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Old March 11, 2012, 02:20 PM   #1
mikthestick
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BP Internal Ballistics

My computer will not work many ballistic programs (win7) even if I was prepared to pay what they cost.
My interest is BP, I know for example a 44-40 from a 24" barrel gives about 1310ft/sec and about 975ft/sec from a 7.5" barrel. I would like to be able to do the maths can anyone help.
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Old March 11, 2012, 05:30 PM   #2
mikthestick
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Can't believe I found it myself
Don Miller's formula for estimating muzzle velocity for black powder cartridges.
[ From Black Powder Cartridge News, # 76, Winter 2011, pp. 27-30 ]

V = K x L1/4 x ε1/2 x ( 1 - 0.3 x ε1/2 )

OR

V = K √ √ L √ ε ( 1 - 0.3 √ ε )

where
V = muzzle velocity fps
K = constant for powder used
L = barrel length in inches
ε = c/m
c = powder weight in grains
m = bullet weight in grains
Powder K
Cartridge
(preliminary)
Goex Fg 1418
Goex FFg 1544
Goex FFFg 1627
Swiss 1.5 Fg 1544
Swiss FFFg 1627
For a 44-40 24" barrel with 2f powder K=1544 c/m =40/200 L1/4 the hard part for those who don't like maths is 2.213. 40/200 to the power .5 = 0.447
Put this in the formula to get 1323ft/sec near enough for me.

Last edited by mikthestick; March 11, 2012 at 05:36 PM.
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Old March 12, 2012, 05:56 AM   #3
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Mik

Did the article give any idea what the variation might be in practice?
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Old March 12, 2012, 07:03 AM   #4
mikthestick
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No this is the bit I left out
Don Miller's formula for estimating muzzle velocity for black powder cartridges.
[ From Black Powder Cartridge News, # 76, Winter 2011, pp. 27-30 ]
If you google estimate black powder velocity you will find it. attached is an online calculator which does the calc for you.
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Old March 12, 2012, 07:57 AM   #5
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I know an M1 carbine has an 18" barrel Cartridges of the world says 1900ft/sec with 110gr bullets and 14gr of H-110 powder therefore the powder must have a K of 2896. A 20" barrel would give 1951ft/sec.
A 34" rifle 54cal round ball(230gr) should go 1716ft/sec with 70gr of 2Fg The published figures for a 44-40 24" barrel is 1310ft/sec making K 1530 not 1544. This is still too high to give the published 1389ft/sec. The gun is flintlock and doesn't have a breech face and will leak pressure. Using the formula to find K for the gun (1250) I would expect an 8" barreled pistol with 35gr of 2Fg powder to give 724ft/sec. With a 222gr ball 735ft/sec is predicted. 792ft/sec is published in the Lyman handbook. Not a bad formula I think.
1389ft/sec comes from the internet. Lyman state 1409ft/sec for a 28" barrel and Geox 2Fg. Someone has a batch of poor powder.

Last edited by mikthestick; March 12, 2012 at 08:36 AM.
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Old March 12, 2012, 09:30 AM   #6
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Agree

The formula is interesting.

My question had to do with my observed variation in Muzzle Velocity. I use a CED chrono.

I am recalling these figures from memory but I think I am close. I have to shoot about 30 rounds to get a good idea of the average MV. On a system (I define "system" as one revolver on a given day with all shots fired in sequence so as to reduce the time differential, same powder charge, same powder from the same container and same bullet casting run. Barrel swabbed after each round of six. All chambers loaded) in which average MV is 750, I might get a standard deviation of 40 FPS if I am lucky.

I am fairly careful with measuring the charge as I use that contraption I came up with last year so I may not know the exact weight of the charge but I know that all charges are very similar in volume. I think I am getting very close to the indicated charge plus or minus one grain. I mold my own round balls and can get standard deviation in diameter down to less than .001. I think I am at least moderately successful at reducing variation in the factors contributing to the formula. Yet if SD is as I have observed, I get as much variance from shot to shot because of unidentified factors than I would if I randomly chose a different powder. Both factors equal about 95% to 105%
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Old March 12, 2012, 11:34 AM   #7
mikthestick
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Looked at your profile

Don't Know how to put up a profile of my own so:.I am a retied Electrical/electronic engineer. More importantly I am a Brit and don't own guns although I'm very interested. I wanted the formula so I could do in my head what you can do in practice (with your chrono). Somewhere on this sight I found a link to a site which calculates Muzzle velocity but needed "a published load", case capacities, lengths etc, and gave no formulas. When I tried to use it with what Info I had it seemed very inaccurate. It gave a velocity which was supposed to be 65% of the shots. The string deviation was always about 50ft/sec or more above and below the 65% value. I always thought published figures were about average for a string, perhaps plus or minus 25-30ft/sec.
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Old March 12, 2012, 01:09 PM   #8
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Mik,

Our backgrounds and interests are little similar in that I did electronics in the U.S. Navy for 26 years and then taught it in University for another 10 years.

