Optimal Barrel Length Calculations

[K470]

Is there a source for calculations to determine the optimal barrel length for a given cartridge?

I've searched the forums but I didn't find a source for the formulas.

I'm not smart enough to figure this out myself, but I think I am smart enough to understand the formulas if can find them.

Any assistance would be appreciated.

 

[spife7980]

Optimal how?

 

[K470]

Optimal how?

To determine the length where you get the most efficient use out of a given powder charge.

 

[Aftermath]

MDT Builds World's Longest Rifle To Find Out How Long Is Too Long

MDT engineers built the world's longest rifle that has a six foot long barrel to find out how barrel length affects the muzzle velocity.

www.thefirearmblog.com

 

[K470]

MDT Builds World's Longest Rifle To Find Out How Long Is Too Long

MDT engineers built the world's longest rifle that has a six foot long barrel to find out how barrel length affects the muzzle velocity.

www.thefirearmblog.com

I've seen this but I am looking for formulas that would allow you to calculate velocities taking into account variables such as caliber, case capacity, powder burn rate, etc.. to determine and optimal barrel length.

 

[Rob01]

Won’t work as barrel’s are different. Would all be a guess. Stop worrying about formulas and load some ammo and shoot it.

 

[waveslayer]

There a lot of things to consider, how many groves, how tight the barrel is, how it's made, caliber, bullet being used. As Rob01 said, go shoot more and don't worry

 

[Cascade Hemi]

Is there a source for calculations to determine the optimal barrel length for a given cartridge?

I've searched the forums but I didn't find a source for the formulas.

I'm not smart enough to figure this out myself, but I think I am smart enough to understand the formulas if can find them.

Any assistance would be appreciated.

32" * 1 / 1=Optimal barrel length.






/s

 

[Old Man with Gun]

Depends on your goals, I know people shooting 308 to 1000 with 30" barrels and they would still get more velocity with a longer barrel.

There is a point with no gains, but that is impractically long. When is one more inch not worth the velocity gain vs the weight and balance depends on what you are going to do with it.

 

[Supersubes]

Is there a source for calculations to determine the optimal barrel length for a given cartridge?

I've searched the forums but I didn't find a source for the formulas.

I'm not smart enough to figure this out myself, but I think I am smart enough to understand the formulas if can find them.

Any assistance would be appreciated.

In the barrel lengths we’re likely to use, gain or loss of velocity per inch of barrel is minimal and quite linear. Quickload software will calculate powder burn percentage for you if you're curious.

 

[diggler1833]

32" * 1 / 1=Optimal barrel length.






/s

Dude, that only works with rimfires...

 

[diggler1833]

On a serious note, I think that optimal barrel length has more to do with intended purpose than it does with cartridge.

Some dudes run shorter magnums with suppressors now for hunting, other dudes run long tubes with already efficient cartridges to squeeze every last FPS out of them. I'd certainly look at the application first, before deciding on cartridge and barrel length.

 

[biggershooter]

I've seen this but I am looking for formulas that would allow you to calculate velocities taking into account variables such as caliber, case capacity, powder burn rate, etc.. to determine and optimal barrel length.

Formulae I don't know, but you can experiment iteratively with QuickLOAD.

 

[Aftermath]

I think you are looking for just how long the barrel needs to be to get all of the acceleration available from a particular charge.

Just to consider some of the actual variables...in no particular order and by no means intended to be comprehensive

barrel length
rate of expansion of barrel due to internal explosion
bullet weight
friction coefficient of bullet to barrel
friction coefficient of bullet to unseat from case
seal coefficient of bullet to barrel
rate of gas expansion of burned powder
percentage of complete burn
efficiency of initial ignition
amount and rate of loss between case and chamber
amount of rearward movement of case in chamber
amount of time to seal between case and chamber

Now...even if there were an actual formula for what you are looking for, if you are capable of using that extremely complex formula, you should be able to derive your own.

 

[Oldloser]

People still believe in this OBL voodoo?

The variations obturation swamp any transverse waves created by the barrel being slightly bent. And all that is lost in the noise of your own NPA issues.

A very straight bore, perfect bullet seating in the case, a clean bore, and a great bullet are all you can control.

 

[K470]

My nerdy engineering side is showing and I am looking at this from a theoretical standpoint more than for practical purposes. Maybe asking about optimal barrel length was the wrong approach.

If you look at the data MDT collected from their testing, there is a curve there that should be able to be predicted for various calibers, powders, bullets, barrels, etc.. by calculations. The formula to do those calculations is what I was looking for. It's all physics.

I have done a lot of searching and haven't been able to find anything so I'm guessing it hasn't been done. Maybe because of the numerous variables.

Thanks for the feedback and input.

 

[Rover31]

Formulae I don't know, but you can experiment iteratively with QuickLOAD.

And with GRT

 

[Herb Stoner]

Dude, that only works with rimfires...

…and if you have a tuner on it.

 

[45-90]

I shoot the 308 with 30" barrel 8 twist with a long action shooting 200 gr 2856 fps to 230 gr Atip bullets at 2620 fps. Lapua brass. Then there is the hybrid case.

The 9 mm Luger keeps gaining speed, the 16" barrel is faster than the 14.5" or 10" buy alot with certain loads.

