Setting is contemporary but it might as well not be, as my characters are working with homemade medieval-style bows (long for men, short for women) and arrows.
I have searched: medieval shortbow; what's the longest distance you can shoot accurately with a shortbow (and various permutations thereof); target archery women primitive; and various
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Have you tried searching for the speed an arrow leaves a bow, to try and get some idea of what your character may be capable of? Because when it comes to distance, it's all about how fast the arrow is traveling when it is released (and then some basic physics can tell you how far an arrow going that fast could travel before hitting the ground).
So, if you could find a good estimate of how fast an arrow is released from a bow, depending on the tension and weight of the string, that may help you more than searching specifically for distance.
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And unfortunately, modern Olympic-style shooting uses compound bows and special high-tech arrows, so looking up the current records for target shooting aren't going to tell me much about what could be done with basic wooden bows and arrows, either.
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Just a suggestion - have you tried looking into the Society for Creative Anachronisms (SCA)? They do archery with these kinds of weapons, and I'd bet they keep contest records, too. At the very least, you may find a more knowledgeable group to ask. A google search of "SCA archery" brings up a slew of pages. How many might be useful to you, I can't even guess.
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Also, in terms of accuracy a quick search showed that the longbow is more accurate than the short bow, though it's from wiki-answers so who knows.
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I don't know if this will help, but it has information about shortbows needing longer arrows to be more accurate or at least that's what I'm assuming.
I don't know if this'll help either, but it might give you some ideas about distance:
This site is wicked confusing but if you can figure out the table halfway down it might be a great help: I wish I could figure it out for you, but I'm a bit bad at things like that aka math. But this page might help (just make sure do like ctrl-a so ( ... )
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We routinely shot a Royal round which was 6 arrows at 20 yards, 30 yards and 40 yards and a 30 second speed round at 20 yards. I was never very good and practiced only once a month or so, but I knew people who shot 2-3 times a week and they were amazing. They could nail the bullseye repeatedly at 40 yards. Some of the best would go back and shoot from 60 yards as well.
One thing you will want to take into consideration is the draw weight on the bows of your character. I used to shoot a 35 lb recurve and if I hit the haybale, let only the target face at 40 yards I was happy :)
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