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I'd like to point out that at the height of archery, longbowmen were not permitted to practice archery at a distance LESS than 200 yards. The average poundage for a longbow back then was a whopping 120 pounds, so you can imagine how far they might shoot under ideal conditions. Now, crossbows, or I should say arbalests, were pretty much portable ballistae. Honestly, the poundage on those suckers was massive and the quarrels were essentially short dowel rods. So, I'd say on the order of at least 3/4 of a mile.
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