Calculate Barrel Stretch
I wanted to ask for help on calculating the amount of stretch of a rifle barrel when it is fired. The length of the barrel is 22", bore is .308, od. of barrel is .582. Barrel is 4130 alloy steel. We were talking about this in the shop but we couldn't come up with an answer. I think a typical cartridge is about 2550 psi(?). This is for discussion purposes only, just curious about how much stretch there might be. And would the stretch be different if the barrel was stainless steel? Thanks.
The chamber pressure is 55,000 psi or higher, BUT that pressure drops off rapidly.
I think you would find that book very interesting.
Another interesting question that might be easier to calculate, how much does a rem 700 receiver ring stretch at peak chamber pressure ?? or rather how much would it stretch if all the pressure avail for that sized ctg was applied to the bolt face ?? it is not all applied because the cartridge case absorbs part of the thrust (PO ACKLEY proved this in a series of experiments)
Without knowing the profiles and pressures you cant estimate the streach very easily, but this is a shop discussion (just for fun). Lets start with the easy question - Stainless vs carbon.
My references show that stainless steels have an elastic modulus around 27.6 MPA and carbon steel is around 30 mpa. High strength, low alloy steels (41, 43, 86 and other series) have about the same modulus as carbon steels.
This is a measure of the fundimental stiffness of the raw material, before it yields. It does not change much within a family of alloys or with heat treatment.
So carbon steels are about 8% stiffer than stainless so they should move about 8% less under equal loads.
Now the more complicated question - lets simplify by just looking at a tube with these specks and only consider axial forces.
.580 OD, .308 ID, 55000 PSI applied to the ends of .308 dia and 22" long
308 dia at 55000 psi puts 4100 lb of axial force on the system.
The tube has a cross section of about 0.19 in sq
Tenslie stress from line pull (ignoring hoop stresses and radial stresses) is F/A is about 777 PSI
Stress = modulus X strain.
So 777/30,000,000 = strain = 0.0000259 inches per inch of barrel, or about 0.00057 inches of streach in a 22 inch barrel (8% more for stainless)
Thats going to be a high side estimate becasue the pressure drops rapidly as the bullet moves down the barrel and the full length never sees the full load. Also, the hoop and radial stressses from the pressure will cause some shortning of the barrel (rember Poissons ratio)
ask ken oehler, he sells a strain gage system to estimate chamber pressures, he will probably now this off the top og his head. IIRC he can be fount at accuratereloading.com and is a very nice person.
Thanks all for your replies. Ahall, your figures are right on and match my calcul ations. And you also supplied the chamber pressure, which I failed to do. I'm learning about the difference between true modulus and barrel whip. A manufacturer has designed a different style of rifle stock and stated in their text that they measured the amount of barrel "stretch" at .1875 (3/16"). When I quoted them elsewhere I was soundly pounced on by the pundits. It would seem that the mfg. used the term somewhat loosely. I have a rifle that suffers from barrel whip and I am trying various ideas out trying to tame it.
In the book I mentioned X, the author found that asymmetry in the rifles receiver ring caused a barrel whip(measured with accelerometers mounted on the rifle barrel during firing). One source of asymmetry was the gas port that is on only one side of a rem 700 action, the solution to that was to drill a matching hole on the other side.
Another source he finally isolated was due to stiffening the upper part of the reciever with a scope mount, the solution there as I recall was to only use one screw and soft solder it so that it was a sort of mini cantilever mount that allowed the tube shaped reciever ring to stretch equally.
This is why what at first sounds like a GOOD idea (building a scope mount into a rifle action) actually is not because it causes an asymmetry in the stressed portion of the action. This also may be true with the massive one piece scope mounts that have some moa built into them.
Many other experiments are in the book as well, the authors pet rifle was a wildcat 270 cartridge that holds a lot more poder than a 270 win. His experiments and refinements eventualy improved the rifle to where bullet quality prevented further improvement.
Another device he built was a plexiglass fixture that was suspended from field phone headset speakers, it had a hole precisely bored in it with air ports located so it would suspend and rotate a rifle bullet, hooking the speakers to an oscilloscope allowed him to measure bullet imbalance.
He was test firing over a field of LONG grass and he noticed the muzzle blast would deflect the grass stems, BUT not the same place every time. As best I recall the reason he theorized with proof that the bullet transitions from being controlled by it's geometric center (in the rifle barrel) to it's center of balance (free flight)...this transition period causes a "flutter" or wobble that points the bullet base in a random out of square position as the muzzle blast is blowing around it. that caused the random effect of the muzzle blast on the fieled of grass.
Right on. I just finished reading the barrel joint part of that book. I'm going to read it again.
Originally Posted by willbird
Barrel whip is a complicated issue with a lot of different forcing functions.
Another good read on that general subject is here:
http://www.varmintal.net/apres.htm There is a "lot"of good reading on that WEB page.
Good link, Fitch. The info from Varmintal is quite helpful. It explains how and why some of the modifications made to my Mini-14 work. Took the Mini out to the range today, shooting at 50 yrds my best grouping was 7/8", using 55 gr FMJ. If it weren't for the ammo shortage I'd try other bullet weights, such as 62 gr HPBT. No problem with flyers or stringing, even with a hot barrel. What are your thoughts on having the barrel/receiver assm cryogenically treated? And is there any hope for getting tighter groups?
I don't know anything about cryo treatment - it's not in my experience database.
Originally Posted by X - Man
I also don't know anything about a Mini 14's potential for group size.
But you are welcome for the Varmint Al link - I've enjoyed that WEB page a lot.
Looks like the guys have covered most of the angles on barrel stretch, and given the best references.
I've just read Vaughn's "Rifle accuracy facts" for the first time in the last couple of weeks. absolute brilliance. Is he still with us and working on the remaining problems?
Got my copy direct from precision shooting magazine.
barrel stretch on firing will occur in two directions. The stresses trying to make the barrel fatter (and shorter) are 3 times stronger than those trying to stretch it longer (and thinner), but the barrel length is much greater than the circumfrence.....
I don't know, haven't done the calcs, but, I'd be very interested to see some measurements.
Put a Shadetree Engineering tuner on it.
Did you mean huge potential for improvement? Or potential for huge groups? 7/8" at 50 yds is better than 2 MOA-sounds pretty good for an off-the-shelf Mini-14 to me. I'm not sure you're going do much better without some major work.
Originally Posted by delloro