Author Topic: What bullet diameter to use with Greenhill's Formula?  (Read 8881 times)

Naphtali

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What bullet diameter to use with Greenhill's Formula?
« on: March 31, 2010, 08:12:09 AM »
When using Greenhill's Formula to identify maximum bullet length, what do I do with patch thickness? What I'm asking is whether the nominal bullet diameter to plug into Greenhill's is just the bullet diameter I intend to use, or do I include patch thickness (.010-.015 inch) as [part of] bullet diameter?

Since I'm wanting to have a mold made that will yield the heaviest bullets for the bore diameter and twist, kvetching out the last few grains of weight is important.

The rifle in question is a double rifle, bore size will probably be .72-caliber and 1:72 inches twist.

The other DWS

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #1 on: March 31, 2010, 05:00:28 PM »
If I recall correctly the Greenhill data is mostly for conical bullets--at least in the contexts I'm more familiar with--- though he may discuss round ball projectiles as well, or in his earlier research. 

I know it has been discussed on the Single Shot Rifle Site (ASSRA.com) which is pretty much breechloader oriented.   If you go there and  use the search tool for "Greenhill" you should be able to pull up the threads.  I don't remember any discussion that involved patching, unless it was paper patching.

If your rifle's twist is fast enough you might be able to stabilize a conical bullet.  I know that the BP M/L slug gun shooters have put a LOT of time and effort into research in that arena.  "Picket bullets, "sugar-loaf bullets" and even two part bullets of different alloys were used in heavy bench type target rifles prior to the Civil War and some of the elite marksmen and snipers of that conflict used their target rifles with some effect.  The germanic-tradition M/l schuetzen rifles were also designed with "fast twist" barrels for there conical bullets

Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #2 on: April 01, 2010, 12:38:57 AM »
72" twist is OK for a 12 bore, trust me - however, make certain the muzzle crown will allow a snug combination. What feels tight with factory Pedersoli crown is way too loose to seal and give proper accuracy.

Anything slower than 60" and faster than about 90 to 100" will work just fine.  Even a 56" twist will work, but probably not well with heavy hunting loads unless the ball and patch are very tight indeed, or you will have to be one who likes swabbing the bore so you can re-load it.  You've got to seal the bore or it will foul badly.  The faster the twist, the tighter the ball and patch have to be.  The deeper the rifling, the thicker the patch must be as well as bring tight.

I say faster than 100", as at that slow a rate of twist or even slower, you will not like shooting the amount of powder it would take to give descent accuracy.

Doubles are fun - some of them regualte quite well with a number of loads - while others , well, not so good.

My .58 double needs 100 to 110gr. of 2F powder to shoot resonably well.  I've heard of the Italian double 12's needing 150gr. to regulate, while one chap had his crossing badly with only 50gr., a charge which is useless for anything. Sending a gun back to Italy if the barrels won't shoot anywhere near each other can be difficult.

 

Offline Dan

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #3 on: April 01, 2010, 02:42:05 AM »
Measure the lead, not the paper.

Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #4 on: April 01, 2010, 04:32:47 AM »
In a .720" or a .730" bore, not the groove diameter, I'd probably use a .715" ball with a .022" patch.
Yes- measure the ball, not the patch inclusive. Too, plug in the figure of 100 for the constant instead of 150.  Note that the formula gives the slowest rate of twist that is useful, not the fastest.
In large bore balls guns, the formula usually gives twists way slower than we normally use.  Anything slower than 90" will be hard put to get good accuracy from, normally. There could be exceptions to this 'rule'.
Buddy of mine has a rather deeply grooved .75 cal. with a rapid 56" to 66" twist. Don Getz would knwo what they used.  Keith uses a .735" ball with a very thick canvas-like .030" patch of the heaviest denim.  With either pure lead or WW alloy, it shoots well, but due to the too-deep grooves, it fouls after a dozen shots or so.  3 of us shot an offhand group at 50 yards with it using a ligth-for-the-gun load of 100gr. 2F. One of the guys would only fire that one shot.  With the three of us shooting we put all 5 shots into a 2 1/4" group, on centres at that range. I doubt you could do that with a 100" twist with only 100gr. of powder.

Offline Dphariss

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #5 on: April 01, 2010, 08:20:56 PM »
When using Greenhill's Formula to identify maximum bullet length, what do I do with patch thickness? What I'm asking is whether the nominal bullet diameter to plug into Greenhill's is just the bullet diameter I intend to use, or do I include patch thickness (.010-.015 inch) as [part of] bullet diameter?

