Good point, bookworm... As I said, I can't explain the exact mechanism, but there's a lot more going on inside the AI than you might think, particularly to do with "pendulous vanes" and the like. The rotation of the earth over time might also be a factor...
From
this PDF (the rest of the book is
here ) :
------------------
Another group of errors, associated with the design and operating principles of the attitude indicator, are induced during normal operation of the instrument. A skidding turn moves the pendulous vanes from their vertical position, precessing the gyro toward the inside of the turn. After return of the aircraft to straight-and-level, coordinated flight, the miniature aircraft shows a turn in the direction opposite the skid. During a normal turn, movement of the vanes by centrifugal force causes precession of the gyro toward the inside of the turn.
Errors in both pitch and bank indications occur during normal coordinated turns. These errors are caused by the movement of the pendulous vanes by centrifugal force, resulting in the precession of the gyro toward the inside of the turn. The error is greatest in a 180° steep turn. If, for example, a 180° steep turn is made to the right and the aircraft is rolled out to straight-and-level flight by visual references, the miniature aircraft will show a slight climb and turn to the left. This precession error, normally 3° to 5°, is quickly corrected by the erecting mechanism. At the end of a 360° turn, the precession induced during the first 180° is canceled out by precession in the opposite direction during the second 180° of turn. The slight precession errors induced during the roll-out are corrected immediately by pendulous vane action.
Acceleration and deceleration also induce precession errors, depending upon the amount and extent of the force applied. During acceleration the horizon bar moves down, indicating a climb. Control applied to correct this indication will result in a pitch attitude lower than the instrument shows. The opposite error results from deceleration. Other errors, such as "transport precession" and "apparent precession," relate to rotation of the earth and are of importance to pilots and navigators concerned with high speed and long-range flight.
------------------
Interesting stuff!
cbl.