Catapult physics is basically the
use of stored energy to hurl a projectile (the payload), without the use of an
explosive. The three primary energy storage mechanisms are tension, torsion,
and gravity. The catapult has proven to be a very effective weapon during
ancient times, capable of inflicting great damage. The main types of catapults
used were the trebuchet, mangonel, onager, and ballista.
The Mangonel:
The mangonel consists of an arm with a bowl-shaped bucket attached to
the end. In this bucket a payload is placed. Upon release, the arm rotates at a
high speed and throws the payload out of the bucket, towards the target. The
launch velocity of the payload is equal to the velocity of the arm at the
bucket end. The launch angle of the payload is controlled by stopping the arm
using a crossbar. This crossbar is positioned so as to stop the arm at the
desired angle which results in the payload being launched out of the bucket at
the desired launch angle. This crossbar can be padded to cushion the impact. 
The mangonel was best suited for launching projectiles at lower angles to the horizontal, which was useful for destroying walls, as opposed to the trebuchet which was well suited for launching projectiles over walls.
However, the mangonel is not as energy efficient as the trebuchet for the main reason that the arm reaches a high speed during the launch. This means that a large percentage of the stored energy goes into accelerating the arm, which is energy wasted. This is unavoidable however, since the payload can only be launched at high speed if the arm is rotating at high speed. So the only way to waste as little energy as possible is to make the arm and bucket as light as possible, while still being strong enough to resist the forces experienced during launch.
The physics behind a mangonel is basically the use of an energy storage mechanism to rotate the arm. Unlike a trebuchet, this mechanism is more direct. It consists of either a tension device or a torsion device which is directly connected to the arm.
The figure below illustrates a mangonel in which the energy source is a bent cantilever, which is a form of tension device. This can consist of a flexible bow-shaped material, made of wood for example.
The point P in the figure is the pivot axle, attached to the frame, about which the arm rotates.
In groups of three or four, we researched how we could construct a working model of a mangonel using ice block sticks.
After construction, we took the time to test our creations, recording their capabilities in terms of distance of the projectile and height.
