# Bows and Arrows against the Bullets...

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</David Essex voice>

does anyone know how to calculate or work out the similarities between a bullet projectile using Foot/Pounds and a bow and arrow with a draw weight of 55 pounds?

my bows a 60 inch Ben Pearson 3350, with a drawing weight of 35-55 pounds, how does it compare to the legal 12 foot pounds (or less) for an air gun?

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Very simply, the energy of the bow will be one half of the draw weight times the draw length. So if you have a 60 inch (5 foot!) draw length and 35-55 maximum draw weight, you will have about 88 to 138 ft-lbs.

I doubt the draw length of your bow is 5 feet, unless it's a ballista, so you have to use the actual length that you draw the sting back (parallel to the shaft of the arrow)

If you're interested in the maths, I can post that too if you'd like.

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lol, the draw power requires 35 to 55 pounds of pressure the bow is a 5 foot bow (top to bottom, thats how theyre measured).

the draw pull length off the top of my head is about 2 foot+ Ide need to measure that to be exact though.

its also a recurve bow (not sure if that makes any difference though?).

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Yeah, it will work for a recurve, longbow, or crossbow. (A ballista too, I guess.) A compound bow is slightly more complicated, but this should still give a resonably good approximation, I'm guessing.

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If you want an answer in ft. lbs., you will need to know the velocity of the arrow and the weight of the arrow.

Then square the velocity and divide that by the constant - 450240 - then multiply that result by the arrows weight in grains. The result will be the ft. lb. of energy.

Now the so-called "killing power" will be all out of comparison to the pellet gun because the arrow is designed to penetrate the body and cut a hole from which you will belld to death.

On the other hand, if the arrow is fitted with a blunt end on it instead of a broadhead, then it is no where neare as lethal.

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you do not need to know the weight or velocity of the arrow. The definition of work is

$\int F dx$

the force of a spring:

$F=kx$

so, $work= \Delta KE = \frac{1}{2} kx^2$ or, if you subsitute,

$KE = \frac{1}{2} Fx$

where x is the draw length and F is the force of the bow at the draw length.

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Very simply' date=' the energy of the bow will be one half of the draw weight times the draw length.

...

If you're interested in the maths, I can post that too if you'd like.[/quote']

Why 1/2 ?

edit- you posted while I was responding!

You've assumed a spring, which may or may not be accurate, and within that you've assumed all of the bow's PE is transferred to the arrow. i.e. no vibration, no energy transferred to your other arm.

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I did a quick msn search. This data:

http://www.alcheminc.com/drawdata.HTM

seems to suggest that a spring is accurate.

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OK, so that tells you they've made the same assumption about how much energy is stored in the bow. Graphs here show deviations from F=kx (i.e. nonlinearities) and also show efficiencies of around 75-80%.

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so if we say the average draw weight is 45 (fits nicely between the 35 and 55).

then we halve that to 22.5, and we take the draw length as 2 foot (its a bit more but Ill keep it simple), we then Double the 22.5 and that gives us our 45 again.

so its 45 foot pounds?

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so if we say the average draw weight is 45 (fits nicely between the 35 and 55).

then we halve that to 22.5' date=' and we take the draw length as 2 foot (its a bit more but Ill keep it simple), we then Double the 22.5 and that gives us our 45 again.

so its 45 foot pounds?[/quote']

IF your bow is still in the linear regime (the force is increasing with larger draw) then you will store 45 foot pounds of energy in the bow. The arrow will get some fraction of that when you launch it, somewhere about 35 foot pounds.

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thats great, Thanks

so its still in excess of that which is legal for a Gun in this country, but also explains why it doesnt travel as far or as fast as a pellet does, it weighs alot more

Im guessing its related to this f=ma formula in some way?

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thats great' date=' Thanks

so its still in excess of that which is legal for a Gun in this country, but also explains why it doesnt travel as far or as fast as a pellet does, it weighs alot more

Im guessing its related to this f=ma formula in some way?[/quote']

Arrows tend to be more massive than bullets. The energy is 1/2 mv2, so higher mass means lower velocity for the same energy. Also, there is probably more drag on an arrow.

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thats great' date=' Thanks

so its still in excess of that which is legal for a Gun in this country, but also explains why it doesnt travel as far or as fast as a pellet does, it weighs alot more

Im guessing its related to this f=ma formula in some way?[/quote']

There is a limit on the energy that a gun can generate in the UK?

An arrow traveling at 300 fps (or less) will be lethal all out of proportion to the KE that it produces. The reason is that at that speed, when the proper broadhead is affixed to the shaft, will completely penetrate a deer or a human and cause death due to blood loss in a matter of seconds, or at most in just a couple of minutes.

