Beating Wings Against Still Air; Two Contrary Obliquities
Lifting by striking motionless air, and measuring descent against rebound
Leonardo states the reciprocity of moving air against a motionless body and of a body against motionless air, then shows how a gliding bird lifts itself by beating its wings down against the still air, as if struck from below by a wave of wind. A second passage treats two contrary obliquities—one of descent, one of rebound—and gives a numerical example in which a hundred miles of descending motion return only fifty when the rebound saves half the descent. Small diagrams of a bird with open oblique wings and raised tail, and of a single wing, labelled b, c, a, d, sit in the right margin.
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Lifting by beating the wings against still air
Leonardo notes it is the same to move the air against a motionless thing as to move the thing against motionless air. When a bird glides down slowly without beating and the inclination brings it earthward faster than intended, it lowers its wings and beats them against the motionless air; this raises the bird no differently than if a wave of wind struck it from below.
Two contrary obliquities: descent measured against rebound
For a bird descending by two contrary obliquities, the motion is longer the more the rising obliquity resembles the descending one. Leonardo's example: if the descending obliquity alone makes a hundred miles per hour over a hundred braccia of drop, and the opposite rebounding obliquity saves half that descent, then the hundred miles of motion return fifty. The margin figures label the wing b, c, a, d.
