I noticed that people who shoot 9 mm pistols on YouTube experience quite some recoil but that I don't experience any recoil when shooting my compound bow, even though the projectiles of both have similar momentum. Unfortunately, I don't own any firearms and it's been a decade since I shot one, I don't even remember which one, and I didn't ever shoot a pistol (Europe, you know ...), so I can't do a direct comparison.
My compound bow shoots a 27 g arrow at 82 m/s and a 9 mm Commonwealth standard bullet has a mass of 7.5 g. 27 g * 82 m/s / (7.5 g) = 295.2 m/s So it has the same momentum as my arrows when it travels at 295.2 m/s. Its actual speed is 370 m/s, so my arrows have 80% of the momentum of these bullets.
I already almost dismissed the question after I noticed that maybe most of the recoil comes from the exhaust gases, maybe the energy matters, not the momentum, or maybe it's because a bow spends more time accelerating its projectile than a pistol.
But then I went the other way and calculated that a 1 kg metal ball would have to travel at 2.2 m/s to have the same momentum as an arrow. If one were hit by such a ball, the impact would probably be quite noticeable, even when one catches the ball and decelerates it over the distance a bow needs to accelerate an arrow.
So my questions are:
- What characterizes recoil? Is it momentum? Is it energy? Is it something else?
- How does a compound bow manage to have no recoil?