Bombard Ballistics and Pulley Geometry
Conclusions on gunpowder ignition and ball motion; tangency of cord and pulley
This folio sets out Leonardo's reasoning on the physics of gunpowder in a bombard, illustrated with small lettered barrel diagrams. Two marginal "conclusions" state that the fire's power grows through time and that the least-impeded powder moves fastest; from these he argues about a double bombard with opposed equal charges, about a triple charge driving two balls unequally, and about how to test a ball's range by cutting a graduated barrel twelfth by twelfth. Alongside are geometric notes on how a cord leaves a pulley (in obtuse or right-angled conjunction with the radius) and on which of two equal-sided angles is more acute. Divider and knot studies and a small marginal figure sketch also appear on the sheet; further untranscribed marginalia may be present.
On this page
Two conclusions on the ignited charge
First conclusion: the power of the fire kindled in the bombard gains degrees of power at every degree of time. Second: that part of the ignited powder moves faster which is less impeded. These are set as the principles from which the demonstrations follow.
Charge and ball travel in a bombard
A barrel diagram lettered a b c d e poses the case: if four pounds of powder placed at a-h drive the ball through the whole space d-e while the bombard stays fixed in its place. This sets up the comparison developed in the following figures.
The double bombard with opposed equal powers
A figure lettered c a b asks what a double bombard a-b will do when its powers are contrary but similar to the first. Leonardo answers that the three powers will be equal among themselves, because when the causes are equal and similar the effects are similar and equal.
Triple charge and unequal ball motion
In the figure lettered d b n a c the powder n-a is set at triple the powder n-b, so ball b is driven more than ball a. Once b has left, the bombard acts like a galley-trumpet, blowing back the remaining powder and wasting much that should have served ball a; venting escapes more easily at mouth d than at c, so ball a moves slowly and weakly. He then generalises to a barrel open at both ends, charged in the middle with a ball at each end: the ball nearer the ignition flees sooner.
Graduated barrel to measure range
In the figure lettered c d b a the charge a-b is fixed by rule at one-fourteenth of a-e, the ball b-d likewise at 1/14, and the plain barrel d-e is divided into 12. After each shot one twelfth is sawn off, so the range of the same ball with the same powder is recorded degree by degree, yielding "your true rules."
Cord leaving a pulley; the more acute angle
A pulley-and-cord figure states that no arc-shaped cord separates from its pulley unless in obtuse conjunction with the radius, and no straight cord unless in right-angled conjunction with the radius. A separate note (written with the sheet turned upside down) adds that of two angles with equal-length sides, the one with the smaller base is the more acute.