# Compensating for rotation when accelerometer not at center of mass?

It's dawned on me that the accelerometers of a rocket will generally not be at the center of mass. In part because the center of mass varies widely as fuel is consumed.

This means the acceleration (or dv) measurement will include undesirable terms from angular velocity and angular acceleration about the center of mass.

"Undesirable" because those terms say nothing about the translational motion of the center of mass, which is the thing you'd want to measure with an accelerometer. You already have gyros to track rotation.

So it seems that the reading from an accelerometer will generally need to be corrected for the accelerometer's offset from the center of mass.

Is this done in practice? If so, is the correction updated continuously to reflect the latest estimate of the center of mass?

• It's a great point! In fact signals from several distributed accelerometers could be used as a makeshift gyro. If acceleration vectors from devices on opposite sides of a craft both point outwards, then it's either in the process of rapid disassembly or it's spinning.
– uhoh
Commented May 23, 2021 at 2:28
• @uhoh A third possibility for different sensed accelerations from multiple accelerometers is gravity gradient. This requires either a very large spacecraft or very sensitive accelerometers. GOCE used six extremely sensitive accelerometers to map the Earth's gravitational field. Commented May 23, 2021 at 15:38
• Yes, and the apollo LM familiarization manual describes the corrections used in some detail. Commented May 23, 2021 at 16:36
• hmm, I'm sorry, I thought it was in that one. I've definitely seen this mentioned in one of the official apollo pdf manuals for the LM, but I don't know exactly which one as it wasn't something I was paying attention to at the time. From memory, it accounted for the position of the accelerometer, but not a shifting center of mass.. Commented May 25, 2021 at 12:46
• @uhoh: here is a paper mentioned elsewhere that shows how to do just that---to calculate angular velocity using only accelerometers (arrays of them, really). The paper: ncbi.nlm.nih.gov/pmc/articles/PMC4208239
– user39728
Commented May 28, 2021 at 18:53