Author Topic: Barrel length  (Read 796 times)

Offline Dan Fruth

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Barrel length
« on: October 17, 2019, 12:40:13 AM »
Is there a minimum barrel length to powder charge ratio, or better said, a barrel length that is too short for black powder muzzleloaders?
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Offline smylee grouch

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Re: Barrel length
« Reply #1 on: October 17, 2019, 12:55:50 AM »
I have thought about that too but think maybe barrel volume might be more of a factor. The bigger bores would have more volume per inch so I,m guessing they would burn more powder per inch.  I think that the way black powder burns, more of a flash instead of a progresive  burn that most charges would be burned up in the first feww inches. I think The Mad Monk would probably know about it than me so hope he chimes in here.

Online rich pierce

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Re: Barrel length
« Reply #2 on: October 17, 2019, 01:18:10 AM »
I guess pistols answer that question. I think its pretty hard to get 1500 FPS in a pistol.
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Offline Mtn Meek

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Re: Barrel length
« Reply #3 on: October 17, 2019, 01:28:03 AM »
Henry Deringer made pistols with barrels less than an inch long and often in .41 caliber.  They were effective enough to kill Lincoln with a singe shot.  (Booth's pistol had a barrel length of just over two inches.)

On the other end of the spectrum, Civil War mortars came in various sizes from bore diameter of just under 6 inches with tube lengths of a little over 16 inches up to mortars with 13 inch bore diameters and tube lengths of 56.5 inches.

Depending on the purpose of the weapon, the minimum bore length needed is just a little longer than that necessary to accommodate the charge and the projectile.
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Offline stikshooter

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Re: Barrel length
« Reply #4 on: October 17, 2019, 02:37:12 AM »
My TC custom shop (Buckeye Special )50 cal with a Great Plains conical and 85 grains of O.E. 3F runs 1200-1221 FPS with a 19 inch factory barrel . It does kill deer ! /Ed

Offline Hungry Horse

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Re: Barrel length
« Reply #5 on: October 17, 2019, 05:57:28 PM »
 I would discount the Deringer pistol reference, because they are always shot at very close range. But, the journals of the Lewis and Clark expedition references a Harpers Ferry that their gunsmith shortened after the barrel ruptured, that surprised them with it accuracy when they shot it. I think it was the only gun they gifted on the expedition.

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Offline Daryl

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Re: Barrel length
« Reply #6 on: October 17, 2019, 06:06:57 PM »
Longer barrels, as I understand the situation, give higher velocities per powder charge, due to having longer to work with the expanding gasses.
The powder is burned in relatively short piece of barrel, but the length of barrel determines how long those gasses have to, well, expand.
If you had ever seen pressure traces on a graph, it would be easier to understand this. The pressure peak is very close to the breech, then reduces
 with the length of barrel, however is still in excess of atmospheric pressure or pressure in front of the ball, thus the longer the barrel, the higher the
terminal velocity.
« Last Edit: October 17, 2019, 08:59:48 PM by Daryl »
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Offline Mtn Meek

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Re: Barrel length
« Reply #7 on: October 17, 2019, 09:32:50 PM »
I would discount the Deringer pistol reference, because they are always shot at very close range.

  Hungry Horse

The OP's question is too vague or broad to provide a meaningful answer to.  He does not specify whether he is asking about long range or close range, so the Deringer pistol is a valid reference.  Probably not what he was thinking about, but then we can't read his mind--only what he wrote in his post.

Darly and smylee grouch do point out some important variables in terms of velocities and energies as they relate to barrel length and bore volume.  They are right in their intuitive thinking.

I hesitate to provide this link because the math is pretty intimidating and tends to make one's eyes glaze over, but this is some very interesting work on internal ballistics of black powder.  I think the author is Henning Umland.

https://www.celnav.de/muzzleloaders/internal_ballistics.htm

This graph is Fig. 1 in the link above.  The blue line represent pressure and the orange line represents mechanical work which can be equated to muzzle energy.  The x-axis is bore volume from Vp, the volume of powder, to Vb, the total bore volume.  In other words, the x-axis represents the bore volume from in front of the powder to the end of the barrel.  This graph illustrates Daryl's point, "due to having longer to work with the expanding gasses.  The powder is burned in relatively short piece of barrel, but the length of barrel determines how long those gasses have to, well, expand."  Daryl is describing the principle of Boyle's law.



There is a point of diminishing returns on the orange curve where it starts bending over and approaches an asymptote.  Longer and longer barrels increase the muzzle energy or velocity by smaller and smaller amounts.

The orange curve also illustrates the Deringer pistol and mortar situation.  The orange curve is bending in the other direction at the very low volumes or barrel lengths.  The projectile is accelerated by the initial combustion and expansion of the gases, but doesn't get the benefit of the additional acceleration of the gases continuing to expand in a longer barrel.

In between these two areas of curvature, the orange curve is almost a straight line where increasing volume or barrel length has a proportional impact on muzzle energy and velocity.

I would guess that this is the part of the curve the OP was most concerned about and the area most of our pistols and rifles operate in.

There are some other interesting insights in Mr. Umland work.

It takes some special equipment to measure the blue pressure curve in the graph above so he took a bunch of experimental data published in Blackpowder Loading Manual, 3rd Edition by Sam Fadala and used the measured velocities and muzzle energy along with barrel dimensions, ball weight, and powder charge and performed some multivariate statistical analysis on it.

As a reminder, muzzle energy, E0, is proportional to the square of the muzzle velocity, v0.


The end result is an equation (eq. 7 in the paper) relating muzzle energy, E0, to mass or weight of powder, mp, and mass or weight of round ball, mb, and length of barrel, LB.  The constants "a" and "b" are derived from the regression analysis.



