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Evil Dave said:
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Saber Cherry said:
Firing a crossbow ballistically is like firing a handgun ballistically - possible, but never done (aside from corrections of a few feet of drop, generally calculated by the scope) since you only have control over a single factor, angle. At least, that's how it would seem to me...
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but that's how rifles and (some) artillery work today. 
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I know, field artillery is like that, but they do a bunch of calculations before firing... and rifles have adjustable scopes that account for drop over distance... and medieval xbowmen had neither calculators nor scopes. The only crossbow I've ever seen with a scope was in Deus Ex, and I put it there myself
I think it would be very hard to fire a crossbow accurately with more than a minor (<5 degrees) arc... and any arc-firing requires more training than direct firing, which would defeat the point of cheaply raising masses of untrained crossbowmen. Assuming, of course, that crossbows were used by cheap masses of poorly trained soldiers, which could be another false premise on my part.
Your point on the longer trajectory negating a lower velocity is interesting... it would take several complex integrals to figure out how much energy ends up being saved, if any, by firing at a 30-degree angle or so. It would be much simpler to model in Excel (in .01 second intervals), given the drag formula. I did something like that once, to find the ideal angle to launch a water balloon for max distance, but I have a pretty poor memory...