If you took an armour piercing bullet, and repurposed it as an arrowhead, how effective would that arrow be at armour penetration, compared to historical arrows with armour piercing arrow heads?

So the question is whether a bullet can be designed to travel at the velocity of an arrow and achieve the same or better penetrating power? I would think not, and the reason is that with the arrow you would have significantly more mass behind the point of impact when you consider the arrowhead fletching and shaft. If you are asking if mere replacement of bullet shells for arrowheads on shafts would augment the penetrating power of the arrow, I would think not.

No, you put the bullet on the arrow.

I finally understood that and revised my answer. What you should do is look at some arrowheads with claims of penetration superiority and compare their tips to bullets designed to the same purpose.

Bullets are blunt and penetrate things mainly because they move very quickly. They move very quickly not just because they have an explosive charge, but because the explosive goes off when trapped inside a confined space behind the bullet leading to a barrel designed to do that.

A bow doesn’t accelerate an arrow very fast. Arrowheads penetrate things by also having sharp tips. A bullet (even an armor-piercing bullet) would be a poor arrowhead.

The explosive charge would likely not go off, and even if it did, the lack of a chamber and barrel would make noise but not accelerate the bullet much.

i.e. I’m pretty sure this would not work very well at all.

Against armor an arrow would do nothing either way. Against flesh an obsidian or chert arrowhead is likely more deadly.

The effectiveness of arrows is not improved by a stronger arrow head.

The very tough hard metal of an armour piercing bullet would be difficult to reshape as an arrowhead. If you were able to do it I don’t think it would make an effective arrow. I would guess it would be difficult to shoot straight due to the imbalance in weight and the increased mass would mean the arrow would be released at a slower speed from the bow. As kinetic energy is proportional to the square of the velocity you would have a weapon that would be ineffective even against the chain mail of the day.

If the steel was a higher grade strength than the steel arrowheads of yore, the penetration would be somewhat improved because the bullet steel would be less likely to bend or distort on impact.
If you really wanted to hurt some dude in armor you might be better off to run up and smack him upside the head with a big stick.

Good points above. Arrows, and bolts, also have to weigh a certain amount. An AP round, would likely be too heavy. It would probably throw off the balance of arrows, and it would be very dangerous to put one on the tip of a crossbow bolt.

Maybe a stainless steel tip would be an effective upgrade to a cross bow bolt. Interesting question. @ragingloli

Weight and balance wouldn’t matter much if the bolt was fired from a ballista.

A typical armor piecing bullet is a copper jacket over a tungsten carbide penetrator with an accelerator charge behind it. The copper holds the unit together while passing through the air until it reaches the target. At that point the front deforms out of the way, the rear pushes against the accelerator charge which thrusts the extremely hard and dense tungsten carbide payload into the armor. The kinetic energy required to do this work is well over 15 times the kinetic energy you will get from a a modern crossbow.
At 150 meters/ sec you will not see a difference between an armor piercing round and a conventional bullet.
Go with a hardened tip on a three blade, fixed blade broadhead like a Muzzy.