Since I'm wanting to have a mold made that will yield the heaviest bullets for the bore diameter and twist, kvetching out the last few grains of weight is important.

The rifle in question is a double rifle, bore size will probably be .72-caliber and 1:72 inches twist.

Greenhill is irrelevant to the RB and is marginal even for 45-70 etc being about 10% in error for optimal twist in most cases.

Check the actual *bore size* of the rifle. If a true .720" I would use a .710 or .715 (preferred) RB depending on the land/groove ratio etc.  Weight difference, 11 grains in the above case, will prove to be irrelevant.  Any weight gained in using a bullet will be paid for in reduced velocity ahd increased recoil. A round ball of this diameter is a very powerful and effective projectile when driven to 1500-1600 fps. It is capable of killing most game animals on the planet if used properly within its range with the proper lead alloy for the purpose. Find a load that the rifle shoots well and quite worrying about bullet weight, kinetic energy etc. In this context its really not applicable.
I would not shoot a bullet in a ML double rifle in any event unless its patched tightly in cloth like a RB. Naked bullet will almost certainly move under recoil when shooting the first barrel and could form a bore obstruction.

If you determine to use a "expansive" bullet you must not use its diameter coming from the mould but its diameter when fired, which, in bullets that expand to fill the grooves the diameter will be groove diameter perhaps .020 larger than as cast. This also shortens the bullet to some extent. But again these bullets are not tight in the bore and are not suitable for double rifles.

Dan
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Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #6 on: April 01, 2010, 09:44:13 PM »
Bullets and muzzlelaoding double rifles are a no-no- as Dan says.  They must be very tight, engraving when loading in order for the second barrel's projectile to remain fixed on the powder under recoil. I'm not sure if a REAL bullet would remain fixed, but is irrelevent in this case, as .58 is the largest made.
Any slug, ie: minnie, as in the .69 rifled musket minnie is way too small - could be cloth patched perhaps, but already weighs 730gr. and kicks like a mule - I know. 

A slug in a .72 or .73 turned the gun into a mortar - no point blank range at all and very difficult to hit at unknown ranges.  Poor choice they are. Round bal is it in any of the bore guns (and below).

Naphtali

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #7 on: April 02, 2010, 04:32:51 AM »
In a .720" or a .730" bore, not the groove diameter, I'd probably use a .715" ball with a .022" patch.
Yes- measure the ball, not the patch inclusive. Too, plug in the figure of 100 for the constant instead of 150.  Note that the formula gives the slowest rate of twist that is useful, not the fastest. . . .
What is the result of changing the constant? Why revise the constant? Greenhill devised the calculation based upon black powder [and] velocities available to artillery projectiles at the time - that is, velocities essentially identical with what is achievable with a muzzleloading double rifle.
***
Measure projectile ONLY. And since the result of the calculation is the slowest rate of twist compatible with stability of the projectile, I guess it can't hurt anything to fudge slightly to create a slightly shorter projectile - slightly shorter.

Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #8 on: April 03, 2010, 06:21:25 PM »
Changing the constant is supposed to give a more accurate representation of useable twist. It isn't my idea.
As Dan said, the Greenhill formula isn't really needed nor applicable to round balls.
Anything from 30" to 144" to smooth can be used.  One need only feed it the proper amount of powder to get it shooting well.  The slowe the twist, the more powder it's going to need, to the point where the gun or shooter fails in an accuracy attempt due to not being able to handle the recoil.
My .69 has a 66" twist, and shoots as accurately with 140gr. as it does 200gr.  Not many guys want a second shot.
A slower twist than that could require even more powder - and of course with it's heavier ball, kicks more.
I find with the 66" twist I can get reasonable accuracy at close range, ie: 25 yards with as little as 30gr. of powder, but it takes 110gr. to get bug hole(big bugs) groups at 50 yards - go figure.
 A mild charge, easy on targets and easy to shootout to 100 yards is 82gr. (3 drams).  Guilt edge accuracy cannot be obtained with that charge as even the relatively fast 66" twist needs even more powder than that for guilt edge accuracy at 50 yards and beyond.
The big bores give us the potential for exceptional accuracy and killing power to 200 yards and beyond - but that takes powder to give the accuracy needed and the flatteness of trajectory to allow good hitting.  Proper sighting is also a requisite.

