The design and physics of airplanes is such that they hold a certain trimmed altitude and speed, following the curvature of the earth automatically, even without any intervention of the pilot or autopilot system. Pilots don't have to drop the nose to correct for curvature. The interactive physics simulation of an airplane on this page shows how this works. The physics model and the corresponding behavior of the airplane are explained. The Source code and the equations are described in detail.
Move the sliders and observe how the airplane always finds a new equilibrium altitude. When Pitch Damping is disabled, move the sliders slowly to prevent oscillations. Speed up the simulation up to 100 times using the Time x slider. Change the radius of the earth to observe that the airplane automatically follows the curvature of the earth, no matter its size. Set EarthRadius = 100,000% to simulate a flat earth. Click Reset Pos to move the coordinate system to the airplanes position so the airplane is horizontal again.
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