Some years ago I read an article in a respectable modelling magazine regarding gyro placement on a heli where it was conclusively proved by experiment that the placement of the gyro was irrelevant, i.e. it didn’t matter whether you placed the gyro on tip of the nose, on the tip of the tail or anywhere else on the heli, it’s effect was exactly the same. I'm not talking about orientation of the gyro, just it's physical placement on the airframe.
Is this the same with the APM board? Could the board be placed on one arm of a quadcopter, for example?
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There are quite a few experts on IMU control theory in this forum, but I do not count myself among them. However, based on what I do know combined with a smattering of classical mechanics, I can offer a theory.
Gyros specifically are angular momentum devices. They sense if the device is twisting about one axis or another. As such, there is really no difference where on the hypotenuse of the right triangle you place it - the root angle is always the same, and therefore the dynamic angular rate change is also equivalent.
However, the APM also contains accelerometer devices to provide linear positional data. Those definitely would be affected by placement. The farther away from the center of control axes of the craft you place it, the more the accelerometer would report an angular change falsely as a change of position. In other words, it would think the craft is moving when the only thing changing is the attitude.
How much this error practically effects the APM is the question. In my opinion, it would be a best practice to locate the APM as close to the intersection of the control axes as you can (~= center of mass), but the potential for erroneous behavior is probably negligible if you don't.
Well, I'll go ahead with what I suspect and proclaim that it can be put ANYWHERE practical on the plane or multicopter.
No-one?