The catapult is an object of fascination for young children and others who, say, watch films depicting warfare during Medieval times or visit a museum featuring weaponry from centuries ago.
Catapults come in several basic forms. The one that you are perhaps most familiar with is arguably the most dramatic, sweeping through a large arc before dispatching its contents toward whatever unfortunate target or targets lie downrange.
Catapult physics offer a nice introduction into the world of projectile motion, which deals with "free-fall" situations, that is, problems in which the only force affecting a moving particle is that resulting from the acceleration owing to gravity (usually Earth's).
The first known catapults were built sometime around 400 BCE in Greece. The very earliest model resembled a traditional crossbow, in which an arrow is ejected in a forward direction (i.e., parallel to the ground unless the mechanism is angled upward). In fact, a traditional slingshot, while perhaps seen as a toy to some, is a kind of catapult of this sort.
The main type of crossbow-style catapult to emerge during this period was called a ballista. The force was generated by the methodical twisting of rope, which would fling a spear great distances at opposing armies when the taut ropes were cut. This device had the disadvantage of being useful only against enemies the users could see and aim closely at.
The mangonel catapult was also called the Onager. If it seems as though the Romans had an answer to everything the Greeks did in ancient times, or maybe the other way around, the mangonel represents one more example.
This catapult looks like a transitional species between the ballista and the traditional catapult. It makes use of torsion (tension around an axis) "stored" in ropes, but these drive a "flinging" arm when cut rather than hurl contents such as rocks or even fire in a "piston-like" motion.
While having a greater range than the ballista, the mangonel was notoriously inaccurate. It was, however, lighter and easier to move from place to place.
The basic design of a trebuchet is a lever, with a short arm facing the enemy and a longer arm being the business portion; an axle separates the two. A counterweight is applied to the shorter arm to add force at the point the projectile is released from a sling.
This catapult comes in two forms. The first, a traction trebuchet, was operated by a group of soldiers pushing down on the short arm before release. The other, a counterpoise trebuchet, worked by having the soldiers focus their efforts mainly on pulling down the long arm instead before release.
The science behind catapults is easily explained using the equations of projectile motion. The key thing to remember about any projectile-motion problem is that once the projectile has been released, the only force it is subjected to is that of its own weight (resulting from gravity).
When a projectile is released, it has both horizontal and vertical components of motion. Luckily for physicists and students, these can be analyzed separately, since gravity does not affect horizontal motion. The result of this analysis produces an equation for the distance R a projectile will travel if released with a given initial velocity v0 at a specified angle θ with respect to the ground:
If you experiment with different values for the launch angle, you find that the value of sin 2θ has its greatest value, 1, when θ is 45 degrees. Thus if you want to launch a projectile as far as possible, point it exactly halfway to a point directly overhead and fire away!
- See the Resources for a handy guide to making your own small-scale catapult.