Space Grant Consortium - University of Wisconsin - Green Bay

successfully fit the necessary components inside this size dart, but concluded the further
reductions in size were not practical.
The second major design objective for the dart was to ensure stability. Stability is of major
importance in rocketry. As a rocket flies, all the drag forces and wind forces effectively act as
though a single force is applied at one location—the center of pressure (CP). If the CP does not
exactly coincide with the center of gravity (CG), then the resultant force causes rotation of the
rocket about the CG. Three classes of flight stability depend on the relative positions of the CG
and CP:
1) CP is in front of CG: Rocket is unstable.
2) CP is just behind the CG: Rocket is stable.
3) CP is far behind CG: Rocket is over-stable.
It is clear that case 2 is the most desirable. As a rule of thumb, a rocket with a CP that is located
between 1 and 2 rocket diameters behind the CG falls into this category. Barrowman’s theory
was used to approximate the CP of the rocket. This theory was submitted by James Barrowman
as a practical means to compute a slender rocket’s center of pressure under general
considerations (most prior theories involved detailed assumptions that made them invalid for the
majority of applications). Avoiding such limiting assumptions, Barrowman’s theory applies to
most slender rockets flying at subsonic speeds and low angles of attack. Barrowman found his
theory’s predictions to be within 10% agreement of wind tunnel testing in most cases.
The following scale drawings show the CPs and CGs of the dart. Note that the rocket falls in the
stable range, where the CP is 1-2 calibers behind the CG.
CG CP
Figure 2: Scale drawing of 1.5 inch diameter dart showing CP and CG
Entire Assembly The booster and dart cannot be designed individually; rather, they must
operate in tandem and be designed with compatibility in mind. For the interface between the dart
and booster, two design features are of great importance: the method of joining/separating, and
the stability of the assembly.
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