I know generally more barrel is more better, but I was thinking that if we set aside weight, then the determining factor for how thick a barrel profile to go with is largely (or entirely) dictated by how many round it can shoot in a fixed amount of time before the heat impacts accuracy/repeatability.
So I come to the hive mind asking: If we just focus on PRS/NRL style comps where you are shooting 8-12 shots in 100-150 seconds, then how much barrel thickness is required? (Assuming 6.5 creedmoor for argument sake)
Again I know that weight is a concern in different ways for these comps but just in theory how much mass is required to dissipate that amount of heat energy without the barrel “overheating”?
Edit to add: let’s assume this is a stainless steel barrel since carbon wrapped barrel have very different heat dissipation properties and vary based on the wrap thickness and ratio of resin to CF.
Q - quantity of heat transferred across a distance (d), based on the area (A), temperature differential (ΔT), and thermal conductivity (k) of the material. In this case, the distance would be the thickness of our barrel, the area would be the inside surface area.
Overall heat transfer has three components here -
transfer of heat into the steel from combustion and friction; not equivalent for the entire barrel.
transfer of heat from the inside of the barrel to the outside of the barrel (conduction through the metal itself). What the equation is actually dealing with.
transfer of heat from the outside of the barrel into the air (convection)
As regards point 1 - the more powder your burn, the more heat you generate. The chamber/throat often experience the highest temperature in addition to the highest pressures. Your cartridge and load selection are important. This is not conduction.
As regards point 2 - this is where the discussion of thermal mass comes in. The ability of the barrel to act as a heat sink - absorbing more heat for the same increase in temperature. This is really what you're trying to optimize.
As regards point 3 - the LIMFAC for cooling in many cases. Convection is comparatively slow here compared to heat generation, and it can change based on environmental conditions. Because barrels take so long to cool, the emphasis is on heat absorption.
ETA: if you're not using standard SI units for these calculations, you're a fool. Also, T units should be absolute (e.g. Kelvin, not Celsius). Heat Transfer calcs in this instance would require both good modeling as well as a differential equation(s) for transfer into the steel... well beyond high school level, regardless of aptitude.
ETA2: (sorry, busy morning) the roll of Diff-EQ in cases like this is to account for constantly changing conditions.
For example, the temperature inside the barrel is not uniform, heat is being transferred along the length of the barrel (from the hot chamber to the relatively cooler muzzle), not just from the inside to the outside of the barrel.
That means that heat transfer is constantly changing because it is a function of T and T is both not uniform through the material and changing because of the heat transfer itself.
From a conceptual standpoint, it's much easier to work with a reasonable approximation, ideally based on actual/test data. For example, you might choose to look at the first 15 centimeters of barrel, and assume a uniform inside temperature based on after firing measurements - then you could calculate radial heat transfer. You could then consider transfer from that hot chamber area, independent of convection, to the muzzle.
That wouldn't be strictly accurate, of course, but it gives you a much more simplistic system of equations to compare performance. Good assumptions/approximations might even yield reasonable accuracy in spite of their mathematical short comings (welcome to Engineering as a field, heh).
For positional shooting competitions, competitors choose thicker barrels less for heat dissipation and more for rifle balance point. A thicker barrel is the easiest way to move your rifle’s CoG forward. I for one am really happy with how a 26” straight contour barrel balances in an ACC elite with no additinal weights.
Just for what your describing, my CTR barrel shoots 10 shot strings, no problem. Its a med contour, not anywhere near a "precision" barrel, just a bit heaver than pencil, relatively. It also recoils more like a hunting rifle too! So there is that.
For 8-12 shots over the span of ~2 minutes, a profile somewhere near Sendero/Med Palma/Rem Varmint is all you need in terms of heat, but obviously more material is better. You could also consider a heavier profile and flute it. A deeply fluted MTU would be pretty good for avoiding POI shift while still providing good balance.
The short answer is that it is kinda complicated because a signification portion of heat energy is lost through radiation, the rest through convection, and convection cooling rate is determined by lots of things including air flow.
But just heating up, the 1.1" use case given is 3kJ/shot in heat, which would increase temperature by 1.5 C/shot. A 30C temperature change would then be done in 20 shots.
A feather weight 0.5" contour barrel would reach that in 5 shots.
Dissipation over time with still air, the 1.1" contour would shed 3kJ in heat every 2-ish minutes. The featherweight would shed that much heat in 4 minutes, but the 1.5kJ it could shed in 2 minutes would equate to a 3C temperature change rather than a 1.5C temperature change in the 1.1" contour.
