AR-15 HBAR's

[Varminterror]

Surface area grows in proportion to the square of the linear dimensions. The mass/volume grows in proportion to the cube of the linear proportions.

This isn’t true for the case of rifle barrels. We’re not talking about squares and cubes, or circles and spheres here. Check your math/geometry, because this is WAY off.

If you double your length, 2x linear dimension, you double your area. If you double your diameter, you double your surface area. Recall - external surface area of a cylinder: A = pi * D * L. So doubling diameter doubles area, nothing more.

For volume/mass of a rifle barrel, doubling length doubles volume/mass, doubling diameter doesn’t even quadruple the volume/mass. They aren’t cylinders, they’re annuluses. Recall - volume of an annulus, which is the same as the volume of a large cylinder, minus the volume of a small cylinder: V = L * pi * (OD^2 - ID^2)/4. If the ID of the barrel is unchanged, then doubling the OD only increases the value of the OD^2 term by 4x. So if the ~5” of 0.64” diameter barrel between the tapers of a Government profile barrel increases by 56% to match the 1.0” diameter of the Hbar profile (D2 = D1 * 1.56), you only increase the relative volume of that section by 164% (V2 = V1 * 2.64), which is a power factor of 2.19, not the cube. In other words, for that particular increase in diameter, the proportionality between diameter increase and volume increase is NOT the cube of diameter ratio. The volume increase is proportionate to the diameter increase to the 2.19th power.

So, without intent to be insulting, your math which lead you to believe doubling diameter lead to 4x and 8x and your belief that result means smaller diameter barrels cool faster is wholly incorrect.

 

[Varminterror]

As I described in detail above, “cooling faster” means the heat transfer is faster. Again, the fundamental thermodynamic equation for cooling rate is Q• = UA(Th-Tc). U is a constant, Tc is our cool air temp, Th is the hot barrel temp, so the only variable there is Area A. Increase A, you increase your heat transfer rate Q•. It’s really that simple.

Think about why your radiator in your car has fins - to increase its surface area. The U value between air and aluminum is a constant, the operating temp of the antifreeze fed to the radiator is largely fixed, as is the air temp. The only way to improve cooling rate is increasing Area.

Equally, think about boiling a pot of water on the stovetop. The bigger the pot, the greater the mass, the longer it takes to bring to boil.

This stuff is around us every day, and it’s the reason we can live.

Bigger diameter barrels take more shots to heat up, and they expel heat faster.

We can talk about the asymptotic approach of the differential temperature over time as the barrels cool, or about thermal transmittance rates from the inner surface to the outer surface in the transient state vs. the heat transfer coefficient from the outer surface to the air, or about the dynamic and transient temperature gradients within the length of the barrel during the dwell time, even talk about convective air flow through handguards vs. the insulative properties of the flow-resisted air mass inside the handguard. Heck, I probably know a couple guys I could text wh would translate the pressure strain from firing into thermal energy values for us... but largely, it’s academic and not hugely productive... The fundamentals remain simple...

Bigger diameter barrels heat up more slowly, and expel heat more quickly than smaller barrels.

 

[1KPerDay]

Ok, so if I understand you correctly, if we heat both to 500 degrees, the bar on the left will take longer to cool down than the bar on the right?

http://allthingsstainless.com.au/co.../product/3dfc0b8fc4a1becb424c3a63c1fef35b.jpg

 

[Varminterror]

Speed and time are different things. Taking longer doesn’t mean slower if you travel farther. By heating to the same temperature, you are giving one barrel, or one bar, more work to do than the other, and then saying it is “slower” because it takes longer. It’s not slower, it has more to do, so even though it’s doing it FASTER, it takes longer.

Think about it this way - it’s a race:

If you put the same amount of heat into both bars, aka, shooting the same number of shots you’re putting them the same distance from the finish line. The larger bar won’t be as hot as the smaller bar, even though you gave it the same amount of heat. The larger bar expels heat faster, so it finishes faster.

Alternatively, your “both at 500F” scenario isn’t a fair race, and not really applicable for what we’re talking about in terms of equal rate of fire. You are starting the bigger bar, heavier barrel, farther from the finish line. It’s easy to finish before your competition if you have a headstart, even if you aren’t actually faster.

So... to use your example:

Two 6” long bars of mild steel at 500F. One is 1/2”, one is 2” (neglecting end losses here), air cooling to 72F.

The 2” bar will expel 156.9 BTU/hr through it’s surface, whereas the 1/2” bar will only expel 39.2 BTU/hr. The larger bar expels heat faster than the smaller bar. Or said differently, the larger bar cools faster. Four times faster.

The 2” bar has to expel 274.9 BTU to reach ambient temp, while the 1/2” barrel only has to expel 17.2 BTU.

So it takes the big bar 1:45 to expel all of its heat, and it takes the small bar 0:26.

But you don’t have to be fast to cross the finish line first if you have a head start. You’re not faster, you just didn’t run as far. You would fire 16 times more shots to get that barrel, rather 2” bar, as hot as the 1/2” bar.

For fun, let’s run a more realistic scenario: shooting the same number of rounds, for example, in a 3 gun match with a fixed course of fire.

So let’s pretend our equal course of fire - equal heating load given to each bar - is 100 BTU. So we started at 72F, the 1/2” bar would have reached 1317F, whereas the 2” bar would only reach 150F. Resultingly, the 2” bar will come back to room temperature in 5.25hrs, whereas the 1/2” bar will take 11.5hrs to cool back to 72F.

So the 2” bar will return to ambient temp in half the time as the 1/2” bar, following the same course of fire.

And it won’t have started to flex from nearing its melting point.

As I stated in my first:

Heavier barrels take longer to heat up, dissipate heat more rapidly,

 

[tark]

This is gonna be real subtle and I won't mention names, but I think someone posting here must live in Oakland, California.

 

[Varminterror]

Worked in Livermore for a while, but that was way back before weed was legal, let alone shrooms.

This thread does remind me of something my graduate advisor used to say, “most folks don’t know a BTU from their btuhole.”

 

[Skylerbone]

Im curious then, as it relates to our discussion, how thin a profile is really too thin? I’ve carted and dumped a pencil profile middy several times over the past few months, worried I was about to make a costly mistake on a lighter weight build.

This particular rifle is meant to be a rather spartan carry. I cannot actually conceive of a reality that finds me traveling a post-apocalyptic road defending myself from small groups of bandits, and I’ve never been a weight weenie, but is a govt. profile as light as is sensible for real world use discounting hunting? I have one of those already with an fsb and heavy aluminum half-quad. Maybe save weight with a lightweight rail then?

 

[Varminterror]

Eh, handguards with integrated heat shields help a lot. Without, pencils can get exceptionally hot in hand under sustained fire. If you’re not rattle trap mag dumping a lot, barrels don’t get terribly hot, and if you don’t mind a little heat, all the better.

I personally just hate the way they balance. There’s a lot of mass in the AR receivers, pencil barrels handle fast and carry nice, but they don’t point for **** for me. I’m an odd AR owner tho, even when I shoot fast, I like to hit small stuff, and I’m a 200lb relatively muscular dude in relatively not terrible shape, so carrying an extra half pound of barrel never bothers me. I don’t favor .875” or .936” blocked barrels for field/carry rifles, but an HBAR/National Match/Service Profile suits me just fine.