principal of mechanical advantage, and is what allows the payload to reach a high launch velocity. However, because the counterweight pivots around a much shorter distance, its weight must be much greater than the weight of the payload, to get a high launch velocity. However, increasing the mass of the counterweight beyond a certain point will not help, since the limiting speed of the falling counterweight is free-fall speed.
The sling releases when a certain angle α
is reached. At this point the ring (which is connected to the sling and loops around the finger for support) slips off and the payload is launched. The release angle α
can be adjusted by changing the finger angle δ. For a greater δ the release angle α
increases. For a smaller δ the release angle α
The figure below illustrates the trebuchet at the release point.
As the beam rotates clockwise (due to the falling counterweight), the payload experiences centripetal acceleration which causes it to move outwards (since it is unrestrained). This results in a large increase in linear velocity of the payload which far exceeds that of the end of the beam to which the sling is attached. This is the heart of the physics behind a trebuchet and is the reason why a trebuchet has such great launching power.
For a more in-depth explanation on how a trebuchet works see Trebuchet Physics
. In this page the basic equations describing the physics of a trebuchet will be introduced.
To assist you in building a trebuchet you can use this simulator
to help you come up with the design that throws the payload the farthest. This is very useful for helping you come up with the winning design in a trebuchet competition!
In the next section we will look at the mangonel.
Catapult Physics – The Mangonel
Source: http://en.wikipedia.org/wiki/Catapult. Author: ChrisO
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 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 great