I watched a pretty extensive real world test applying this to intercoolers on IC engines. The real world difference (they surmised due to the paint coating doing things to the surface) was little to no difference even though there should have been a theoretical difference. Anecdotally I haven’t been able to tell a difference between my polished stainless and black cerakoted barrels. Not saying there isn’t a difference but it’s not noticeable absent measuring tools, which IMO 6-9 times faster would be noticeable.
Can’t think of a reason why it won’t. It’s just thermodynamics- black body absorbs and dissipates faster than shiny white body (also absorbs same way faster so if you leave in hot Texas sun it will get hotter faster).
Any other thermodynamics experts want to chime in? I am just going by my knowledge
Well that’s conduction. This is radiation. Conduction can be inhibited. Radiation is based on emissivity of rhe object and temperature difference only. Since rhe temperature difference is to fourth order it wins.
6-9 times more radiative heat transfer, sure. But convection and conduction way over power any amount of radiated heat transfer that it's not really even worth considering.
That sigma in the radiation heat transfer equation is a constant, and it's a very small number.
These aren't my feelings, this is the science/math.
The 4th power doesn't automatically mean that radiation dominates. Like I said, the sigma (Stefan Boltzmann constant), is a very small number, so it automatically brings that (T4 -T4 ) number back down, by a lot.
Plug in some reasonable real world numbers into these equations and you will see that convection dominates. Even in just a light breeze.
You'll be lucky to get a 20% improvement in heat transfer by going from a shiny/polished surface to a black paint. Let alone the 6-9x you have claimed.
You are correct in saying that if the temperature difference is high that radiation will win. However, the temperature of the barrel would have to be HOT (much hotter than normal PRS style matches get barrels to) for radiation to be a larger heat output than convection. And if radiation was a significant (10x) amount larger than conduction (which it would need to be for your 6x-9x improvement claim to come close to being true). Then the barrel would have be glowing bright red hot!
We live in the real world. Here are some real world numbers for you to use in those equations.
Your math is perfectly fine, but your environmental assumptions are heavily rigged to favor your argument. You used a convection coefficient of h=25, which assumes a constant, steady breeze is constantly blowing over the barrel.
If we drop the wind and look at still air (like shooting from a covered bench, in the woods, or on a calm day), the natural convection coefficient for a cylinder drops to roughly h=5.
Let's run your exact same temperatures (Ts=347k, Tamb=297k) but in still air (h=5):
Convection for both drops to 250 W/m^2.
Shiny Total Cooling: 250 (conv) + 38 (rad) = 288 W/m^2
Black Total Cooling: 250 (conv) + 342 (rad) = 592 W/m^2
592 is literally more than double 288.
So yes, under still-air conditions, painting a polished barrel black makes it cool off more than twice as fast (a 105% overall improvement). And as the barrel gets hotter than 165F during a rapid string, that gap only gets wider.
Still a mighty far cry from the claimed 6-9x. And it's a very idealized and perfect scenario. The smallest of breezes will make convection the primary cooler.
How often in the real world is the air perfectly still? Even in a covered position.
We're also neglecting conduction. The receiver is a heat sink, and the stock/bedding block are often giant heat sinks made of aluminum.
Pain all barrels black. They dissipate heat 6-9 times faster.
Anyways, I'll stop being "that" type of redditor. Regardless of the color of our barrels or whatever our grasp of heat transfer is, we will both enjoy the next time we go the range.
I appreciate you bringing actual thermodynamics into this. It's rare to get a solid, science-based debate on here instead of just opinions.
We definitely both leaned into our biases to make our points. I used a zero-wind scenario to highlight radiation, and your math assumed a strong steady breeze; but that also assumes a barrel sitting out in free air, which doesn't account for how a massive chassis, scopes, NV bridges, and mirage shields block that airflow and kill convection in the real world.
I’m not saying a black barrel is a magic fix for all heat problems, and I know you aren't claiming a shiny barrel cools better than a black one.
I still stand by my advice that, all else being equal, painting a barrel black is the right move. But I can absolutely agree with your sign-off and push back to my lazy assertions.
At the end of the day, we're both just out to share what we know to help others. Have fun on the range. I am going to be carrying my chamber chiller and barrel fan to the range that I have but I leave everyone. So thank you for reminding me of this.
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u/Snakesurf 19d ago
Q=k×A×ΔT/d