An airplane relies on the lift from its wings, which depends on the airplane’s speed and the air density. As a result, a cruising airplane will fly at a constant altitude, following the curvature of the Earth.
Flat-Earthers claim if Earth is a sphere, an airplane has to dip its nose down periodically, or it would fly into space. In reality, an aircraft will follow Earth’s curvature and is unable to fly to space even if the pilot deliberately attempts to do that
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During cruising, an airplane is practically level. It is flying perpendicular to the direction of gravity. The aircraft is still flying following Earth’s curvature and continuously changes its orientation. However, not only its orientation changing but also the direction of gravity, having the same amount of change. As a result, a spirit level on a flight will not show us the difference in orientation of the airplane due to its motion following the curvature of the Earth.
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