Naphtali

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #9 on: April 03, 2010, 11:00:03 PM »
Changing the constant is supposed to give a more accurate representation of useable twist. It isn't my idea. . . .
Then were I to experiment with a short cylindrical projectile (similar to a Wide Flat Nose revolver bullet's shape), I would work with the 150 constant while an RB's twist would be calculated with a 100 constant? While the sense of this is not obvious to me, if this procedure will accurately identify the proper projectile length for a given rate of twist, that's that.
« Last Edit: April 03, 2010, 11:00:50 PM by Naphtali »

Offline Dphariss

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #10 on: April 04, 2010, 05:26:39 PM »
Changing the constant is supposed to give a more accurate representation of useable twist. It isn't my idea. . . .
Then were I to experiment with a short cylindrical projectile (similar to a Wide Flat Nose revolver bullet's shape), I would work with the 150 constant while an RB's twist would be calculated with a 100 constant? While the sense of this is not obvious to me, if this procedure will accurately identify the proper projectile length for a given rate of twist, that's that.


Your rifle is designed for ROUND BALLS ::)


Dan
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Offline longcruise

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #11 on: April 05, 2010, 05:57:45 AM »
Bit off the track here, but when it comes to this regulating thing, why not just develop a different load for each barrel where each shoots to the same POI instead of looking for one load that works with both barrels?
Mike Lee

Naphtali

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #12 on: April 05, 2010, 08:20:48 PM »
Bit off the track here, but when it comes to this regulating thing, why not just develop a different load for each barrel where each shoots to the same POI instead of looking for one load that works with both barrels?
Two minds with a single thought. That is my intention. The problem I hope to avoid is severe limitation of range the barrels shoot together - that is, they shoot together at, let's say, 50 yards, but at 80 yards they are 'way out of regulation.

Offline T*O*F

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #13 on: April 05, 2010, 11:12:21 PM »
Quote
The problem I hope to avoid is severe limitation of range the barrels shoot together - that is, they shoot together at, let's say, 50 yards, but at 80 yards they are 'way out of regulation.
The problem is that you don't understand what regulation is.  Shotguns are regulated so that the patterns cross at the distance which gives maximum shot density for the type of game being shot; ie, 70 yards for a goose gun but 40 yards for a pheasant gun.

Double rifles are regulated so that both barrels shoot parallel to one another to infinity.  When fired at a target, the bullets will strike side by side, never in the same hole.  To do otherwise would render "express sights" as a fool's folly.

Also the ballistic coefficient of an elongated projectile changes during its flight.  A roundball's does not.  To make a roundball shoot farther and flatter, you slow down the twist and up the powder charge.  Poor range estimation, and fixed sights make distance shooting impractical.

Dave Kanger

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Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #14 on: April 06, 2010, 08:56:32 PM »
Double rifles are regulated so that both barrels shoot parallel to one another to infinity.  When fired at a target, the bullets will strike side by side, never in the same hole.  To do otherwise would render "express sights" as a fool's folly.

Also the ballistic coefficient of an elongated projectile changes during its flight.  A roundball's does not.  To make a roundball shoot farther and flatter, you slow down the twist and up the powder charge.  Poor range estimation, and fixed sights make distance shooting impractical.
Double barreled round ball rifles 'should' be regulated to shoot parallel - as should all double rifles, fixed ammo or muzzleloading.  They generally do this, if regulated correctly, with one load only and will cross or diverge with any other weight of charge or 'ball' weight.
Unfortunately, cheap well regulated guns are like frog hair.  As well, properly regulated guns costing many thousands of dollars are like hen's teeth - few and far between.  To properly regulate a set of barrels, the gun smith must shoot, separate then re-solder, shoot, separate and re-solder the barrels several or many times before he gets it right. No mass produced guns have proerly regulated barrels.

We get lucky sometimes and find a load that will put the barrels close enough together to be useful. As with mine, I would shoot the left barrel first(rear trigger), it being zeroed at 50 yards, while the right barrel is zero'd at 100. The groups run one over the other, a scenario fairly useful with practise.

Using a separate charge for each barrel, or as these Pedersoli guns are designed, a set of sights for each barrel - I don't agree with, but if having a gun that cannot be brought to shoot well, either is the only answer, I guess.

Forsyth spoke of moving the sight to split the difference, then learning where to hold for each barrel - this sort of thing has been done since the mid 1800's.  Out of all the double muzzleloading guns Forsyth owned over the years, he'd only had a couple that actually shot parallel.

