Bat and Eagle: Wing-Span, Weight and the Strength of Reeds
Why small wings sustain the eagle as large ones the bat, argued by a bundle-of-reeds proof
Leonardo confronts an apparent paradox of flight: a bat weighing 2 ounces spans half a braccio, so by simple proportion an eagle should need a 60-braccia span, yet an eagle spans no more than 3 and flies with great agility. To resolve it he turns to strength of materials: a single reed bends to the ground under a coin's weight, but a thousand reeds bound tightly bear far more than the sum of their separate strengths, more than 40 pounds where the parts would give about 3.5. By analogy the air compressed under a large beating wing gains disproportionate supporting power, so the eagle's small wings suffice. The upper sketches show winged creatures, a bat and an eagle, with their weights and spans noted.
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The bat-and-eagle paradox of wing-span and weight
If a bat of 2 ounces spans half a braccio, an eagle by that comparison ought to span 60 braccia, yet experience shows it spans no more than 3. Both are borne with great agility by their wings, the bat especially, dodging flies and gnats with swift turns. Leonardo asks why the eagle sustains itself on small wings as the bat does on large ones.
A bundle of reeds is stronger than the sum of single reeds
A single reed bends to the ground under a coin's weight, but a thousand reeds bound tight, fixed at the foot and evened at the top, bear more than 40 pounds where the separate reasoning gives only about 3.5. By the same reasoning the air pressed by a beating wing gains disproportionate supporting power.
