Bookworm,
The air-driven gyro in a normal light aircraft AI needs to have some form of "vertical sensing" so that it can erect itself correctly when first starting The gyro's centre of gravity is below its gimbal's "rotational" centre (if you see what I mean) so that it hangs vertically when the gyro isn't spinning. So I guess it would make sense that, if held at a steady non-vertical angle for long enough, it would eventually decide that it *was* vertical...
(I'm no expert, by the way; it just happens that I was reading about this recently in the IMC Confuser - there's a lot more going on inside the AI than I'd thought!).
I once looked into the possibility of producing a cheap "bank angle" indicator to flog to sporting motorcyclists (they tend to rate each other's machismo according to the amount of lean they get round corners), but it seemed that keeping the system calibrated to true vertical during an hour-long ride, during which the bike might never be truly vertical for more than a second or two, would be a big problem....
Maximum,
I'm confused - you say:
When the aircraft is properly trimmed out for a specific speed and thrust setting asymmetric, then with the aircraft steady on heading, the wings will be level and the ball will be slightly out towards the live engine.
Surely the ball is just the simplest possible "vertical indicator"?? If the aircraft is in steady, unaccelerated, wings-level flight, how can the ball *not* be centred? It would be centred if both engines were running, would it not? How does the ball "know" that one engine has stopped...?
cbl.