I think one of the conditions will be that it has to be weight driven
rather than spring driven (assuming we are talking about the same da vinci catapult ( www.hucbald.ramst.ca/articles/leonardo_catapult.html ), so that would be out.
I've built one before (very roughly, but got a good 20m out of a 50kg counterweight on a worryingly bent axle (firing water ballons (at dave))) so could probably do fairly well on a standard design with a bit of fine tuning, and actually managing to cut things straight (the only reason the previous one fired straight was that all the wonky bits cancelled each other out just right that the axle was the only level bit on there (though, as said, it was rather bent when under load).
( Tedium Alduce me to interlow myself., Thu 4 Nov 2010, 23:20, 1 reply, 15 years ago)

Yeah, roughly the same design I was talking about
My flatmate used to want to build a floating arm trebuchet, which is a bit different from what most people do.
I built a traditional one from lego once, and fired marbles about 10 metres using a counterweight full of AA batteries.
(PenguinOfDeath is Scottish, and most likely angry, Thu 4 Nov 2010, 23:25, Reply)

My brother's aristocratic college friend
made one and used it to fire old pianos across the lawn of his parents' country pile. I have seen photos.
( Monty Boyce, My cheese game is strong, Thu 4 Nov 2010, 23:30, Reply)

Well, that fairly trumps my lego one
Some day if I live in the countryside, I'll get round to making one to fire pumpkins and the such. What could possibly go wrong with that?
(PenguinOfDeath is Scottish, and most likely angry, Thu 4 Nov 2010, 23:34, Reply)