and
2) I'm a bit skeptical about the launch velocity numbers for the Trebuchet. I wouldn't be surprised if those guys simply ballparked numbers similarly to how I'm going to do it, perhaps even ignoring the vertical speed and focusing exclusively on the horizontal speed (aka: If it took X time to land at location Y, that gives us an average speed of Z). I might be wrong of course.
3) It’s not the kinetic energy at the muzzle that matters, but the kinetic energy on impact: Drag increases exponentially with velocity. The tenfold speed of the musket bullet compared to the trebuchet means ~100 times more drag for the bullet, making it bleed energy fast and hard.
That speed loss hurts the bullet doubly, as the kinetic energy is ½mv². So if you’ve lose half the speed, you lose 75% of the kinetic energy.
The trebuchet on the other hand is playing the system with its extremely curved flights path. Not only does the low velocity mean rather energy bleed in spite of the larger stone surface, it’s also cheating the system, losing speed fast in the first half of its flightpath due to gravity before reconverting said potential energy into kinetic energy. The musket fires much less ballistic. Even at the maximum distance the warwick trebuchet could fire (300m according to google), the bullet would have made that trip in less than a second.
So I did some quick math with what I presume to be the same dataset you did, extrapolating the velocity it would have had at 300m as well.
data used to start with |
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What I got is this: and
Note that the numbers in red are ballpark numbers, as I didn't bother do the exact calculations, but they don't matter to calculate the others regardless. They can just help you picture it better.
I'm not going to bother doing similar calculations for the trebuchet. It'd be too time consuming for me to do so. But let's just spitball and say it loses 10% of its energy (probably much less), that'd mean it'd still hit a target at 300m distance with a force of roughly 17 kJ. The musket bullet on the other hand has lost more than half its energy at a distance of 100m (though its kinetic energy would still be roughly twice that of most modern assault rifles and unquestionably kill you), but by 300m it would have dropped to a mere 550 Joule. Arguably survivable for a soldier wearing a spanish helmet and a cuirass.
Now I know what you're going to say: That muskets probably weren't used at such great distances. True. But then again: Trebuchets and muskets were used for entirely different purposes in entirely different periods of history.