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Arralen said:
energetic efficiency of the bow
I'm not confusing it with the aerodynamic efficiency of the arrow. In fact, I thought to leave it out of the discussion, but I found a nice comparison which should make it easy to understand: "Barrel Length" .. the distance over which the missile is accelerated by propelling forces.
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Which is only relevant if the applied force is the same. It is much, much higher in the xbow, hence the need for very stout bolts.
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With a X-/bow, it roughly equates to the length of the arrow minus some "overhead", which is 80cm with the Longbow and 25cm with the X-bow. Equations are most likely non-linear ...
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Yes, they are. Acceleration is a squared term. Friction is as well. Your point?
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examples: (from Payne-Gallway, actually) 85 g bolt shot 420 m from a 550 kg pull medieval crossbow. Longbows attained lengths of ~275 m. Article authors cite another historian claiming 2x pull weight xbows were common, fwiw.
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That's shurely a 55kg-Xbow. And 110kg-Xbows where shurely not common before 1475.(Steel Xbows in general date from 1350 and later).
And think about the reloading time: I would rate such a Xbow as a last try to keep up with a)the very heavy armors and b)firearms. And it shurely would have been used in siege warfare only - much to heavy to use it in the field...
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By this logic, a 55 kg draw weight xbow can out shoot a 90 kg draw weight longbow. That's aerodynamic efficiency far beyond what's been measured and makes the longbow much less efficient than the crossbow.
I'm skipping the rest of your comments because they are based upon similar logic.