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.
Catapult Physics — The Mangonel
The above picture of the mangonel is what people are most familiar with when they think of catapults.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 catapult 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.
Catapult Physics — The Trebuchet
Among the various types of catapults, the trebuchet was the most accurate and among the most efficient in terms of transferring the stored energy to the projectile. In addition, it allowed greater consistency in the throws due to the fact that the same amount of energy could be delivered every time, by way of a raised counterweight.
A trebuchet works by using the energy of a falling (and hinged) counterweight to launch a projectile (the payload), using mechanical advantage to achieve a high launch speed. For maximum launch speed the counterweight must be much heavier than the payload, since this means that it will "fall" quickly.
