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The controller that drives the wheel is incredibly straight-forward. Because we have no position requirement, only a simple physical relationship between the inertias of the rocket and the reaction wheel define the proportional speed of the wheel to the rocket. This can be calculated with very high degree of certainty, and compared to measured values obtained with a bifilar pendulum test. The rocket’s roll rate can be derived either directly from the gyros or be received from the Kalman filter (or other filter). To determine the cumulative set of effects on the 6-DoF dynamics (although they are expected to be minimal) an OpenRocket plugin has been developed to allow for the stabilizing effect of the wheel and the additional angular momentum to be incorporated into pre-flight models. Representative graphs are shown below: . This plugin adds the flywheel assembly as a additional mass and inertia located at the center of mass of the given OpenRocket model. It models both the flywheel as an inertial mass and the brushless motor as an electrical circuit to accurately simulate the effects of torque drop-off at higher speeds with electric motors. From initial simulations using an L2-scale minimum diameter rocket. We were able to use a 300g mass to reduce the maximum roll rate of the rocket from ~6 rad/s at motor burnout to ~1 rad/s at motor burnout. Graphs showing this result can be found below:
The capability of the flywheel will scale well to a larger rocket because the larger tube diameter allows for the flywheel radius to be increased which increases the inertia of the wheel by the square of the radius. larger inertia allows us to exert more torque authority before the brush-less motor saturates at its maximum speed.
Failure Mode Analysis
The worst-case scenario would be a sudden liberation of the reaction wheel from the motor and support bearing. Ignoring what could cause this to happen (one of the bulkheads would need to deform by over a quarter of an inch) we can demonstrate that the composite tube will contain the failure with no damage to other systems. A moderate failure would be the seizing of the wheel during flight, after it was already spinning. If this occurs, the roll rate would be exactly the same as not having flown the reaction wheel at all. This is still a net benefit though as the vehicle is likely higher in altitude so the aerodynamic forces on the fins/nose cone if the vehicle did eventually cone would be lower.
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