There are several different ball diameters that can be tried, along with different granulations of powder, along with different patch thicknesses and material make, along with a wide variety of powder charges- soemwhere in there, with experimentation, you might find a load that is useful - I did, on my first trip to the range with my double .58, fine tuning on the second trip.  I xcan even shoot the black powder trail, making lefts and rights on all targets - quite impressive to see and do.

Knowing where to start helps.  ie: ball at the most .015", better .010" to .005" under bore size and .015" to .025" patch thickness.  The smaller the ball, the thicker the patch.  If it's hard to load, you didn't re-crown the muzzles well enough. The big bores load easily with a heavy patch.  Cloth of .010" to .012" is panty material for Canadian winters, it is not patch material for round balls ulless those balls are larger than the bore.

The crown needs to be addressed before going to the range - otherwise you are wasting powder and shot.

Offline T*O*F

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #15 on: April 06, 2010, 10:05:51 PM »
Quote
To properly regulate a set of barrels, the gun smith must shoot, separate then re-solder, shoot, separate and re-solder the barrels several or many times before he gets it right.
It can be done mathematically by measuring the thicknesses at the breech and muzzle and then filing the breeches to get them close.  Then fixture a couple of cheap pocket lasers in the bores and use them for fine tuning.

Besides they're for shooting rhino, elephants, lions and other game close up and requiring a fast 2nd shot.  They ain't target rifles although some smallbores are used for leopards and ungulates at farther ranges.  Nothing gives a faster followup shot than a double.
Dave Kanger

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Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #16 on: April 06, 2010, 11:41:37 PM »
Many have tried to regulate guns by measuring - Pedersoli does it this way, with generally much less than good results. Today, people who make doubles use lazers, etc, to get the bores barely crossing at a given range - usually 50 yards. The only way to fine-tune this regulation is to shoot them. No formula works well, as different guns recoil differently due to make, barrel harmonics, bullet weights and powder charges.  A number of guys are making double guns over on another forum and in every case, they have to shoot the gun and separate, then re-solder wedges and ribs to get them fine tuned.

A properly regulated double should shoot into 4" at 100 yards with the 100 yard sight, the bullets or balls falling on top of the bead.  The last one Seyfried worked on, was a Lancaster and after many trials of bullet diameter, bullet hardness and powder charge changes, managed 2" for 4 shots at 100 yards - not bad for a double rifle with oval bores, made in the 1880's.

We do the same evaluations with the muzzleloading doubles, but have the advantage of testing many more combinations while on each trip to the range.

Some of them work OK for hunting purposes - one major problem is learning to hold the barrels perfectly level, as any canting at all really puts in a lot of elevation, along with the horizontal problems of crossing or diverging.

If they cross, more powder will usually help to uncross them.  If they doverge, lightening the ball or bullet will usually reduce each barrels recoil to bring the ball or bullet in.  It's all about tradeoffs and ending up with a single load with single sight that will work.

Double rifles had some following here in North America back in the percussion era - S. Colt, W. Read & W. Billinghurst are only 3 of the makers. Some of the original Colts have the outside of the muzzles filed, to bring the balls back in to the sights on guns that diverged each barrel from centre.  In "Firearms of the American West 1805 1865", there is a a picture of a hunting camp, eveyone in the picture with muzzleloading rifles, one of which is a double barreled rifle mounted with a bayonette.

I should also have noted that differing patch thicknesses and lubricants will create slightly different drag properties in the bore, thus changing the recoil slightly and thus will also effect regulation of the barrels.

Ain't working with doubles fun!
« Last Edit: April 06, 2010, 11:46:32 PM by Daryl »

Naphtali

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #17 on: April 07, 2010, 08:43:09 PM »
While I'm confident parallel regulation is beyond me, having a cone of fire where points of impact [may] cross while staying within my kill cone may be achievable. I have no preference to points of impact crossing or non-crossing with acceptable divergence. Result wanted is an eight-inch impact area to what I decide is my maximum range. And, yes, my maximum range will have a sense of reality - I won't ask for the moon.

I will, simultaneously, verify whether one barrel maintains my cone at a greater distance. Never can tell.

Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #18 on: April 08, 2010, 12:49:12 AM »
With a gun that isn't regulated well, Forsyth recommended that the sights be set true for one barrel so that one could be trusted, while learning to hold for the other. There is wisdom in this method.

