The Bent Wingtip: Condensing Air and the Circle c d b r
The curved tip presses air below and sideways; its force-lines converge on center n of circle c d b r.
Leonardo argues that the curvature of the wing-tip greatly aids flight, because in striking the air it presses not only the air beneath but also condenses the neighbouring lateral air. He grounds this in two principles - that every violence seeks to undo itself along the lines of the motion that made it, and that a body bent by force sends the lines of its power toward the center of a circle. Taking the wing a b c d curved at its tip c d b, he completes the circle c d b r with center n and draws the tangent force-lines n f, n e, n m, so the tip's force runs along b f, d e, c m. He also notes that air is endlessly condensable and rarefiable, and that a steadier wind would spare the bird its constant fanning and balancing; a diagram of flowing condensed air and a geometric diagram of the wing-tip circle appear at the right.
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A steadier wind would spare the bird its balancing
Leonardo opens by observing that if the wind blew with a broad, uniform force, the bird would not need to fan and balance itself so continually with its wings.
Air is endlessly condensable and rarefiable
A caption to the diagram of air condensed beneath the wings states that air in itself can be condensed and rarefied toward infinity. The neighbouring drawing shows streams of flowing, compressed air.
The bent tip presses the air below and beside it
The curvature of the wing-tip greatly aids flight, for in striking it presses not only the air beneath but also condenses the neighbouring lateral air. Leonardo grounds this in the maxim that every violence seeks to undo itself along the lines of the motion that generated it.
The circle c d b r and the tip's force-lines
Taking the wing a b c d curved at its tip c d b, Leonardo completes the circle c d b r with center n, then draws the tangent line n f at the tip and further lines n e and n m, imagining infinitely many between. All meet the curve b d c perpendicularly, so the tip's force runs along b f, d e, c m - and b f falls outside the bird's space, as the line b o shows.