On Motion: Helical Movement and Spinning Cannonballs
Rotating-rod diagrams demonstrating how combined circular and straight motion applies to bombard shot
Under the heading 'On motion' (De moto) Leonardo analyses how a body carried at once in a circle and along a straight line produces a helical path, illustrating this with two diagrams of rotating rods labelled b-c-a and e-f-g at the right of the sheet. He argues that a body in revolving motion travels a shorter course than one in straight motion, citing water-wheels that stir the surrounding air into a great wind. He applies the principle to artillery: cannonballs that spin about their center travel a shorter path than those that do not, so he recommends shaping the balls accordingly, judging this better than loading two balls into a single gun.
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Helical motion from combined circular and straight movement
If the body parallel to a b is turned in a revolving motion about the pole e while the round weight is carried in a circle, the circle moves from c to b, so the body performs two motions at once, one circular and one straight, whose combination yields a helical (elico) motion. The lower figure e f g behaves in the same way for the same reason. Leonardo adds that the motion is ineffective if the moving body is not proportioned to the power of its mover.
Spinning bombard balls travel a shorter path
Because a revolving body covers a shorter course than one moving straight, cannonballs that turn about their own center travel less far than balls that do not spin. Leonardo therefore urges shaping the balls to a particular figure so that their weight is matched to the immense power of the gun. He judges this preferable to putting two balls into the same piece of artillery.