 The constants thus found with 3FG powder are:
a =     −92.665
b =     3.112
u =     0.738
v =     0.282
w =     0.417
Mr. Umland notes some limitations or restrictions with this approach.
Quote
Equation 7 yields an average value of the muzzle energy resulting from a given combination of powder weight (3FG), ball weight (round balls only), and bore length. The equation is only valid for powder charges in the usual range and should not be used for exotic charges, for example 100 grains of powder in combination with a .32 cal (45 grains) round ball. Further, the equation will lead to inaccurate results when used for pocket pistols with extremely short barrels since these are outside the observed range (LB = 6.0"- 41.5").

Mr. Umland's emperical equation gives results as we would expect such as shown in his Fig. 8.  The muzzle energy for a given powder charge is much higher in a 24 inch rifle barrel than a 9 inch pistol barrel.  Both rifle and pistol are .45 caliber.


Similarly, his Fig. 9 shows a .54 caliber barrel compared to a .50 caliber barrel of the same length yields higher muzzle energy for a given powder charge.  No surprise here.


One result he got that I didn't expect is his comparison of a .36 caliber barrel to a .32 caliber barrel shown in his Fig. 11.


Quote from: Mr. Umland
The .36 cal ball shows the same behavior as seen in Fig. 7 through Fig. 9, i. e., a more or less linear rise of E0 with increasing powder weight. As expected, the energy gained from 50 grains of powder is smaller in this case than with big-bore rifles (compare with Fig. 9). The real surprise is the behavior of the .32 cal ball. With a light powder charge (20 grains), it delivers almost the same muzzle energy as the bigger .36 cal ball. However, the curve is not linear here but flattens out rapidly as the powder weight increases (u<1). As a result, the .32 cal ball needs about 50 grains of powder to produce the same energy as a .36 cal ball with a powder charge of only 35 grains. How can we explain this? Apart from the smaller expansion ratio, the unfavorable ratio of powder weight to ball weight probably becomes a dominant factor here. Above 45 grains, the powder weight surpasses the ball weight in this case. This means that a high portion of the mechanical energy released by the powder is consumed to accelerate the inert mass of the combustion products (gases and solids) and is not available to accelerate the ball. Accordingly, energy efficiency decreases considerably. Further, the shape of the curve may also be an indication that even 3FG powder is too slow for a .32 cal round ball. In other words, the inertia of this ball is so small that the latter gets blown out of the barrel while the combustion process is still in full progress, possibly not far from the pressure maximum. Remember, a heavy powder charge takes more time to burn than a light one. There must be a reason why the old .32 cal squirrel rifles sometimes had barrels as long as 40" or even more.

These results suggest that using the faster 4FG powder or Swiss Powder #1 might be the better choice for .32 cal rifles when firing round balls.

Maybe the OP will come back and explain further what he was trying to get at with his question.
Phil Meek

Offline smylee grouch

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Re: Barrel length
« Reply #8 on: October 17, 2019, 10:13:17 PM »
Outstanding  Mtn Meek.  It has been awhile but I think  I reviewed that info some time back. Thank you for taking a significant amount of time to post that and your explanation .   

« Last Edit: October 18, 2019, 07:19:16 PM by D. Taylor Sapergia »

Offline hanshi

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Re: Barrel length
« Reply #9 on: October 17, 2019, 11:16:09 PM »
One thing to remember is that powder charge effecting velocity is not a straight line.  "Chronographing" increasing charges in guns has shown that it's not unusual for the next - say 5 grains at a time - charge increase to have a velocity that's actually lower than the previous lower charge.  There can be real increases beyond that, of course. 

Figures from tests done with 20ga trade guns of increasing barrel lengths are also very interesting.  A 20" barrel was giving velocities not far behind a 30" tube.  The difference from 30" to 35" was very small.  Going to a 40" barrel gave only a few fps over the 35" gun.  The 30" gun gave near 94% the velocity of the 40"  and the 35" about 98%.

A .40 X 38" rifle I've worked with extensively gave double digit, as expected, speed increases with each 5 grain charge increase.  But going from 35 grns to 40 grns gave a whopping 235 fps added velocity!  After that each 5 grns added went back to the same double digit added fps.

Nothing definitive here except that each gun will likely behave differently as well as experiencing jumps and starts rather than a gradual, steady rise in speed.
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Offline Dan Fruth

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Re: Barrel length
« Reply #10 on: October 18, 2019, 05:10:20 AM »
Thanks everyone for your info....I'm asking this for a friend. I must admit I was unaware of the thought that has gone into the pressure/ballistics of black powder. I have never had a gun with a short barrel, more for the reason of building pieces from a particular period in history....
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Offline Mike Brooks

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Re: Barrel length
« Reply #11 on: October 18, 2019, 02:23:05 PM »
Charts and graphs....my eyes just glazed over....
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Offline Hungry Horse

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Re: Barrel length
« Reply #12 on: October 18, 2019, 06:31:57 PM »
 An old friend asked me to help him build a trade gun out of a pile of parts he had amassed over about ten years. The gun used a 20 gauge shotgun barrel from Dixie that was 27 long. He took it elk hunting in Idaho, and killed nice bull with one shot through the lungs, at 80 yards. A local guy that witnessed the shot, said he never saw an elk hit any harder, even with modern firearms. Plenty of velocity from that little 27 barrel.

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Offline bob in the woods

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Re: Barrel length
« Reply #13 on: October 19, 2019, 12:36:57 AM »
My 2 cents is that while a certain velocity is necessary, anything beyond that is mainly desirable for it's flattening of trajectory.   As long as I have adequate penetration, 100 gr FFg beyond a .735 ball kills just as well as 140 gr FFg from my experience .   For European boar hunting, the distances were rather short if my research is correct, so great velocity really wasn't necessary from a trajectory standpoint