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If a humanoid that is identical too a human but stands at roughly 9 feet and has at least twice the strength a human in say the top ten percent of the strength demographic had a bow of equivalent proportion in relation to body size as a medieval English longbow, what would be a realistic draw weight and penetration? (assuming the arrows would become larger in proportion as well as the other parts of the bow, as well as the bow being made of materials capable of using the strength of the pull mentioned above, and that the need for such penetration is fighting other armored humanoids and giant creatures around elephant size)

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    $\begingroup$ I'd assume it would be...proportionally larger? $\endgroup$ – Jakob Lovern Jan 4 '18 at 22:22
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    $\begingroup$ @Jakob and you would probably assume wrong. Bow must be made of something, and there is only so much medieval tech can do. Christopher, you tagged it magic, please explain what magic has to do with it. Also, what are they hunting? Any reason for them to even want higher penetration? Too much of it and if you miss, your precious arrowhead is lost inside a tree if you miss. Too much draw weight and your soldiers and hunters will get needlessly tired. So what's the reason to go higher than we already did? $\endgroup$ – Mołot Jan 4 '18 at 22:50
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    $\begingroup$ No, the OP is probably just creating a race of people who are 9ft giants. He doesn't necessarily want anything, he's probably just performing an internal reality check. Also, bow penetration really depends less on the person drawing it and more on the bow itself. You need to define springiness, etc. for the bow, then let physics do the heavy lifting. Depending on the material the bow is made out of, penetration and weight could vary immensely. Wood bows vs. metal ones, for example. $\endgroup$ – Jakob Lovern Jan 4 '18 at 23:06
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    $\begingroup$ The advantage would not be so much in penetration, but in distance. Apparently, 400 yards was possible by a trained archer in Edward III's time. Think 'height of Empire State building'. That is pretty much the limits of targeting the enemy. You could blanket cover a field, for instance, of an attacking army, but individual targets? So what functionality would more distance add? $\endgroup$ – Justin Thyme Jan 5 '18 at 1:14
  • $\begingroup$ Ok lets say that this character is hunting giant beasts (around elephant sized) and also for combat against armored targets of varying sizes ranging from human to his own, his want is to penetrate the thick skin and armour of his enemies, also lets say that the bow was specifically constructed of materials and of thicknesses that could handle the strength i described above. $\endgroup$ – Christopher Void Jan 5 '18 at 8:23
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For real life information, I suggest you watch this show: Agincourt's Dark Secrets Battlefield Detectives. The discussion of the draw weights and penetration of the English longbow is quite illuminating, and quite different from what we generally assume for the performance of the weapon.

Short answer, a longbow delivers @ 38J of energy to the target, failing to penetrate plate armour (see @ 22min into the documentary).

Scaling up bows will deliver more energy, but not huge amounts of energy. Even late Medieval steel crossbows could only deliver @ 200J of energy, while a firearm from a short time later could deliver @ 1000J of energy to the target.

Since the bow is still made of Yew, the OP's bow is likely only going to deliver between 60 to 100J of energy to the target. The larger and heavier arrows will deliver more energy to the target, but may still fail to penetrate plate armour. There could be a knock down effect of being struck by a large, heavy arrow if you are already unbalanced (say from moving around fighting, or balanced on a moving horse), and given enough arrows, there is always the possibility that you will be struck through an opening in your visor or a gap in the armour, but realistically, even a longbow drawn by a giant of a man (or a giant man) isn't going to be the super weapon most people would expect.

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    $\begingroup$ And given that the maximum distance of the wood ballista was 500 yards, it is unlikely that even a nine foot giant could do better. The Romans could do 1200 yards with an all-metal one in the 3rd century, but I don't think even a nine foot giant could hold and draw it themselves. $\endgroup$ – Justin Thyme Jan 5 '18 at 1:27
  • $\begingroup$ A steel crossbow requires a spanning or cranking mechanism to draw, so I think you are quite correct with the pull of giant longbows. $\endgroup$ – Thucydides Jan 5 '18 at 17:51

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