Bottle rockets.

Introduction

Launching bottle rockets is a rite of passage of every high school experience. Often, we, the students, try to analyze the resulting behavior of the rocket using the concepts learned in class. Unfortunately, many of the foundational principles we base our theory on are not sufficient to describe the exceptionally complex behavior of a bottle rocket. Here, we explore a new approach to analyzing the flight of bottle rockets and describe how we get there.

Initial assumptions

Initial equations

The first thing we use is the Tsiolkovsky rocket equation: $$m\frac{dU_{R}}{dt}=-u_{1}\frac{dm}{dt}$$