Cal Poly ACS: Why Are Reaction Wheels Angled at 29.3 Degrees?

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SUMMARY

The Cal Poly Attitude Control System (ACS) utilizes reaction wheels angled at 29.3 degrees to optimize performance and redundancy. This specific angle is strategically chosen to ensure that each wheel is directed towards the center of mass (CoM) of the spacecraft. The design avoids the use of three reaction wheels, which would create a single point of failure, and also circumvents the weight issues associated with using six wheels. Instead, the reaction wheels are arranged on the edges of the triangular faces of a right square pyramid to achieve effective control with minimal weight.

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Swankie
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Here is a link to Cal Polys ACS they built. My question is: they claim each reaction wheel is angled at 29.3 degrees. Why would that be? My only guess is that they are each pointed at the CoM.
 
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You certainly don't want three reaction wheels (one per axis). What if one fails? You certainly don't want six (two per axis), either. Too much weight. One way to get redundancy at a minimal cost is to get a bit creative in the layout, arranging the reaction wheels on the edges of the triangular faces of a right square pyramid.
 

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