Imagine the situation: you are heading East, and you start to increase your bank angle. Initially, the pendulous magnet inside your compass will still remain aligned with the magnetic North of the Earth. However, as you increase the bank angle even more, the dip, which is the angle between the horizontal plane and your magnet, will get increasingly higher. At some point, when the bank angle gets too big, the compass will just ‘fall’ and rotate 180° towards the lowest wing which is into the turn, and the compass will indicate West instead of East. Therefore, the total error of the compass would be 180° on an easterly heading in a steep right turn.
Conclusion: beyond the critical bank angle (90 minus the dip angle), the compass will lag by 180 degrees when the aircraft is banked towards the equator.
Nothern Hemisphere:
- HDG 090 -> right steep turn -> (dip + bank angle > 90) -> 180 error
- HDG 270 -> left steep turn -> (dip + bank angle > 90) -> 180 error
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