My approach to shooting is similar to yours as well since I like the scientific aspects. Although my interest does not manifest itself in better accuracy since I am a lousy shot.

I did not read the article you have cited but I think there is no reason to believe it is any less reliable than anyting else out there.

That includes what you said about the "spread" of the shots in terms of MV which seems to agree with what I have experienced. 65% of shots form the first SD (well duh!) and the rest are a little out there including the outliers.

I think that several of the members of the forum have used chronographs more extensively than I have. In previous discussions I can recall some complaints about the accuracy and reliability of the data they provide. Others question the rationale of using them in the first place stating that MV is not important to them since they shoot CAS which uses very light loads to the detriment of MV.

I went through three of them before I found one which would give me descent results. That is the CED M2 at about two hundred bucks. Some would say that is not a lot of money for a highly precise electro-optical instruments but the process of making the measurement is (as you might imagine) quite simple and not requiring much in the way of expensive components. We did it in one of my digital principles classes for about twenty dollars worth of parts.

I am not familiar with the rules on handgun ownership in the UK or the ease of getting the things you would need to shoot. But if you could and did, I think you would find the article and the formula to be pretty good when put to the test and pretty interesting in practice.
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Old March 12, 2012, 09:02 PM   #9
B.L.E.
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Quote:
Originally Posted by Doc Hoy
I am fairly careful with measuring the charge as I use that contraption I came up with last year so I may not know the exact weight of the charge but I know that all charges are very similar in volume. I think I am getting very close to the indicated charge plus or minus one grain. I mold my own round balls and can get standard deviation in diameter down to less than .001. I think I am at least moderately successful at reducing variation in the factors contributing to the formula. Yet if SD is as I have observed, I get as much variance from shot to shot because of unidentified factors than I would if I randomly chose a different powder. Both factors equal about 95% to 105%
You might try chronographing five shots loading the same chamber every time. A lot of people who shoot NMLRA revolver matches mark the most accurate chamber in the revolver and use it for every shot on the slow fire targets.
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Old March 12, 2012, 09:25 PM   #10
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Here are some recent chronograph results from my Ruger Old Army.

20 Grains Schuetzen 3fg, Circle Fly nitro card and fiber wad soaked with 50/50 crisco/beeswax between the powder and ball as a filler, and .457 Hornady round ball. Ampco nipples by Treso.

652.3
647.9
639.0
650.3
643.3
average 646.6
sd 4.7

Hand cast TC .45 MaxiBalls, 220 grains grease grooves filled with Bore Butter, 30 grains Schuetzen 3fg. Stock nipples.

715.2
731.4
772.2
727.1
754.9
average 740.1
sd 20.5

Last edited by B.L.E.; March 12, 2012 at 10:02 PM.
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Old March 13, 2012, 02:58 AM   #11
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BLE

Good point on the chamber marking. This is not something I have done or even tried to do.
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Old March 13, 2012, 06:12 AM   #12
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Another factor in velocity variations could be variations in bullet pull. People who have chronographed muzzle loading round balls report that if you load without cleaning, the velocities climb as the barrel gets more and more fouled. The initial resistance to movement of the bullet by the fouling increases the chamber pressure, same as a tight crimp verses a loose crimp in a cartridge.
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Old March 13, 2012, 06:39 AM   #13
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I think this is my point

I have only looked at a couple attempts to commit what happens as a revolver is fired to a mathematical progression.

But I don't recall any which was able to include all of the factors that could impact speed.

For example, I have not seen any which considers lubrication or variations in lubrication effectiveness. Amount of lube, density of the lube, variations in lube density because the day is hot or the pistol is hot.

Has the barrel been shot in? What was the condition of the tool used to cut the barrel? Finish on the inner surfaces of the chambers. If it is a revolver, what is the impact of the barrel gap?

I think one might reach a point of diminishing returns in terms of the effort invested in building the formula compaired with the accuracy and the reliability of the data returned.

