varying mass is investigated to construct a function that can describe the velocity and position of the rocket as a function of time. This research is geared more towards small scale rockets where the nonlinear drag term is of great interest to the underlying dynamics of the rocket. A simple force balance on the rocket using Newton’s second law of motion yields a Riccati differential equation for which the solution yields the velocity of the rocket at any given time. This solution can then be integrated with respect to time to get the position function. The Differential Transform Method (DTM) is applied to the Riccati differential equation while yields a polynomial series solution approximation. This solution is then compared to numerical solutions from existing commercial rocket flight simulators, and to experimental data from rocket flights. A parametric study is also performed to survey the effects of density, diameter of the rocket airframe, drag coefficient, mass flow rate, and thrust on the overall motion of the rocket. The comparisons of the DTM solution to existing data showed almost a perfect match and the parametric study provides an insight into the various effects of the variables listed above. The goal of this research is to aid rocket design teams, especially in university rocketry competitions, to use as an additional tool with the flight simulators. While the flight simulators yield outstanding results, it is difficult for the user to study the fundamental physics of the flight from the simulator alone, and therefore the DTM solution and its results can be enlightening and helpful.


My deep appreciation goes first to Dr. Trevor Elliott, who proficiently guided me through this research and mentored me throughout my undergraduate studies during my time at UTC. His unwavering support for both my studies and future endeavors has been incredibly beneficial. He has played a huge role in helping me accomplish the things I have, and I hope to carry the wisdom he has so kindly parted with me, for the rest of my life. My appreciation also extends to the Office for Undergraduate Research and Creative Endeavor for funding all my research projects including this one. Their support with URaCE and the SEARCH grant made it possible to financially support all my research goals at UTC while also training and providing me with the means to become a better scientist. Finally, I am extremely grateful to my family whose value to me only grows with time.


B. S.; An honors thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Bachelor of Science.




Differential equations; Rockets (Aeronautics)--Mathematical models


Analytical solution of rocket flight; Differential transform method; Mathematical modeling; Rocket flight simulation; Rockets; Small scale rockets


Ordinary Differential Equations and Applied Dynamics | Other Mechanical Engineering

Document Type



26 leaves