Space Grant Consortium - University of Wisconsin - Green Bay

Area dramatically
influenced by flow
over body
Figure 5: Model of Booster Boattail showing fin areas under significant influence of flow over the body.
Although Barrowman’s theory accounts for the effects of fin-to-body interference, it provides no
concession for the effects of fin-to-boattail interference. As a result, the predicted center of
pressure is probably closer to the nose of the rocket than the actual CP is. However, this effect is
not expected to be large enough to push the rocket into a state of instability.
One additional stability concern was considered: As the motor burns, the center of gravity of the
rocket assembly moves forward. It is likely that this effect will couple with the boattailinterference
effect, resulting in a stable flight until the dart separates.
Optimization
There is an optimal mass of the dart for which the dart reaches the greatest altitude. In order to
find this mass, the differential equations governing flight were derived and a MATLAB script
was written to integrate these equations of motion. The numerical method accounted for the
varying mass of the rocket as fuel is burned. The following chart shows the predicted maximum
altitudes for different dart weights.
Maximum Altitude of Dart [ft]
6000
5500
5000
4500
4000
3500
3000
2500
2000
0 1 2 3 4 5
Weight of Dart [lbf]
Figure 6: Maximum Altitude of the dart for various dart weights. The drag coefficient of the dart was
assumed to be 0.3 and the weight of the booster was 4.3 lbf. The booster + dart assembly’s Cd was 0.35.
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