# Bow with supersonic arrow

1. May 17, 2015

### kroni

Hello,

I am asking if from your point of view, is it possible to build a bow that can lunch arrow to a supersonic speed (speed superior to 350 m/s) ? I make some calculus, estimating cinetic energy needed but, is it possible to build a bow where this energy can be obtained ? In which material ?

PS : The bow have a classic size.

2. May 17, 2015

### A.T.

I don't think anything in physics rules it out. It's more of an engineering problem, which might be unsolvable with current technology.

3. May 17, 2015

### rumborak

A quick back-of-a-napkin calculation I just did seems to indicate that the archer would need to pull the equivalent of a 100kg weight, the weight of a full-sized adult. That's probably not feasible.
(assumptions: 20 grams arrow weight, 1m draw distance)

4. May 17, 2015

### sophiecentaur

Perhaps a crossbow could get enough energy into your arrow. The arrow could be made extra light to make life a bit easier than rumborak's calculation suggests. Maybe ear protectors could be necessary to deal with the shock wave???

5. May 17, 2015

There would be no shock wave or sonic boom observed by the archer. He/she is already behind the projectile.

6. May 17, 2015

### rumborak

The arrow would have to be a special material too probably, as it would have to withstand the acceleration without snapping.

7. May 17, 2015

Staff Emeritus
Like a lead ball? In a brass casing? Maybe propelled by gunpowder?

8. May 17, 2015

### JakeBrodskyPE

If you could find the materials to do this safely, a crossbow could theoretically do the job. The problem is finding a string that can withstand the forces, a very low mass bolt (that's what a crossbow shoots) strong enough not to break from the acceleration, and the limbs capable of delivering the force without shattering. Believe me, if such a crossbow were possible, it would have been invented by now. I've seen high end crossbows capable of up to 130 meters/second, but not much more.

This is actually not a new problem. It is an exercise in material science more than anything else. As Vanadium 50 pointed out, this is why guns were invented.

9. May 17, 2015

### stedwards

This is an interesting challenge. In the realm of nonexplosives, only a bullwhip seems to be doing this--no exotic materials required.

10. May 17, 2015

### rcgldr

What about a (electric) rail gun that shoots arrows?

11. May 18, 2015

### sophiecentaur

You could be right but the string would be at full speed as it passes within a few cm of your ear.

12. May 18, 2015

### JakeBrodskyPE

Actually, the string wouldn't reach sonic speeds until it was well past your face (assuming you were endowed with the super-human strength to actually draw such a thing).

That said, even if this were a cross-bow, I wouldn't dream of firing something like this without ear protection.

And of course, the comic side of this is that as you reduce the air pressure, the speed of sound decreases. So to fire your supersonic arrow, first develop a bow that could shoot at 300 meters per second, and then take it to the summit of Mt. Everest...

13. May 18, 2015

### kroni

I am planning to build a crossbow. I hesitate between carbon fiber + epoxy resin and steel. I will make some computation to estimate the optimal form of the limbs.
I think that a good solution for the string is to use a piano wire.
I estimate that the piano wire will explode at the end of the propulsion step, when the arrow left it because limbs stop.
So it's a one shoot string but i can use a thinner one so the speed is higher.

14. May 18, 2015

### JakeBrodskyPE

Even if this works, you should expect everything to self destruct, especially the limbs.

You might also want to spend time watching slow motion video of what happens to the limbs and string of a compound bow. It is a complex motion. Consider using extremely eccentric cams with the limbs, mounted on very heavy duty bearings. I would also use steel for the limbs because a carbon fiber system will probably shatter, where steel may not.

In another post
Allow me to add another non-explosive device that can break the sound barrier: Aircraft propellers. If the governor of an aircraft is not set properly, the engine may turn the propeller faster (typically 2800 RPM or more). This not only increases stress on the propeller significantly, it also doesn't yield any additional thrust. The reason is that the tips are breaking sonic speed. You won't notice much from inside the aircraft, but from the ground you'll hear a very loud, rasping roar as the plane of the propeller passes by.

Yet another possibility: Use pneumatics. See You could use the bow string on a very large piston that then launches the arrow...

15. May 18, 2015

### A.T.

Or the aircraft designer decides so...
http://en.wikipedia.org/wiki/Republic_XF-84H

16. May 18, 2015

### Staff: Mentor

Be aware that the end of a snapped steel wire lashes around unpredictably and can do an amazing amount of damage... Slice an eyeball in two... snip off an earlobe.... If you're going to experiment beyond what off-the-shelf technology offers, invest in a setup that allows to you to trigger your awesome toy infernal device superbow from a few meters away.

And treat the cocking process with at least as much respect (which is to say, a lot) as you would the compressed coil springs in a MacPherson strut.

17. May 18, 2015

### cjl

This is a common misconception - the speed of sound in air is actually almost entirely independent of pressure. It basically only depends on the temperature of the air - speed of sound scales as the square root of the temperature. Yes, speed of sound decreases with altitude, but this is because the temperature decreases with altitude, not because the density or pressure does.

18. May 18, 2015

### kroni

Clearly i am realy concient of the dangerosity of such bow, wire and limbs. I will build a simple system to trigger the device without problem.

Thanks a lot for all your remark ! I will post picture if i have time to build it.

19. May 19, 2015

### JakeBrodskyPE

It is popular among ultrasonic ranging instrument vendors to use just temperature to estimate the speed of sound. As you say, temperature is the most sigificant effect. HOWEVER: The speed of sound is actually dependent upon air density. Density is a function of both pressure and temperature. In most applications, you tend not to see significant variations in barometric pressure, though the temperature can and does change significantly. In this hypothetical case, BOTH are significant.

By the way, although I am joking about the Everest quip, I did take the time to look up the speed of sound in a standard atmosphere at 30,000 feet.

20. May 19, 2015

### Bandersnatch

Can you show us how? The only relevant equation I know is for the speed of sound in an ideal gas, and there's no density nor pressure factor in there since they conveniently cancel out:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html
How much of a correction is needed for a non-ideal gas? Is it really at all significant?

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