You can build them any size you like, from desk top hurlers to football field monsters. The choice is yours. Once you've built your catapult, field test them for maximum range and the thrown weight compared with "real" catapults. (You are responsible for local laws on firing projectiles in public!)
Gather 3 sets of results (in metric or imperial units only)
1. maximum range possible & the thrown weight used
2. maximum thrown weight and the range obtained
3. a third set of results somewhere in between the first two. Try and find the optimum balance between range and thrown weight.
Measure and report the length of throwing arm, length of counterweight lever arm (measured to c.g. of weight) and post your results and a picture of your machine here and I'll scale the results for you and compile them into a graph to see who's machine is the most effective. To enable a equal basis for comparison, I might scale directly all results to projectile weights close to the 100gms (0.1kg) range for starters. This of course is not really realistic since a direct upward or downward scaling of a catapult makes for some ridiculous sizes but for a simple comparison of throwing efficiency, I believe this should suffice.
To limit the range of types, choose only from three types of catapults (no wheels because wheels on hanging bucket catapults increase their range).
1. (Chinese) counterweight trebuchet (hanging bucket)
2. (Chinese) counterweight trebuchet (fixed weight)
3. Roman Mangonel
Go here for the Physics of a Trebuchet. It gives very good pointers on the various ratios required and the optimum lengths to go for when building a catapult.
http://www.geocities.com/SiliconValley/Park/6461/index2.html
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As a start, I'll use my little trebuchet as the challenge for anyone to beat. It shouldn't be too hard since I didn't build it for performance but more to look good.

Here are the stats for my trebuchet and the first benchmark to be beaten.
430mm throwing arm - 140mm counterweight lever arm.
1. 8.5m - 0.01kg (20mm diameter stone @ density 2400kg/m3 (concrete density))
2. *results pending*
3. *results pending*
Feel free to ask me for help if you need any info but half the fun is in researching the information to help you build your very own catapult.
Those based in Singapore are welcome to challenge my trebuchet directly. I'd gladly take you up and we can "match" catapults at a deserted section of Marina South or something.
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LET THE GAMES BEGIN!

*this graph at the moment is pretty meaningless since we only have one result from each of the two catapults and the values don't represent the optimum or maximum throw ranges of the catapult. I will update this chart when we have more values to compare with, (minimum three values- max possible projectile weight, max possible range and one value in between)