Quick load predictions of powder burt 100% in shorter barrels but the bullet keeps gaining speed as the barrel gets longer until it doesn't...friction over comes the gas push from the powder.
The point of no return...and that could be ridiculously long for some calibers.

9mm 2620 fps average with a 16" barreled AR and 50 gr copper bullet with deep hollow point.
I scrapped the 10" and hardly use the pinmed 14.5," in favor of the 16" the 9mm AR because becomes a viable 200 yd gun on steel... so what is the optimal barrel length. Well for me, the 9 mm with a 16" barrel, but 18" could offer even more.
But then somewhere ya gotta draw the line on length, because it may become too long and unwieldy for your purposes.
Then ya hear the short barreled guys go, "it always burns all the powder in 8", maybe even says so in the QL program...but then the chronograph says the tiny 9mm with its tiny powder charge, is still gaining speed in 16" barrels in most every case.
Optimal barrel length? A lot of variables.

 

[Macht]

My nerdy engineering side is showing and I am looking at this from a theoretical standpoint more than for practical purposes. Maybe asking about optimal barrel length was the wrong approach.

If you look at the data MDT collected from their testing, there is a curve there that should be able to be predicted for various calibers, powders, bullets, barrels, etc.. by calculations. The formula to do those calculations is what I was looking for. It's all physics.

I have done a lot of searching and haven't been able to find anything so I'm guessing it hasn't been done. Maybe because of the numerous variables.

Thanks for the feedback and input.

It's been done many times at various levels of complexity, from 0d lumped parameter codes to full 3d sims that take days to run. A relatively simple lumped-mass internal ballistics solver like QuickLOAD or GRT is decent enough at predicting muzzle velocity and will do what you want.

If you want to see the math that style of solver is based on I would suggest Corner's Theory of the Interior Ballistics of Guns or Carlucci's Ballistics: Theory and Design of Guns and Ammunition.

 

[Doom]

Is there a source for calculations to determine the optimal barrel length for a given cartridge?

I've searched the forums but I didn't find a source for the formulas.

I'm not smart enough to figure this out myself, but I think I am smart enough to understand the formulas if can find them.

Any assistance would be appreciated.

The problem is in the question. While it sounds simple in reality it cannot be answered. Some of the definitions of optimum are:

1. The most favorable condition, greatest degree, or largest amount possible under given circumstances.
2. Greatest degree attained or attainable under implied or specified conditions

You mention your engineering side. There are always limiting factors that require compromises in any engineered solution in relation to the desired outcome. In the case of barrel length it becomes a trade off of velocity in relation to weight, ability to manufacture, maneuverability, center of gravity, powder burnout, cost, and intended function that makes up the circumstances above. Looking at something simple like terminal velocity at 1000yds will yield vastly different answers if one case is to remain supersonic and the other case is to be at 1800 fps.

@Aftermath listed just some of the variables that affect internal ballistics. There are complex tools (calculations and combinations of calculations called models) that can be used to determine what happens with variations of these variables. But the answer may involve other aspects of ballistics. In this case it likely involves the internal ballistic calculations and external ballistic calculations and possibly terminal ballistics requirements.

 

[ma smith]

Problem seems like and endless number of equations being solved in endless number of variables.

 

[45-90]

This is a very non exact science, with too many changing variables. We all know models and modeling, some weather models are a fair guess for the day... Or part of the day. Some not so much...hurricane paths, strength, storm surge, and destruction come to mind.

Covid 19 models were way off...as most seem to be.
Garbage in garbage out... plus here you are dealing with nothing that is exact and all the standards constantly changing...even the barrel length will grow slightly as the barrel heats up.
Some things are machined and inspected in a controlled atmosphere of 68°, as metal parts will grow out of print if the temperature changes much from machining, inspection, to installing on sight in clean rooms...variables are sometimes impossible to deal with... so one ends up with a guesstimate, scientific or otherwise.

 

[PreciseLoad]

If you're only looking at velocity, you might say a barrel is "optimum" up to the point where no further length increases speed. The graph below, for example, is a simulation for a .308 Win with a Varget load, a 168-grain Sierra MK, and a barrel length of 150 inches.

But what if you define "optimum" as the point where all powder is burned? Well… that depends—mainly on the burn rate of your propellant.

• With Varget, about half of the powder burns in a 2-inch barrel—obviously not ideal for a .308. But who would use a 2-inch barrel for a 308 Win. anyhow?
• Switch to a faster-burning propellant like Vihtavuori N133, and that number jumps close to 75% in the same barrel length.

So, what’s the best barrel length? It all depends on your powder, bullet, cartridge and application. Want precise answers? Just let PreciseLoad.com do the math for you!

Bests - Bene

 

[K470]

It's been done many times at various levels of complexity, from 0d lumped parameter codes to full 3d sims that take days to run. A relatively simple lumped-mass internal ballistics solver like QuickLOAD or GRT is decent enough at predicting muzzle velocity and will do what you want.

If you want to see the math that style of solver is based on I would suggest Corner's Theory of the Interior Ballistics of Guns or Carlucci's Ballistics: Theory and Design of Guns and Ammunition.

"If you want to see the math that style of solver is based on I would suggest Corner's Theory of the Interior Ballistics of Guns or Carlucci's Ballistics: Theory and Design of Guns and Ammunition."

Thanks, these are a couple resources I have seen before.