It is an awful lot of fun to think about and without putting words in his mouth (Mik's) I think this may have been his original motivation. The other way to learn how fast a system is, is to shoot it a lot. Regretably he can't do that. So he gets his enjoyment from doing what an engineer does. All electronic engineers are part physicist since the theories of electronics have their origin in physics.

This is a lot of fun Mik. Thanks
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Old March 15, 2012, 07:38 PM   #14
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as a general guideline its nice. however there are some things that are not taken into account. ive seen published load data reviews in guns of the old west, using the same powder measurer on one setting, that between powders you can have a 100fps difference in velocity, in the same gun, same day, same run of bullets.

on the other hand, ive seen where guys had a 20 guage single shot flintlock pistol, and when they used that exact powder charge and bullet in there 20 guage musket, they barely increased muzzle velocity by 40 percent even though barrel length increased by a factor of 3.
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Old March 15, 2012, 08:15 PM   #15
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http://dragonflybridge.com/cgi-bin/M...y/Cartridge.pl
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Old March 16, 2012, 04:42 AM   #16
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I believe this formula may be derived from a similar formula by Powley. Powley needs expansion ratios. I have tried Don Miller's formula with different gun specs and found very reasonable results until I tried BLE chrono results. The predicted Velocities are way over. All that means to me is sheutzen powder is very different from Geox 3f. The K Value for that powder seems to be 1050.

Last edited by mikthestick; March 16, 2012 at 04:50 AM.
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Old March 16, 2012, 06:18 AM   #17
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My chronograph was about 20 ft in front of the muzzle, as far as the cables on a CED chrono would let be get in front of the gun. I find that if the chronograph is too close to the muzzle, you get inconsistant junk readings due to muzzle blast.
I would have corrected the velocities to muzzle velocities but I can't find my Lyman Black Powder guide which lists BCs of round balls, Maxiballs, and some common Minie balls.
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Old March 16, 2012, 07:17 AM   #18
mikthestick
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Dontcha love ballistics

If you can't find your manual use the formula.
BC = Bullet weight(gr) divided by (7000 x Cal squared x ff)
ff is the form factor for the balls velocity. 1.4 for more than 1300ft/sec, 1.7 for 1000-1300ft/sec, and 2 for less than 1000ft/sec.
220gr bullet BC = 0.0752
143.4gr bullet = 0.0491
This came from Hatchers notebook I bet its not far away from your handbook.
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Old March 16, 2012, 06:33 PM   #19
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The velocities I measured from my ROA are not that out of line with the velocities measured by Lyman. Most of the serious muzzleloader target shooters say that Schuetzen is pretty much interchangable with Goex. With a revolver, you have a lot of gas leakage from the cylinder to barrel gap and that will give you lower velocities than a comparable single shot pistol of the same barrel length will give you.

One thing I have noticed is that if you calculate kinetic energy of the bullet, the relationship of kinetic energy to powder charge is nearly linear. Cut the powder charge in half and you cut the kinetic energy of the bullet in half.
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Old March 19, 2012, 05:45 AM   #20
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Goex vs Schuetzen

I had an opportunity to chronograph my TC Hawken with a .36 caliber Green Moutain roundball barrel 28 inches long.

Hornady 000 buckshot, .350 diameter, 65 grain, patched with .020" teflon coated patching. Barrel wiped between shots with one cleaning patch dampened by Windex followed by a dry patch.

2.5 cc of powder were used, I was using a Lee powder measure calibrated in cc to measure the charges.

The chrono screens were about 20 ft away from the muzzle.

Goex.

1601
1620
1629
1667
1662
average 1635

Schuetzen

1609
1631
1649
1678
1658
average 1645

It looks like the two powders are pretty much interchangable, with only a five shot strings to compare, the difference between the two may be a statistical anomally.

P.S. Both powders were fffg, forgot to mention that.

Last edited by B.L.E.; March 19, 2012 at 10:10 PM.
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Old March 19, 2012, 10:00 AM   #21
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It appears that 2.5 cc's of powder equals about 37.5 grains.

http://www.curtrich.com/BPConversionSheet.htm
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Old March 19, 2012, 10:42 AM   #22
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Shuetzen powder still seem very different according to BLE but I'm not sure why. I redid the calcs K seems to be about 1400 ( my mistake). Calculations I find to be fun BUT THEY SHOULD REINFORCE THE CHRONO RESULTS. I think they do in most cases. You can't argue with a chrono.
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