What a bow does not have in comparison to a rifle is range. Normal hunting range for a bow is on the order of 50 to 60 feet.

Anyway, getting back to the calculations - the KE is calculated from the weight and velocity of the moving projectile. If one can calculate the velocity accurately from the draw length and the draw weight of the bow, well OK, but I would be surprised if a 45 lb bow would produce the same KE with an arrow that weighed 8 oz. as it would in an arrow that weighed 2 oz.

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"foot pounds"! *shudder*

I heard someone claim recently that the English army at Agincourt would have defeated a similar sized Napoleonic army. His argument was that the lowbongs had better range and accuracy than muskets. The only reason that muskets were used was because it was much easier to train troops how to use them, but the English army at Agincourt had a huge number of soldiers who had been trained to fire a bow from childhood.

I don't know how true this is...

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"foot pounds"! *shudder*

Yeah, I'm slummin' it. Not using SI units for the numerical stuff. I was also, at first, confused why one would use a torque as a firearm measure, then realized that the "foot pound" vs "pound feet" convention was being ignored (the former as torque and latter as energy, to either increase or decrease the confusion, depending on how much physics you know)

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There is a limit on the energy that a gun can generate in the UK?

An arrow traveling at 300 fps (or less) will be lethal all out of proportion to the KE that it produces. The reason is that at that speed' date=' when the proper broadhead is affixed to the shaft, will completely penetrate a deer or a human and cause death due to blood loss in a matter of seconds, or at most in just a couple of minutes.

What a bow does [b']not[/b] have in comparison to a rifle is range. Normal hunting range for a bow is on the order of 50 to 60 feet.

Anyway, getting back to the calculations - the KE is calculated from the weight and velocity of the moving projectile. If one can calculate the velocity accurately from the draw length and the draw weight of the bow, well OK, but I would be surprised if a 45 lb bow would produce the same KE with an arrow that weighed 8 oz. as it would in an arrow that weighed 2 oz.

in order, Yes theres a limit for ownership of any airgun (or CO2 and related) that exceeds 12 foot pounds, anytjing higher and you need an FAC and suitable storage facilities etc...

as for range, I noticed that also, 150 to 200 feet is the most Ive gotten out of it without extreme elevation, and yet up close 25 feet or less a blunt knockout head will punch a hole through a .5 inch plank of wood no problem, its not a bow Ide use for hunting anyway, its simply there just for target practice fun, although I have killed a few water rats with it in the past, it has no Serious application beyond being nice to practice with and not have your muscles ache for a few days afterwards

the arrows I have are just over 32 inches long without a head/tip, ive no idea of the weight though, it certainly isnt much without a tip, so Ide have to get back to you on that one.

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Here is a web site that is a regular little treasure trove of information regarding "bone arras" as my old daddy used to say.....

http://www.martinarchery.com/faq/facts.php#system

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hey Nice!

I just had a quick cursory skim through it, and then added it to Bookmarks, Ill have a good read of that in the morning, it looks like just the sort of thing I could do with at the moment, as Im making my own arrows too.

Thanks man

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I am intrigued by the 12 lb. limit of pellet guns in the UK. What is the purpose of this?

I know that the UK is down on gun ownership, but the way I figure it, if a man can swing a 1 pound ball peen hammer 100 fps, and I think most good men can, that would generate 155 ft. lbs. of energy.

They don't regulate hammers, axes and chainsaws -- do they?

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Im not altogether sure of their "Logic" behind it either, the other semi-crazy one is the outright ban of ALL handguns, now I agree to an extent that these shouldnt be out on the streets, but even at a propper registered gun club, theyve all had to be destroyed, they just dont exist anywhere legaly now unless its a muzzel loader???

ok granted it takes about 5 mins to load all 6 chambers on a 44 mag handgun and about 4 seconds to empty them, but its STILL a 44 mag handgun! it just means the re-load time is longer, explain that one... I know I can`t!

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It kind of scares me because what is legislated in the UK is often cited as a good idea for the US.

We, thanks to the efforts of the NRA, are still allowed fairly liberal access to firearms.

I guess I am getting a little off-topic though, aren't I?

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We' date=' thanks to the efforts of the NRA, are still allowed fairly liberal access to firearms.

[/quote']

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To protect ourselves from all the other people with liberal access to firearms obviousely </sarcasm>

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The 3 main reasons are; self defense, hunting and sport shooting.

The other reason - a reason that I consider unlikely - is that I may someday need a gun to resist a tyranical government.

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