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There exists a bow capable of sending a 1000 gram arrow flying at about 1900 mph. The bow is a re-curve resembling the old Mongolian style bows and is made of steel.

What sort of modifications would have to be done to an arrow to keep it stable at this speed?

This includes materials, fin length and size, as well as rigidity. Keep in mind that this speed doesn't have to be maintained. This is simply the highest reached velocity.

Also it is important to just handwave any harm to the user. The bow is about 1.5 times bigger than an average Mongolian bow and its parts also are 1.5 times bigger than their equivalents.

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    $\begingroup$ Are you still using a bow to launch these? What kind of bow? $\endgroup$ – Dubukay Jan 23 '18 at 23:58
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    $\begingroup$ i will edit and answer these questions $\endgroup$ – Christopher Void Jan 24 '18 at 1:24
  • $\begingroup$ How long can the arrows stay above the speed of sound? How fast does it's speed drop? What is the bow's and arrow's design? $\endgroup$ – iostreamerX Jan 24 '18 at 2:10
  • $\begingroup$ I think the arrow would fare pretty well, but not the fletching. $\endgroup$ – SIGSTACKFAULT Jan 24 '18 at 3:36
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    $\begingroup$ Assuming that bow is actually possible to make, which I highly doubt because goddamn that's a lot of energy to store in a mere few kilograms of steel, when the archer releases the bowstring either the sheer force of it moving through the air or the recoil from accelerating the sharpened rebar "arrow" will kill him. The energy density of this scenario is just too damn high for it to result in anything less than a loud bang, shrapnel and some pink mist. $\endgroup$ – Cognisant Jan 24 '18 at 4:43
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There are "arrows" which travel at supersonic speeds, but they are not fired by bows, but by large calibre tank cannons. They are technically knowns as APDSFS rounds (Armour Piercing Discarding Sabot Fin Stabilized)

enter image description here

M829A3 round

The "petals" of the sabot serve to keep the round centred in the barrel during firing, and also fill the barrel so the propellant gasses don't flow past the round, providing the greatest energy transfer to the projectile. Once it clear the barrel, the sabot pets peel away, leaving the "dart" to carry on to the target. Soviet and Russian APDSFS rounds have similar properties, but use a different form of sabot:

enter image description here

Russian Bm15 round for a 125mm tank cannon

The specific shape of the APDSFS penetrator is related to factors such as cross sectional density, the need to maintain velocity downrange and the ability to penetrate armour, especially composite armours and various forms of spaced armours. The long, thin "dart" shape provides low drag (preventing the velocity from dropping too much with range), and concentrates the energy in a very tiny area on impact, improving the ability to penetrate armour. Extra fun can be had from using high density depleted uranium, as the material becomes "pyrophoric", spontaneously igniting in the presence of oxygen once it passes through the armour (the frictional heat provides the energy for ignition).

Now you have not mentioned what, exactly a supersonic arrow is needed for, but it would have several of the properties of an APDSFS penetrator. The dart shape for low drag and armour penetration is a must. If you are actually using a bowstring and improbably large bow to provide the launching energy, a stiff metal dart will have less tendency to flex like a wooden arrow or quarrel, allowing for greater energy transfer to the projectile.

enter image description here

Flexing of an arrow when launched

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  • $\begingroup$ Could editors stop changing to American spelling? Thank you $\endgroup$ – Thucydides Jan 26 '18 at 4:54
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Let's have a look at the total energy required. There is the formula: E = 1/2 mv^2, and in this case you get:

E = 1/2 * 1(kg) * 849 (m/s) ^ 2
E = 360 kj

That is more energy than is present in a ... .50 cal rifle (20kj) by more than an order of magnitude. So to say you're going to have issues is an understatement.

The major issue you are going to have with the arrow is splintering. You are accelerating your arrow crazily fast. It goes from 0mph to 1900mph in less than one meter of space. For the mechanics of a bow/arrow, this means all that force is concentrated on the back of the arrow where the string pushes against it. Without the support of a barrel, you'd be hard pressed to stop the back of your arrow "mushrooming" out. It could be done, but you'd likely need some hard material at the back of your arrow.

I'd just go for something more like a long bullet than an arrow. You can't spin the arrow (no rifled barrel), so you will still need fins, but they certainly won't be made from feathers. I'm no aerodynamics expert, but I think funny things happen at supersonic speeds, so I won't give any advice on fin shape. The material will also have to be incredibly stiff to avoid the fin "fluttering."

Then there's the matter of the bow. I tried fooling around with an "arrow speed calculator." I can't ascertain it's accuracy with such large numbers, but using trial and error, it seems to hint that our bow will need a draw weight of around 4500 pounds, or about 2 ton. I hope your archer is very very strong.

Even with a high draw weight there is the issue of the return speed of the limbs of the bow. This is an issue because the drag acting on the limbs of the bow slow them down, and most materials have a maximum velocity they return to "neutral" at. I'm just going to assume our crazy draw weight somehow overcomes these limitations.

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    $\begingroup$ You might want to correct the math: E=½ (m v^2). Otherwise, excellent answer $\endgroup$ – pojo-guy Jan 24 '18 at 9:17
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    $\begingroup$ Finding a material hard enough to resist supersonic speed but able to bend without breaking when it touches the riser is going to be difficult, if not plainly impossible. (+1) $\endgroup$ – Rekesoft Jan 24 '18 at 9:51
  • $\begingroup$ You also forgot to square the speed, so it's about 400 times more energy than in a .357 Magnum. And this is a major issue. $\endgroup$ – Keelhaul Jan 24 '18 at 11:13
  • $\begingroup$ Indeed, I did mess up with the energy calc (oops). I think it's better now? $\endgroup$ – sdfgeoff Jan 24 '18 at 12:15
  • $\begingroup$ still missing a 1/2, but with the order of magnitude it doesn't really matter. $\endgroup$ – user25818 Jan 24 '18 at 12:17

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