How a Bird Climbs on the Wind Without Beating Its Wings
Body and wings at opposite slants; the wind as a wedge; degrees of obliquity
Folio 43v develops how a bird climbs on the wind alone, holding its body and wings at opposite slants so the rising air acts like a wedge driven under a weight, lifting it at every stage. A file of small birds down the right side shows the postures of ascent and descent, and Leonardo insists one must calculate the exact degrees of wing-obliquity, since at no angle does the bird come to rest, while spreading the wings lightens it and drawing them in makes it heavier, as butterflies show in their descents. Lower diagrams include a quadrant of a circle divided into sectors and a small experiment of a weight on two inclined poles. He concludes that a steeper slope lifts a weight more easily but has power only to raise it, not to push it forward.
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Climbing on the wind with body and wings at opposite slants
The bird rises to great height without beating its wings by means of the wind, which strikes it beneath the obliquely set wings and tail and over the back set in contrary obliquity. Because the body's obliquity disposes it to descend against the wind with the same power by which the wind lifts it, the two obliquities work together to carry it aloft.
Rising air acts as a wedge driven under a weight
Leonardo compares the wind condensed beneath the bird to a wedge driven under a weight: the wedge, at every degree of its motion, makes that weight gain a degree of height. In the same way the packed air under the bird raises it as it advances.
Spreading the wings lightens the bird; folding weighs it down
One must calculate the degrees of obliquity, because at no degree does the thing upon water or the bird upon air come to rest, but they move faster or slower as the site is less or more oblique. That bird weighs less which spreads itself more, and weighs more which draws itself in more, as the butterflies experience in their descents.
Weight on two inclined poles: the steeper slope lifts but cannot push
If a b 10 pushes c 9 by the obliquity d e, then that obliquity d e, being greater than the obliquity a b, will lift the weight 9 with less effort, but will not push it against the 10. The reason is that the greater obliquity has power only in raising, not in driving forward.
Quadrant of a circle divided into sectors
A drawn quarter-circle is ruled into radial sectors. On a page insisting that one must calculate the degrees of the wings' obliquity, this graduated quadrant serves to lay off and measure such angles.