doublegunshop.com - home Forums General Discussion DoubleGun BBS @ doublegunshop.com Shot Distribution in Pattern

While sitting around, hopefully recuperating, I have been looking through some old American Rifleman magazines from the 1980's & 90's.
I began looking at the pattern tests on new guns or models in the Dope Bag section. Tests were done on an 8 field 30 inch circle at 40 yards for 10 through 20 gauges & at 25 yards for the 28 & .410. A 21.2 circle was drawn concentric to the 30" one & a vertical & horizontal line divided both he inner circle & outer ring into 4ths. As the 21.2 inch circle has half the area o the 30 inch one the 8 fields are equal & contain 88 square inches each.

This 8 field template was carefully centered on the pattern itself, not on the aiming point which was often different. An average of 10 shots was cited. Two things became quickly apparent. 1st was that regardless of bore size, load or choke there did not seem to be a wide variation of number of hits in the 4 fields of either the inner circle or the outer ring.

2nd was that from 12 through 28 there was not a great difference in central core thickening. chokes of skeet & IC generally ran from around 1.25:1 to a bit higher while quarter choke to modified moved up around 1.5:1 going on up around 2:1 as full was approached, seldom did any exceed 2.5:1.

The .410 however was quite a different bird. while admittedly not a , the other an 70 rem bored full. lot of data, as at present I only have three tests to look at. two of these are the two barrels of a Win Model 23 bored mod full, the other an 870 Rem bored full. The model 23 was tested with 1/2 ounce of #7 1/2 size shot containing 185 pellets. Both chokes made re-markedly similar patterns. The mod choke placed 166 pellets in the 30 inch pattern with 142 going into the inner circle & 24 in the outer ring. This is near a 6:1 ratio of central thickening. The Full choke placed 165 pellets in the 30 inches with 139 in the inner circle & 26 in the outer ring for a bit over 5:1 ratio.

The 870 Rem was the absolute worst of the lot, bar none. Load was 11/16 oz of 8 shot containing 248 pellets. It averaged 88% in the 30 inch circle for 218 hits. 199 of the were in the inner circle with only 19 in the outer ring for a ratio of 10.5:1. Personally I find any core thickening ratio exceed 3:1 unacceptable as too much emphasis is placed n an absolutely perfect hold. I am well aware this is the ideal situation, but lets face it, probably 95% of us are simply not that good.

Another thing brought to light, for a given load, regardless of choke the hits in the outer ring did not vary that much. Thus a 45% pattern of 1 oz of #6's should average about 100 hits in the 30 inch circle with a 75% choke placing about 170 its. Appearance is that nearly all of those extra 70 hits will fall within the inner circle. This agrees with the increased ratio of the tighter chokes. It would then appear that dropping from a Full choke to an IC does not actually increase the "Killing circle" as much as we have been led to believe. What it does do is lessen the mangling of game hit with a well centered pattern at the shorter ranges normally associated with upland shooting, for this it is very worthwhile.

Just a few observations while I had not much better to do, so take it for whatever its worth to you. Keep in mind it did not cost you one red cent, so if you gain any help, you got your money's worth, if not it didn't cost you anything so nothing lost other than the time to read it.

Thanks, Miller. It also helps explain why a .410, in the hands of a good shot, can kill so well. The "inner circle" is the killing zone for the .410, and the fact that it is so dense for it's load extends the range of it somewhat.

All my best, SRH

Good to read your post as I find it very informative. Thanks for sharing and a speedy recovery to you.
Karl

Good post, Miller. Glad to hear you are feeling up to some shotgun research. Have you read "Performance of Sporting Shotguns" by Dr. Andrew Jones? He answers a lot of questions.

Shotgun patterns follow a Rayleigh distribution, which can be nicely approximated with a normal distribution. The Rayleigh distribution describes rifle groups, artillery fire, and bombing patterns, also. The fact that the shotgun launches its projectiles at the same time is irrelevant. There is so much variability from one pattern to the next for the same gun and load that 10 patterns are necessary for reliable statistical analysis. Said analysis is sufficiently complex that a computer is pretty well mandatory.

Jones produced a program, Shotgun Insights, to analyze digital photos of patterns. It works magnificently. He was able to investigate 250 (2500 patterns) combinations of gun/load/choke.

Before meeting Jones, I shot patterns on paper and drew a series of concentric rings and radial divisions (think pie slice shape) with all areas of equal area of 5 square inches (think a edge on clay target). Analysis led me to the Rayleigh distribution. And, this led me to the startling realization that all patterns, on average, are the same.

