How it works
A long wooden beam pivots on a tall frame. The short end carries a huge counterweight, a box filled with earth, stones or lead; the long end has a sling holding the missile. Crews winched the long end down and locked it. When released, the counterweight fell, the arm whipped up and the sling opened at the top of its swing, hurling the stone in a high arc. Because the same weight fell the same distance every time, a counterweight trebuchet could hit the same stretch of wall shot after shot.
It was huge, slow and costly: it had to be built on site by skilled carpenters, took days to assemble and fired perhaps one or two shots an hour. It was exposed to enemy engines and sorties, and its high arc made it better for smashing parapets, roofs and buildings than for breaching thick walls at their foot. Defenders answered with their own engines and with timber frames and hides to protect the wall top.
What the model shows
Three things matter most. The counterweight sets how much energy falls into the machine. The long arm and the sling act as a lever on a lever: the sling's tip moves much faster than the arm's, which is why a trebuchet with a sling throws two or three times further than one without. The release angle is set by the shape of the hook on the arm's tip: release too early and the stone goes up and drops short, too late and it is flung into the ground.
The model is honest about what it leaves out: the counterweight here is fixed to the arm (many real ones hung on a hinge, which made them more efficient), the axle has a little friction, the frame never moves, and the sling never tangles. With a 6 t counterweight and a 90 kg stone it throws about 190 m, which sits inside the range that reconstructions and medieval accounts suggest.
Both charts are worked out by the same toy model as the case above, when this page was built. Release speed at 6 t: 44 m/s.
Before the counterweight: mangonel (traction trebuchet)
A lighter throwing arm pulled down by a team of people on ropes, quick to build and quick to shoot.
Medieval names for siege engines are muddled: writers used 'mangonel', 'petrary' and other words loosely, and we often cannot tell which machine they meant. Many historians now use 'mangonel' for the traction trebuchet, which came from China and reached the Mediterranean by about the 6th century. Instead of a counterweight, a crew of pullers (from a handful to well over a hundred) hauled on ropes tied to the short end of the arm, flinging the sling. Older books picture the mangonel as a torsion catapult with a cup, like the Roman onager; whether such machines were still used in the Middle Ages is debated.
Human muscle gives a less consistent pull than a falling weight, so shots scattered more, and the stones were smaller. It could not batter down strong masonry, but it was cheap, fast-firing and useful against people, hoardings and parapets. It needed large, exposed crews, who were easy targets for archers on the walls.