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... any example of a working device with a pendulum that is able to correct the bank angle of a plane, is welcomed.
Look for a picture of "turn and slip indicator".
"Anyway, you have comprehensively proved to your own satisfaction that the instrument everyone has used for the last 100 years, and the simple wing leveller I've been using for the last 50 years, doesn't work"
but you may find some precursors of the "Navomatic" that used a simple pendulum.