Sharp as a Marble - Short lived when you think of it in those terms

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Short lived when you think of it in those terms

Can’t do the math here (on bus), but someone claims that the lifetime of a barrel is 4 or 5 seconds – the bullet in contact for a fraction of a second with each shot, and 10k shots or so. Higher-end barrels last a shorter time, of course.

Maths are hard, but I did some basic calculations. Granted, muzzle velocity is not constant through a barrel, it's kind of interesting to think of how long the bullet stays in contact with the metal.

Looking at standard .223 mv's, considering a 20" barrel

3,200 fps = 38,400 inches per second. 20" of barrel contacts the metal for .00052083 seconds. 10,000 rounds = 5.2083 seconds.

I'm sure I forgot to carry the two somewhere, but that's pretty damned interesting.

posted @ 1/29/2010 10:21:27 PM

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SayUncle » Interesting on 1/30/2010 9:59:39 AM

Comments

Justin Buist says:

on 1/29/2010 10:46:07 PM

Hmm, let's look at it another way. Say a .224 bullet has contact with 0.25" of the barrel as it travels down it. Multiplied by 10,000 rounds that's like shoving a 208 foot long rod down it. In 5 seconds.

I can see how that'd wear a barrel out.

Grey says:

on 1/30/2010 12:50:36 PM

Actually, bullet to barrel contact would be slightly longer as the bullet is in contact during acceleration up to exit velocity. Acceleration is not instantaneous.

However, the premise is correct.

Robb Allen says:

on 1/30/2010 1:00:01 PM

That's why I qualified the post with

Granted, muzzle velocity is not constant through a barrel

With a bit more math, I could determine the time from rest to 3200fps in a given length and get pretty darned close. But maths is hard.

Ian Argent says:

on 1/30/2010 1:15:03 PM

This was pointed out in one of the Venus Equilateral stories, oddly enough. As an analogy of why their electron gun needed more power, admittedly...

1911Man says:

on 1/31/2010 1:18:42 AM

QuickLoad says that 27gr of Win748 behind a 50gr Nosler Ballistic Tip in a 19in barrel Rem .223 is filled to 105% case capacity, makes a bit over 56k psi, has a muzzle velocity of 3282fps, and that the bullet is in the barrel for 0.807ms from the time pressure reaches 10% of max (which is essentially the same time the bullet actually starts moving). That's 1/1240th of a second per round.

So the maths are that 10k bullets are in the barrel for a total of 8.06 seconds. You guess pretty good, for a guy with no pants.

The interesting thing is that, as far as I have ever seen, barrels wear worse at the slow-bullet end than at the fast-bullet end. My wager is that this is because the slow-bullet end is also the high-pressure end, the high-temperature end, and also the end where the powder itself is moving wicked fast but not all turned into gas yet.

Or maybe not.

Doc Merlin says:

on 1/31/2010 6:05:29 PM

I think its not quite right, temperature matters a lot too, ROF affects cooling which affects barrel wear. So, if you put thousands of shots through a barrel really quickly, it will wear out faster than if you space them out a bunch.

Robb Allen says:

on 1/31/2010 6:10:27 PM

Oh, this is nowhere near a scientific endeavor and shouldn't be considered highly accurate. However I'd say the time frame of 3 to 10 seconds, while fairly wide of spread, is still pretty interesting when you think about total time the barrel is in use for launching bb's.

k says:

on 1/31/2010 10:48:21 PM

I think your math is wrong.

If we assume constant acceleration, which gives us a lower bound on barrel life, we can come closer than what you've estimated.

I compute it as 10.4 seconds for 10,000 rounds assuming 3,200 fps muzzle velocity from a 20" barrel.

It's fairly easy to show* that, if accelerating from rest to velocity v at constant rate over a distance d, then time to accelerate over the distance is given by:

t = 2d / v

It turns out, you really did forget a 2 somewhere in your calculations: the coefficient!

This gives total time spent [near the chamber end] of a barrel as:

t = 2 * 20/12 / 3200 = 1.04 ms

Total barrel life is therefore more than 10.4 seconds if we assume a lifetime of 10,000 rounds. With non-constant acceleration, travel time per round should be lower and therefore overall barrel life a bit higher, but this gives us a good lower bound. These assumptions completely ignore gas cutting or the fact that at one end of the barrel, the bullet isn't moving, and at the other end, it's moving at more than 3000 fps and spinning remarkably quickly.

* To show this, set kinetic energy equal to the work done over the distance of the barrel, and recall distance formula for constant acceleration:

1/2 m v^2 = m a d
d = 1/2 a t^2

Solve the second equation for a

2d / t^2 = a

and substitute into the first, cancelling m:
1/2 v^2 = 2d / t^2 * d

Then group terms
v^2 = 4d^2 / t^2

cross multiply
t^2 = 4 d^2 / v^2

and take the sqrt
t = 2 d / v

Please check my work! This was a neat problem.

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