Another tip on the best range: it comes when the weight falls straight down, converting it's PE to KE as efficiently as possible, with less friction from the grinding rotation/etc. Two ways to make this happen: make the weight hanging, and put the whole thing on wheels. If the base can move while the weight stays pretty much in the same place, falling vertically, you'll see that the trebuchet moves forward some and the sling gets an extra kick of power. Tinker and have some fun! Just make sure that the angled hook that holds the loose end of the sling is finely adjustable via screw or something, and you should be good to go 
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And that, my liege, is how we know the Earth to be
banana-shaped.
This new learning amazes me, Sir Bedevere. Explain again
how sheeps' bladders may be employed to prevent earthquakes.
Oh, certainly, sir.
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