Ah ok, I'm with you on the numbers (it's not my thing!) I was quoting the video clip where the guy said it was the same as a 44 mag bullet.
However, surely a bullet is far smaller than an arrow? So even with the same force and speed behind it, a bullet is more likely to make a clean hole straight through, while an arrow has more surface area so will deliver a harder punch? I am terrible with physics, but if the arrow doesn't penetrate, isn't that more likely to deliver blunt force to the target? All the energy that should be used to punch through the armour is being spent/wasted on the area around it, like a great meaty fist thumping into the chest?
Or have I got that totally wrong?
Well, there a couple of thing about your statement that are not quite accurate. They apparently used a .44 magnum as a comparison, so let's use that.
1. Comparing a .44 mag to
any arrow is the epitome of apples to oranges. The .44 is a far more powerful projectile since it is traveling much, much faster, well over 1,000 fps faster. Now, it is lighter, but you can increase a projectile's energy more by speeding it up than by making it heavier, and a projectile's energy is what defines it's ability to do work.
2. In terms of diameter, a .44 mag, which is .429 caliber, is actually closer to an arrow than you might think. .429 is about 11mm, so slightly larger than 3/8 inch, not too far from warbow arrow diameter. However, a .44 mag typically has a flat fronted projectile, rather than a point as on a bodkin. This doesn't matter all that much for our purposes, since we're talking about non-penetrating rounds, but it is interesting.
3. .44 magnum rounds produce between 900-1300 foot pounds of energy depending on the loading. (Some exceptions, but that's the general area.) Warbow arrows produce about 10% of that depending on various factors, but any bow putting out 130 foot pounds would be an
extremely powerful bow.
4. Given that a man wearing body armor who is struck by a .44 mag, or, as I said, even high velocity rifle rounds like a .308, isn't knocked back, why would a warbow arrow, which only has a fraction of the power, be able to accomplish this? The answer is, it can't. True, either projectile will impart energy into it's target, and in doing so will effect that target, but a man walking forward won't be knocked off his feet by either one.