What is the relationship between sweep length and root chord of the fins with the center of pressure based on the Barrowman equations? CP (cm) 180 175 170 165 160 155 150 145 140 135 130 0 2 4 6 8 10 12 OpenRocket OpenFoam Linear (OpenRocket) Linear (OpenFoam)
Fin Sweep Length 2. Base on the graph, in what can you assume the reason the OpenFoam (CFD analysis) trend is opposite to the OpenRocket (Barrowman equations) data?
The Correct Answer and Explanation is:
Correct Answer:
The Barrowman equations (used by OpenRocket) predict that increasing the sweep length or decreasing the root chord moves the center of pressure (CP) forward, whereas OpenFoam (a CFD analysis tool) shows the CP moving backward under the same conditions. The reason for this opposite trend is that the Barrowman method is a simplified analytical approach that does not fully account for complex aerodynamic effects like flow separation, pressure gradients, or 3D fin-body interactions, which CFD tools like OpenFoam simulate more accurately.
Explanation:
The Barrowman equations are a set of analytical formulas used to estimate the aerodynamic center or center of pressure (CP) of a rocket based on simplified assumptions. These assumptions include small angles of attack, linear aerodynamic behavior, and the neglect of complex fluid dynamics. When analyzing changes to fin geometry, such as increasing sweep length or decreasing root chord, the Barrowman method typically predicts a forward shift in the CP. This is because more sweep and smaller root chords reduce the surface area contributing to stability, concentrating aerodynamic forces nearer to the nose.
However, OpenFoam uses computational fluid dynamics (CFD), which numerically solves the Navier-Stokes equations governing fluid flow. CFD captures detailed flow characteristics such as boundary layer effects, turbulence, vortex formation, and flow separation. When the sweep length is increased or the root chord is reduced, these complex interactions can cause pressure distributions along the rocket to shift differently than predicted by Barrowman. For instance, a highly swept fin may experience delayed flow attachment or stronger vortices, shifting the aerodynamic forces further aft.
The key reason for the opposite trends between OpenRocket and OpenFoam is that Barrowman simplifies the rocket into a 2D model of forces, while OpenFoam accounts for 3D effects and real airflow behavior. This highlights the limitations of analytical methods and the greater fidelity of CFD, especially at higher speeds or for complex fin shapes. Therefore, the difference is due to the increased accuracy and realism of CFD simulations compared to the idealized Barrowman equations.
