On Bicycles, and.... what else is there?

To extract cadence from accelerometer data is the accelerometers need to be properly oriented. So I constructed a simplistic scheme to extract the angle from the accelerations. It's super-simple: just accumulate average accelerations, then calculate a transformation rotation angle which beings one of them to zero. Consider the following diagram: From the perspective of the spindle, radial acceleration is always in the same direction. Tangential (I seem to alternate between calling this "tangential" and "transverse") acceleration is also always in the same direction, as long as the crank rotation is consistently increasing (or consistently decreasing). I also show a vector for road vibration. It's easy to see this will tend to cancel out over time for each spindle. When the spindle rotates 180 degrees, it's in the opposite direction relative to the spindle. The same deal with acceleration in the direction of motion. When the spindle rotates 180 de...