How attitude indicator (gyro horizon) adjusts to the Earth's curvature? Image a plane is flying from North to South and is crossing equator. How gyro horizon would maintain correct pitch angle? (Or East-West?)
I assume that pitch angle is correct at takeoff, so the further plane flights, the more difference would be between pitch angle relative to current g-force and pitch angle shown by attitude indicator.
Or do I understand gyros wrong?
 A: The attitude indicators need to have devices in them to correct for precession in the gyros caused by turns. The system used in mechanical gyros is based on a collection of pendulous vanes. Basically, for short times the gyro controls the attitude indicator, for long term the pendulous vanes are pulled by gravity in the direction of "down" and they adjust the gyros to keep them oriented correctly. More advanced attitude indicators use different technologies to detect "down", and use that to correct the orientation of the gyro, but they are all, fundamentally, linear accelerometers like was used in the original Wii controller before they added gyroscopic sensors in later versions.
Edit, just to make it explicit: the problem of keeping the horizon correct in spite of the Earth's curvature is small compared to the problem of precession caused by turning. So, solving turning precession solves curvature for free.
A: I've been crushing flat earth nonsense with solid facts and mathematics for about two years now. Their understanding of gyro physics (much like any of their other scientific understanding) is flawed, and they base most of their claims on these flawed understandings. 
Gravity is an acting force on the attitude indicator gyro of a plane. This means that the force of gravity is applied to the Y axis of the gyro which keeps it continually vertical relative to earth's surface, or perpendicular to the center of gravity (a.k.a. level). 
