Can a Bow Launch an Arrow at Supersonic Speeds?

[cjl]

Hum ! I think the speed of sound in the air vary with density only at very low pressure. It's clear that empty space has no speed of sound, so there is a gap where the macro behaviour of matter disapear and micro effect like thermal effect are important.

At extremely low pressure, sound waves will just tend to dissipate, but the sound speed is pretty much the same. At high pressure, the sound speed can vary a bit though (you have to get up to a pretty high pressure for this to matter though).

 

[sophiecentaur]

Hum ! I think the speed of sound in the air vary with density only at very low pressure. It's clear that empty space has no speed of sound, so there is a gap where the macro behaviour of matter disapear and micro effect like thermal effect are important.

The transmission / matching loss gets very bad at low densities - because there may not be enough molecules to carry sufficient KE from place to place- but the wave speed will eventually depend upon the speed of the molecules i.e. how fast the movement of the source can reach the receiver. All that is not relevant to sound transmission in our (lower) atmosphere where there are plenty of molecules to deal with normal sound power densities. A shock wave, however, will be formed when an object is moving significantly faster than the average molecular speed and gives large numbers a kick in the forward direction because they can't get out of the way in time due to their thermal motion.

 

[XZ923]

I read the thread and just couldn't resist.

They already do make devices that can propel small objects at supersonic speeds and are widely available already. They're called firearms. No theory necessary, just a background check and a thousand bucks.

 

[sophiecentaur]

I read the thread and just couldn't resist.

They already do make devices that can propel small objects at supersonic speeds and are widely available already. They're called firearms. No theory necessary, just a background check and a thousand bucks.

True but they are not 'hand powered'. Air guns would be a potential solution but their energy output is limited by regulations to 12ft lbs - not for practical reasons, I think. If it were allowed, I'm sure someone would make a pumped supersonic version.

 

[cjl]

True but they are not 'hand powered'. Air guns would be a potential solution but their energy output is limited by regulations to 12ft lbs - not for practical reasons, I think. If it were allowed, I'm sure someone would make a pumped supersonic version.

It's fairly difficult to get an air gun above ~1000ft/s though simply due to the speed of the air molecules themselves. No matter how much pressure you put in, the air can only expand at a certain rate down the barrel. You could get around this by either heating the air, or by using a lighter gas (like helium), but that's getting fairly complicated for an air gun.

 

[sophiecentaur]

It's fairly difficult to get an air gun above ~1000ft/s though simply due to the speed of the air molecules themselves. No matter how much pressure you put in, the air can only expand at a certain rate down the barrel. You could get around this by either heating the air, or by using a lighter gas (like helium), but that's getting fairly complicated for an air gun.

Good reply. The bit about the limit of the flow of the air molecules is very relevant and I hadn't thought of that.

 

[CWatters]

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)

Google says world record is around 90 kg for an 82cm draw..

http://markstretton.blogspot.co.uk/2014/08/10-year-guinness-world-record.html

 

[cjl]

Good reply. The bit about the limit of the flow of the air molecules is very relevant and I hadn't thought of that.

This is also why some of the highest velocity guns in the world (used for things like meteorite impact research) use a multi stage system involving the compression of a light gas (helium or hydrogen) by a piston driven by a normal chemical propellant, with a burst disk between the light gas and the projectile. The chemical propellant fires, compressing the light gas (and heating it at the same time) by driving the piston into it at a high speed, then when the pressure in the light gas gets high enough, the burst disk ruptures and the high pressure light gas propels the projectile at several km/s.

http://en.wikipedia.org/wiki/Light-gas_gun

 

[Aria Darabi]

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.

Modern day rail guns use electromagnets to launch projectiles. However with a bow, you are limited as you cannot put a magnetic coil into a barrel for example. Might work with a crossbow, but with a simple bow and arrow; no.

 

[ken schatten]

Well, I can make a comment that i am not sure is there...
If the arrow exceeds the sound speed, then the typical bow and string type geometry, need have the string to exceed the air speed. In so doing, it would
generate shock waves, and so the power requirement would go up as well... So, the added power need be considered there too.

 

[Lok]

Google says world record is around 90 kg for an 82cm draw..

http://markstretton.blogspot.co.uk/2014/08/10-year-guinness-world-record.html

There are other means to get to more draw-weight and length. Here is a list of Flight archery records:
http://www.worldarchery.org/RESULTS/Records/Flight-Records/Men
As far as I know the 1410m record in the Foot bow section is by puling the string with both hands and pushing the bow with both feet. Thereby increasing both draw weight and length capabilities. Even so it would be far from supersonic.

 

[MidgetDwarf]

Yeah the ancient Chinese archer method.

 

[zanick]

someone answered this ... yes, it is possible.. with the 150m/s cross bow... just go up to 100k feet and shoot it from your balloon

 

[nasu]

Actually at that altitude the speed of sound is around 300 m/s.
You are a little better at around 60,000 ft where the speed is a little lower, around 295 m/s.
See here, for example.
http://www.engineeringtoolbox.com/elevation-speed-sound-air-d_1534.html

 

[Lok]

Thanks for all your answer.

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.

What do you thing about this idea ?

Here is a link of a crossbow dry fire, or with an arrow of 0 mass. The string looks like it reaches around 270m/s (a rough estimation based of the 9000fps and aproximate 30mm travel in the fastest frame).

Carbon fiber will be best for speed. Steel is just too heavy per strength for both limbs and string.
Instead of the piano wire go to plastics as lighter really means more speed. A braided dyneema thread that can hold 70kg with 0.6mm thickness is common in fishing supplies and it is easy to use more strands (5x70kg=a lot and still 4-8 times lighter than the piano wire). It is tough and light enough not to cause a "life threatening backlash".

 

[cjl]

Here is a link of a crossbow dry fire, or with an arrow of 0 mass. The string looks like it reaches around 270m/s (a rough estimation based of the 9000fps and aproximate 30mm travel in the fastest frame).

Carbon fiber will be best for speed. Steel is just too heavy per strength for both limbs and string.
Instead of the piano wire go to plastics as lighter really means more speed. A braided dyneema thread that can hold 70kg with 0.6mm thickness is common in fishing supplies and it is easy to use more strands (5x70kg=a lot and still 4-8 times lighter than the piano wire). It is tough and light enough not to cause a "life threatening backlash".

I'd tend to think a synthetic fiber such as Kevlar or Spectra would be best for tensile strength to weight, but I agree with you that light and strong will be required. Similarly, I'd think you'd need a substantially larger than average bow, with a fairly long draw and a pretty unique cam system designed for maximum acceleration with a light arrow.