　　Mechanism of beating flight

　　　The beating flight consists of “the flapping down run”and “the flapping
　　up run”.

　　　In the flapping down run, the surrounding air is pushed out to back
　　downward direction, and the bird receives the forth upward force as the
　　reaction. Then, if the magnitude of the vertical component of this force
　　is larger than the bird's weight, the bird will be thrown out to forth upward.

　　　If the bird is advancing, the larger force may be produced by the bird's
　　inertia. Particularly for large-sized bird, it is the necessary condition
　　for flying to be going with the velocity close to the critical one.

　　　In the flapping up run, the parabolic flight due to the inertia is essential.
　　If a drag, negative lift or negative thrust appears, the fall will be rash,
　　but if positive lift or positive thrust appears, the fall will be late.

　　　If the subsequent flapping down begins as soon as the bird descends to
　　the altitude the last flapping down had began in, the bird will be able to
　　fly at a constant average altitude.

　　　The mechanisms of the hovering, the ascending and the descending are
　　same as the above.

　　　A bird's beating flight is the same mechanical process as our running.