Introduction
In this project we designed, built, and tested a water bottle rocket.
The rocket was to be
constructed out of two 2-liter plastic bottles and was to hold a payload consisting of a filled water balloon
with a parachute made out of garbage bags and tied to the payload with fishing line.
The goals of the
project were to successfully launch and recover the rocket and its payload, to maximize the descent time
of the payload with the parachute and to successfully implement the rocket trajectory analysis developed
in class.
Theory
Describe in detail the development of the rocket trajectory equations and the Mathcad procedure
used to solve these equations.
Any figures used in this explanation must be referred to in the text and be
labeled.
Use textbook format.
In order to understand the math behind the rockets we tested, we had to develop rocket trajectory
equations to describe the changing mass, height, and velocity of the rocket.
Working in class, we
developed a program that can figure out the mass, velocity, and height of the rocket at any time along the
flight, given the mass of the empty rocket and the volume of water used to propel the rocket.
To start off,
we needed a few constants, such as
A
e
, the area of the opening of the rocket,
D
, the diameter of the rocket,
mdot
, the mass flow rate,
ρ
w
, the density of water,
C
D
, the drag coefficient, and
ρ
, the density of the air.
These values are given in Figure 1.
= .
= .
= .
= .
= .
Ae 0 000349 ft3 D 4 3 in mdot 0 342slugs ρw 1 94slugft3 CD 0 3
= .
ρ 0 00238slugft3
Figure
The program for explaining the trajectory of the rocket relies on four main equations.
Each
equation defines a characteristic of the flight of the rocket at a given time
i
.
The equations give the time
along the flight (Figure 2), the mass (Figure 3), velocity (Figure 4), and height (Figure 5) of the rocket at
the given time.
=
ti ti