What type of altitude change/s an a vertical gyroscope detect?
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|dw:1376983156298:dw|Hi Shu_Yun, you probably need to know 'attitude' changes as gyroscopes cannot detect 'altitude' changes at all. A vertical gyroscope has its spinning axes in the Z-plane, therefore it will always remain oriented along this Z-axis.
Exercising a force in the X or Y direction will cause the gyroscope to 'precess', which is simply stated a reaction force at a 90 deg angle. So pushing against the axis on the top, into the Y direction, will translate in a movement of the top of the axis towards the negative X-axis (so 90 deg in the direction of the turn).
Precession is a complex mechanism which is much better explained on the internet than I can do above. Nevertheless this may help you in finding the right answer to your question.