The range of a bombard and its trajectory
Point-blank shot versus maximum range; where the arc reaches its peak
Two ballistics problems on the firing of a bombard. If it shoots ten braccia point-blank along a straight line, how far will it carry at its maximum range, and conversely, if it reaches three miles at maximum range, how far does it shoot point-blank? A second question asks, for shots fired with different arcs of motion, at what part of the range the arc reaches its greatest height. The lower half of the sheet shows a fan of trajectory arcs rising from a common point.
On this page
Point-blank shot versus maximum range
Leonardo relates the straight, point-blank shot of a bombard to its maximum range. If it carries ten braccia along a straight line, how far will it reach at its greatest range, and inversely, if it reaches three miles at maximum range, how far does it carry point-blank? The two are treated as convertible quantities of a single weapon.
Where a shot's arc reaches its greatest height
For a bombard firing to different distances with different arcs of motion, Leonardo asks at what point of its range the arc attains its highest point. The question probes how the shape of a projectile's path shifts with the elevation of the shot.
Diagram of trajectory arcs
The lower half of the sheet shows a set of overlapping curved paths springing from a common origin at the right, each cresting at a different height. The drawing illustrates how varying the elevation changes the arc a shot describes.