Before anyone has a heart attack, let me explain. Patterns sweep out a trumpet shaped volume. Choke effect controls how quickly the pattern spreads radially; a plot of forward velocity vs sideways (radial) velocity rotated makes the trumpet shape. So, if you look at two patterns from widely differing chokes and shot at the distances where the patterns have equal diameter, you will find the patterns are indistinguishable.

There is no such thing as central thickening. It is only recognition that the center areas of the pattern will always have a higher pellets per square inch than the outer areas. Patterns never have a smooth, even distribution. That is fortunate, indeed, or shotguns would be short range shooters. Fortunately, the Rayleigh distribution has plenty of pellets in the center area to feed into the outer areas as the pattern moves forward.

Praying for your speedy recovery daily, Miller.

DDA

Don, That is an excellent post. All of it. I quote just a couple sentences because "experts" on another board make far too much of the first point, and ignore the second. The second sentence better spells out correct application of the first.

Miller, Don's correct about central thickening. The .410 ratio you observed reflects small payload, not gauge magic. Remember, your ratios use linear measure terms (inches). The distribution formulas express in terms of standard deviations from some mean/center.

BTW, my full M-42 throws a near-70% pattern at.....40 yds......using 3" Rem #6. Interestingly, every single pellet typically falls within the 20" circle (ratio = infinity). This isn't central thickening.

Praying for you, Miller. Get well!

Don, I assume that Jones' work allows for the rare, but existing, shotgun barrel that shoots a pattern with a void in the center every time? These do exist. I have seen one with my own eyes. My first cousin's husband bought a brand new Browning B2000 many years ago, and I promptly began to smoke him on the dove field every time. He was normally a very good shot, and we figured the gun just didn't suit him. That is, until we patterned it and saw the classic doughnut pattern ............every shot. He had the choke recut at a gunsmith in Augusta, GA and the problem went away. He once again became my nemesis on the bird field.

SRH

I will not argue the point that "Central Thickening" is a misnomer. However it has been in use for so long I think everyone understands the term. Sort of like a double action revolver has changed from its original meaning.
No problem with accepting that all patterns/groups follow a similar type of dispersion.

This statement is going to take a bit more explaining to an old hillbilly. I simply find it unbelievable that load with a 10.5:1 ratio would ever be identical to one having a 2:1 ratio at any at range. Other factors also have an effect on the pattern, a major one being the choke. Seems obvious that some influence comes into play when dropping from the 28 to the .410. My "Personal Opinion" until proved otherwise is the major factor here is the much higher percentage of the shot which come under direct influence of the choke.

Don, here's what Brister says about patterns in his chapter on "Choosing Chokes and Loads":

"The improved cylinder pattern, which exposes a higher percentage of its pellets to atmospheric resistance at the muzzle, spreads faster and in more direct ratio to distance. Gough Thomas explains this by suggesting that the full choke stays tight, then spreads out suddenly, something like the bell of a trumpet, while improved cylinder spreads out as a rather constant cone. My wife, after a particularly tiring day replacing test targets and tabulating data, suggested: 'Just tell them improved cylinder goes to hell gradually; full choke all at once.'"

I don't think there's any disagreement to the more open chokes spreading faster. That's what they're designed to do. But there appears to be some disagreement on the trumpet shape issue--full having a narrow tube that rather suddenly transitions to a wide mouth, while IC has a wider tube with a more gradual transition to its mouth. Are you (and Jones) suggesting that the profile of IC and full patterns are actually the same in terms of how quickly they transition from the trumpet's tube to its mouth?

Stan: Mr Griffith thought a "cartwheel" pattern could be produced by an inadvertent groove in the bore that could caused the shot charge to spin
https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA237
Back in my young and dumb days I cut an Invector extended rifled tube to 1" to make a magic skeet choke. The pattern was terrible

Folks have been trying to figure out shotgun patterns for a long time
http://books.google.com/books?id=inQCAAAAYAAJ&pg=PA49

Yeah, I too have dedicated some time. At best, the overall shape of the pattern and an overall density can be estimated. But this thing, shot column, game & all, is 4D(& dynamics or damn-namics as we referred to it in Optical Engineering classes) so actual position or spacing of the shot cannot be calculated in a finite manner as it is random. Spent some time w/ Gil Ash in Bolivia & his barrel cam is impressive as you can see why you miss...... Evidently he knew Brewster well & we spent hours discussing shot columns while I sipped corn chicha.


Cheers,

Raimey
rse