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The primary function of a fin can is to impart corrective forces to the vehicle if it's angle of attack is non-zero. If your vehicle architecture features an active stabilization feature, fins may be eliminated entirely. Fin geometry is the primary method of controlling a fins impact on stability. RasAero2 and OpenRocket are the primary comprehensive methods of simulating vehicle stability. For subsonic cases, or as an academic exercise, the Barrowman Equations can be solved to get an idea of a fins contribution to center of pressure location.
Thermal
Main Article: Fin Thermal Analysis
There are several concerns and constraints when doing the thermal design on a fin can. The primary sources of heating are aeroheating during ascent and conductive heating from the motor burn. The primary constraint is the resin system used in the construction of the fin can.
Aerodynamic
Main Article: Fin Aerodynamics
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