On Percussion: Falling Bodies and a Man's Descent
Which fall strikes harder; a curved sheet tips as it falls; a man steers his descent
Continuing 'On percussion', Leonardo compares falling bodies: of two dropped from the same height, the one that descends by the longer path strikes less, and the one by the shorter path strikes more. A slightly curved sheet, the 'first mobile', is shown tipping as it falls, its front b leading while the heavier edge a drops faster and becomes the guide of the descent, backed by numbered propositions (the ninth through thirteenth) on how a body penetrates air with its narrowest edge. In the margins Leonardo draws a man who can descend through the air, steering himself left or right by bending one arm and extending the other.
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Longer path, weaker blow
Of things falling through the air from the same height, the one that descends by the longer path gives the smaller percussion. It follows that the one descending by the shorter path gives the greater percussion.
The heavier edge guides the fall (a b c d)
The curved 'first mobile' descends front-first at b, moving from a to c; a drops more than b, so a ends at c while b rises to d. By the ninth to eleventh propositions, the body that strikes air with its larger part has less power to penetrate it, the one cleaving air with its least breadth goes faster, and the heaviest part becomes the guide of the motion.
Why the front leads: air resistance and speed (a b)
Even a body a b of uniform thickness and weight, held obliquely, weighs more at the front than at any equal breadth, so the front guides the descent. By the twelfth proposition the more air condenses the more it resists, and by the thirteenth the air with the swifter motion moves more.
A man steering his descent through the air
A man can descend, as shown below. Suspended among the falling objects, he moves to the right if he bends his right arm and extends his left, then from right to left if he exchanges the extension of his arms. The margins show him as a small figure hanging from a bar between the falling plates.