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Assume you're in a world where you can increase your strength with magic and you can get a bow with enough resistance that you can shoot arrows at a supersonic speed.

How strong would the person need to be to wield it? How many pounds of force would they have to be able to apply?

Also, is there another way using not magic but physics to allow a bow to shoot supersonic arrows (beside having insane resistance and resilience)?

Lastly, does a supersonic arrow have any advantages over a supersonic bullet?

Edit: So, it seems that supersonic arrows aren't that great. Are there any range weapons what when combined with super strength would make it as good as a gun?

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  • $\begingroup$ A regular (but high draw, possibly steel) bow with a very heavy arrow. Essentially convert your super-strength individual into a ballista and go from there! $\endgroup$
    – Joe Bloggs
    Dec 21, 2015 at 9:43
  • $\begingroup$ @JoeBloggs but would the damage done by such a arrow do more damage than a bullet? Cause I want guns in my world and I'm trying to figure out does it make sense for people to use other weapons. $\endgroup$ Dec 21, 2015 at 18:36
  • $\begingroup$ Depends on the bullet, the kind of gun and the strength of the person, but I'd say you could make it comparable. Certainly more useful against armoured targets (a properly designed arrow could go through Kevlar as it wouldn't deform on impact), and less pain to manufacture (you just need someone that can cast steel, no theoretical metamaterials required). It would be shorter range than a gun, but so would any bow! $\endgroup$
    – Joe Bloggs
    Dec 22, 2015 at 9:00
  • $\begingroup$ Just make sure you don't go near the speed of light $\endgroup$
    – Möoz
    Mar 18, 2016 at 4:26
  • $\begingroup$ Use a sling to throw supersonic rocks. That would work wonders and would be way easier to build than this bow. $\endgroup$
    – Mermaker
    Mar 10, 2017 at 15:54

4 Answers 4

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You're going to find a lot of physics gets in the way.

The most important detail will be that arrows bend while being fired. Because all of the propulsion is coming from the back of the arrow, the arrow is naturally unstable during firing. This is something archers are aware of at normal archery speeds. However, you will need to break the sound barrier while the arrow is still under power, so you'll need a lot of power in this unstable time.

Let's pretend your arrow is made of unobtanium, and is rigid enough. Let's also pretend your bow has a good enough "dry shot" velocity to accelerate anything to those speeds (which I think may be reasonable, with enough clever geometry). A reasonable mass arrow is around 200 grains (13 grams). In the interest of approximations, let's round down to 10grams, or 0.01kg to make the math easier. The draw length of an average bow might be around 0.75m. We can do the calculations to see how much energy an arrow has to have at the sound barrier: 340 m/s, and then use that to figure out how much force is needed to do that work over the draw length. E=1/2mv^2 = 578J. F=W/d = 770N. That's roughly 175 pounds of draw strength, to accelerate the arrow with no air friction or anything.

That's about triple the strength of a human right now. However it fails to take into account a lot of things, least of all being the inefficiency of the bow near the speed of sound (you're basically going to have to make the string into a bull whip).

However, that's just to get to the speed of sound. The drag of a projectile at supersonic speeds is quite high, about three times higher than you'd expect for a well designed projectile. Consider that a 9mm bullet is supersonic when it comes out of the barrel, but rapidly slows to subsonic. You would actually have to accelerate the arrow to a much higher speed to remain supersonic in flight. Trying to fire at mach 2 would require 4x the force.

All of that presumes access to an unobtanium shaft that can take the stress of launching, a carefully constructed bow with pulls quite stronger than any human can handle, and probably ignores a half a dozen limitations that appear in the transonic region that I am simply not accounting for.

The arrow shafts seem like the most difficult part to solve. Modern archers pay top dollar for ultra-exotic composite arrow shafts to minimize flex at human speeds. The material requirements for that arrow shaft supersonic may simply be outside the realm of known materials.

Want to shoot an arrow supersonic without these problems? Try a sabot. You can use them to basically put a sharp small object (like an arrow) into a gun. The sabot holds the shape as the explosives project the entire construct out of the barrel. Then the sabot falls away and lets the sharp thing fly.

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  • $\begingroup$ The sabot doesn't really help cause, it not that I really want to shoot a super sonic arrow. I'm trying to figure out what kinda projectile weapon can someone with super strength use that is as powerful as a gun. $\endgroup$ Dec 20, 2015 at 18:05
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    $\begingroup$ @user1804234 Couldn't s/he just throw a rock? $\endgroup$
    – Frostfyre
    Dec 20, 2015 at 18:25
  • $\begingroup$ @Frostfyre How strong would someone need to be that just throwing something would be better that shooting someone? $\endgroup$ Dec 20, 2015 at 18:29
  • $\begingroup$ @user1804234 Projectile weapons are simply force multipliers. If someone with a bow can exert the same amount of force as someone with super strength, then a rock is effectively just as effective in the hands of the one with super strength as the bow is in the hands of the normal. $\endgroup$
    – Frostfyre
    Dec 20, 2015 at 18:35
  • $\begingroup$ What if you build a bow with a track the arrow rides in to hold it straight during that boost phase? $\endgroup$ Dec 20, 2015 at 23:04
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Not really on answer, but you should give up on this idea. In all cases if your strength and the resistance of bow go up, it is better to add mass to the arrow than to make it supersonic. So a situation where someone would build a supersonic bow does not really exist. (With magic it could happen by accident, of course.)

