Space Grant Consortium - University of Wisconsin - Green Bay

First Place, Non-Engineering: Schmitt Triggers
2009 WSGC Intercollegiate Rocket Competition
Brad Hartl, Jacob Wardon, Steve Welter, Mark Witte, Michael LeDocq
University of Wisconsin-La Crosse & Western Technical College
Synopsis
Plan of action. Prior to making any major design plans or ideas, a precise plan of action
was created for attacking this problem. The first step was to find out what the ideal shape of the
dart and booster stage should be. There were a few specific restrictions that had to be accounted
for, such as motor and altimeter size, but beyond that, the options were wide open. The first thing
considered was the drag equation (equation 1), which is the force of air resistance on the rocket
and ultimately the most important concern.
(1)
The first two variables of the equation are ρ, which represents the air density, and u, which
represents the velocity at which the object is traveling at. Both of these variables can not be
controlled directly by the shape of the rocket. The last two variables, CD (coefficient of drag) and
A (cross-sectional surface area), can be controlled by the shape of the rocket. In order to decrease
the air resistance on the rocket, both of these terms should be minimized. The cross-sectional
surface area is basically the surface area you would see, as if you were looking at the rocket from
above it. Since there was a four inch required diameter on the lower stage, there really wasn’t
much control over this. However, the width of the fins would contribute slightly and thus their
thickness and length was kept to a minimum.
The drag coefficient is a measure of how smoothly and easily air can pass around the object. The
more streamlined the object, the less turbulent flow there will be, and thus the less resistance.
The profile shape with the lowest drag coefficient is a tear drop shape. [4] Thus, an ideal shape
was found to model the rocket after. While not directly related to the drag equation, the next
most important variable to calculate was the ideal masses of the rocket stages. Newton’s second
law states that
Net Forces = Mass x Acceleration (2)
When the motor is firing, it is the primary force on the rocket, thus it would be ideal to keep
mass minimized in order to allow the acceleration to be maximized. Integrating acceleration
twice will give distance. Hence, the less mass during takeoff, the higher the rocket will go.
However, after the motor has shut off, the dominant force term is the air drag. In this case, the
rocket will actually be decelerating from its maximum velocity. Now, the mass should be
maximized in order to reduce the deceleration of the rocket. In conclusion, the mass of the rocket
will have to be precisely calculated and will need to account for both of these time frames.
Now that there is an understanding of what the rocket should ideally look like, it is now time to
find the appropriate parts in order to build a structure that resembled that shape. Obviously
certain design problems would be met, and only so much of the rocket could be built as
specified. One important part of this process was watching where the weight was being
distributed throughout the rocket. Ultimately the main concern was with where the center of
1