The Trebuchet

The Trebuchet

The roots of the machine go back to at least the fifth century B.C. in China. In its most primitive form, it consisted of a pivoted beam with a sling at one end and ropes at the other. A stone would be placed in the sling and a team of men would haul the ropes, swinging the beam up into the air”1.

“The trebuchet reached the Mediterranean by the sixth century C.E. It displaced other forms of artillery and held its own until well after the coming of gunpowder. The trebuchet was instrumental in the rapid expansion of both the Islamic and the Mongol empires. It also played a part in the transmission of the Black Death, the epidemic of plague that swept Eurasia and the North Africa during the 14th century. Along the way it seems to have influenced both the development of clockwork and the theoretical analyzes of motion”2.

We will now look at the physics of a trebuchet. “The trebuchet uses many different physics applications, we will look at a few of them. Basically a trebuchet is a fulcrum.

First the energy of conservation. The setting of the trebuchet before firing is shown in Fig 1. A heavy counterweight of mass (M) (contained in a large bucket) on the end of the short arm of a sturdy beam was raised to some height while a smaller mass (m) (the projectile), was positioned on the end of the longer arm near or on the ground. In practice the projectile was usually placed in a leather sling attached to the end of the longer arm. However for simplicity, we shall ignore the sling and compensate for this omission by increasing the assumed length of the beam on the projectile’s side. The counterweight was then allowed to fall so that the longer arm swung upward, the sling following, and the projectile was ultimately thrown from its container at some point near the top of the arc. The far end of the sling was attached to the arm by a rope in such a way that the release occurred at a launching angle near the optimum value ( most likely by repeated trials) for the launch height. The launching position is shown in fig.2 where we have assumed that the projectile is released at the moment the entire beam is vertical. In the figures: (a)=height of the pivot, (b)= length of the short arm, (c)= length of the long arm, while (v) and (V) are the velocities of (m) and (M), respectively, at the moment of launching.