This is because energy losses to drag and mechanical resistance will rise rapidly when the speed is increased. Traditional bows and arrows are meant for subsonic speeds so their base drag and resistance from the basic design is fairly high. If you accelerate it to supersonic, you'll get lots of wasted energy. Basically I am talking about the bowstring and the arms having large surface area and relatively bad aerodynamic shape. The ratio of the mass of arrow to the mass of the moving parts of the bow is also important.

Thus while it is actually fairly simple to calculate the force needed in ideal case, I didn't actually do the math because the actual force needed would be dominated by the mechanical and aerodynamic losses which would be difficult to even estimate without an actual bow with known design and materials.

Note that the same rapid increase of drag applies to the arrow afterwards as well. So for the same energy a subsonic arrow with more mass will fly farther and penetrate deeper on impact. In theory supersonic arrow would be more accurate, but in practice that would require the arrows to be precision manufactured from metal. Traditional arrow construction is not optimized for supersonic flight. Modern arrows might be more practical with more precise construction and higher quality materials.

A crossbow can be made very strong with pulleys or cranks to amplify strength. There is nothing stopping you from making it strong enough to propel the bolt supersonic. Except the fact that it would be even more inefficient than magical supersonic bow due to the added mechanics adding their own losses. And you can add the same mechanics to a bow if a crossbow is a no go. It just isn't particularly sensible, since the crossbow construction is more convenient for difficult to load cases.

A supersonic arrow (designed to be supersonic, not just normal arrow going fast) has better mass to drag and mass to front area ratios. Or said simply larger aspect ratio. Larger aspect ratio may result in higher range, better accuracy, and better armour penetration.

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  • $\begingroup$ This. If you have a massive and dense arrow and an extremely high draw strength bow (possibly a steel bow), then you essentially turn the bow wielder into a siege weapon. Where a supersonic arrow might not be much use a steel tipped lead bolt would wreak all manner of havoc. $\endgroup$
    – Joe Bloggs
    Dec 21, 2015 at 9:41
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You've asked for ranged weapons which are alternatives to a bow and arrow where super-human strength would make the weapon more potent.

I would suggest the following:

Most of these may strike the same problems of material strength pointed out by other answers when extreme (supersonic) use is required.

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  • $\begingroup$ Seconding the sling. While they require an insane amount of training to use with a lot of accuracy, a normal human with a few years' training can propel a rock from a string at frankly unbelievable speeds and hit within the general area. A superhuman would (assuming stronger material) be able to fling (a) much heavier loads and (b) much farther, as well as being able to use a longer sling which makes it that much more powerful. I'm not sure about the aerodynamics of trying to make it go supersonic, though; to my knowledge, that has yet to be done. $\endgroup$
    – Nic
    Dec 21, 2015 at 12:17
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It troubles me that everyone went to so much trouble to point out it's a terrible idea, but no one actually answered the question...

First off, is there a way to accomplish supersonic arrows in a non-supernatural way.. no.. but for different reasons than you think. Could we build a mechanical assist longbow? Sure. But when you think about what a bowstring moving at supersonic speeds would do to your face and arm, shiver

For this to even be feasible in reality, you'd need to invent some sort of magnetic launch mechanism because the string would mess you up pretty badly.

But in a supernatural setting? Oh DEFINITELY!

First understand that strength adjusted bows have existed forever in Dungeons and Dragons. Second, to answer your question accurately would require some specifications..

For one.. You'd need a special bow, probably notched, so arrows can fly with minimal flexing.. it would also need to be enchanted to protect you from the bowstring and sonic crack in your face.

Second.. you need to decide what look you are going for.. are you shooting for the long long range sniper? Because now you have a range of about 6,000 feet.. or are you going for the barbarian who can shoot down castles and blast people out of a forest?

An arrow would need to be a mythological metal to survive.. so either something like a 20,000 grain (almost 3lbs) adamantine arrow.. or at the truly ridiculous end, a 27lbs ballista bolt. I'm going to assume you're going for the more "normal" adamantine arrows (which would be ridiculously expensive but almost invincible!)

Assuming a lot, I'd guess a heavy arrow (600 grain) made fully of adamantite would be about 15000 grain (about 2.25lbs, HEAVY! Note that adamantite, steel and dense ironwood have about the same density). Assuming a 75cm (29 inch) draw and an acceleration TO the speed of sound (thus minimum power) giving about 106,000 m/s/s of acceleration. Force equals mass (0.972kg) times acceleration (106666 m/s/s) gives 1,036,793 Newtons of force, or a draw strength of about 232,000 lbs, or a minimum strength of 7,000 in D&D 5e.

But fret not! There's magic afoot! If you use a bow of FORCE then you would only need a STR score of about 21 to fire an arrow (assuming the arrow is normal at draw and until after release) at supersonic speeds and 6k range. Now THAT would be something to see no?

I hope that answered the question. And now I really want a silenced sniper's bow of supersonic force.

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