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.
The figure below shows the mangonel at the launch point. To launch the payload the restraining rope is released.
The other type of energy storage mechanism is a torsion device, which can consist of twisted rope. This allowed for greater throwing power than the tension device, in ancient catapults. The figure below illustrates the torsion device.
The twisted rope is commonly referred to as a torsion bundle. It consists of several lengths of rope with the arm inserted in between them. The rope is then twisted manually on both sides of the arm using levers. Upon release, the torsion bundle rotates the arm at high speed, launching the payload. The figure below illustrates how a torsion bundle is twisted.
The video below shows how to wrap the rope on a torsion catapult.
The fact that a mangonel uses an energy storage device that consists of a deforming material, like wood or rope, means that its throwing distance will not be as consistent as a trebuchet. This is because these materials (unlike more modern materials), naturally wear and lose elasticity during their use. This is something that needs to be constantly monitored during a battle, with replacement materials made readily available, if necessary.
In the next section we will briefly discuss the onager.
Catapult Physics – The Onager
The onager catapult is almost identical to the trebuchet, but instead of a falling counterweight, it uses a torsion bundle to rotate the arm (similar to the mangonel, described previously). Because of its design, it allowed for greater throwing distance than the mangonel (comparable to that of a trebuchet). But the throwing distance wasn't as consistent as the trebuchet since it relied on deformable materials as the energy source, which naturally wear and lose elasticity during their use.
Lastly, we will look at the ballista.
Catapult Physics – The Ballista
Source: http://en.wikipedia.org/wiki/Ballista. Author: Scigeek
The ballista is similar in principle to a crossbow, but much larger. Like the torsion powered mangonel, it used twisted rope as the energy source. The picture above shows the torsion mechanism consisting of twisted rope, located at the pivot location of the two side arms.
In the ballista, the bow string would be winched back and the tension set. It