Offline T*O*F

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #19 on: April 08, 2010, 02:23:46 AM »
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Many have tried to regulate guns by measuring

Daryl,
You need to get off the modern made doublegun websites and learn how it was done originally.  A gunsmith didn't have time to be @$#%&*@ around soldering and unsoldering barrels and shooting them.  "A Gunsmith's Manual" by Harrison & Stelle written in the late 1800's teaches how to regulate mathematically.  This from methods preceeding and prevalent during the period.  Likewise, British guns were done in a similar manner by the "joiner."  In addition, several of the Samworth series of gunsmithing manuals mention the mathematical formula.  It was the "norm" not the exception to do it this way.
Dave Kanger

If religion is opium for the masses, the internet is a crack, pixel-huffing orgy that deafens the brain, numbs the senses and scrambles our peer list to include every anonymous loser, twisted deviant, and freak as well as people we normally wouldn't give the time of day.
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Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #20 on: April 08, 2010, 12:17:32 PM »
Using math to regulate double rifles is a joke.   Just because that 's the way 2 gun makers (or mathematitions) say they did it that way, doesn't mean it was right or gave even a remotely acceptable gun. Most weren't as most didn't regulate well at all.  Forsyth covers that and also some about what was necessary to achieve proper regulation. He also notes many gun makers could not afford to spend the time to properly regulate the barrels.  If you bought one that regulated, great - if not, too bad - that's what math and alignment gigs give you.  The Pedersoli's are regulated with lazers (they say) and math.  About 1 in 12 regulates.  Sounds geat, A.


Offline Dphariss

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #21 on: April 08, 2010, 05:48:40 PM »
The math and assembly jigs were a starting point. If a rifle came off the jigs and shot to the sights as it should it was pure luck.
It also depends on the firearm.
A friend of mine used to occassionally make SXS Kentuckys. Bedfords as I recall.
He set them up with pins etc on his mill bed to get the mores aligned then soldered them together.
Another friend watched this and thought "fat chance" till he went to the range with the maker when it was finished and it shot parallel at 50 yards.
BUT!
A small bore RB rifle that is relatively heavy has no large recoil impulse as a relatively light large bore rifle or a rifle shooting high energy loads.
Doubles simply have to be regulated by a skilled shooter and gunmaker to get them "right".
Then they only do so with a specific load in the vast majority of cases. For example trying to get a good quality BP double to regulate with BP was difficult to impossible with the powder available until recent years. And even then?

Dan
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Daryl

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #22 on: April 08, 2010, 06:52:24 PM »
Round ball doubles were slightly easier to regulate - but even W.W. Greener spoke of trials and tribulations of regulation, shooting, then splitting the tubes and re-soldering, re-shooting, splitting, re-soldering, etc.  As well as Forsyth did 50 years earlier, W.W. Greener mentioned the 'provincial' makers seldom spent nor could afford the time to properly regulate the tubes - as Forsyth said - many trusted to dodges in sighting to make the gun appear to shoot well, or being good shots themselves, knew where to hold for the 'bad' barrel, giving the illusion of proper regulation so that the new owner would be more likely to blame his own shooting than that of the gun.

I did exactly that myself, with a double-gun that crossed badly as well as gave elevation separation between the tubes - yet both shots taken offhand almost touch at 50 yards. The separation of that gun with that load was 1 1/2" crossing, and 2" elevation between each barrel group - at the same 50 yard range - not difficult to hold for.  Splitting the difference would have made this gun appear much less badly regulated, but again Forsyth recommends sighting for the most accurate barrel so it can be relyed upon, then learning how to hold for the poor barrel.

He talked of very poor regulation being 6" at 100yards. I know of 4 modern made muzzleloading double riles that had a foot or more difference in impact at 50 yards.

As to modern black powders in original English and Continental guns, it was only the availability of Swiss black powder that allowed regulation in many of them - but those are ctg. guns, with finite capacity cases.  We know many of the better quality double rifles of the late 1800's were very well regulated. We also know today that some gun makers consider all shots into 4" at 50 yards as being regulated for their Nitro Express rifles, where-as the BP DR's of bore size(16 thorugh 10), shot much better than this at 100 yards - at least some of them did, but it took a lot of work to find out what loads were necessary to carry this out.

You cannot pick just any old load and expect good results.  It's work, which is fun.

Go have fun!

bs2

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Re: What bullet diameter to use with Greenhill's Formula?
« Reply #23 on: April 09, 2010, 12:46:28 AM »
The rifle in question is a double rifle, bore size will probably be .72-caliber and 1:72 inches twist.

I made the mold for these several years ago, they shot OK out of my .729 bore with a 1 in 72 twist.

They tend to have a "FLIER" , one out of four......if I remember right.  Probably need a faster twist.

I made them for more weight than a standard RB.



Bruce