I imagine we’re all familiar with these choke percentages from O’Connor’s The Shotgun Book.

30” circle @ 40 yds)
• Full Choke: 70% or higher
• Improved Modified: 65%
• Modified: 55-60%
• Skeet No. 2: 55-60%
• Quarter Choke: 50%
• Improved Cylinder: 45%
• Skeet No. 1: 35-40%
• Cylinder: 35-40

Anyone know if there’s an expanded chart that gives percentages for the chokes at lesser ranges I.e. 35, 30, 25, etc.

If not, taping some of the math minds out there, could those percentages be accurately extrapolated from this 40 yard chart?

Short answer, no.

Longer answer, is that when looked at from the side (not the front) a shotgun’s pattern looks like a very long trumpet.

The change in width is nonlinear, so, simple algebraic Interpolation would be inaccurate.


If for example, your measured pattern was 40 inches at 40 yards, it would not measure 20 inches at 20 yards.

Not pattern % but pattern spread

Field and Stream Sept 1964. I do not have the original article but assume the shells were Winchester/Western Mark 5 with the polyethylene shot collar introduced in 1961. Modern loads are likely better.


…………………………………………YARDS………………………….
.....…….....10…… 15……20……25……30……35……40
CHOKE
Full…………. 9……..12……16……21……26……33……40 inches

Mod……..……12…….16……20……26……32……38……46 inches

Imp Cyl……..15…….20……26……32……38……44……51 inches

Cylinder……. 19……26……32……38……44……51……57 inches


Another

…………………….Approximate Pattern Diameter (Inches)
Choke
..........................10 Yards….......20 Yds….....25 Yds......30 Yds….....40 Yds
Spreader
..............................23............37............44............51............66
Cylinder
..............................20............32............38............44............57
Improved Cylinder
..............................15.............26............32............38............51
Modified
..............................12.............20............26............32............46
Full
...............................9.............16..............21............26...........40

This should keep you out of trouble 'til the bird season

David J. Compton, “An Experimental and Theoretical Investigation of Shot Cloud Ballistics”, 1996
http://discovery.ucl.ac.uk/1382490/1/396689.pdf

E.J. Allen, "Approximate ballistics formulas for spherical pellets in free flight", 2018
https://www.sciencedirect.com/science/article/pii/S2214914717301459

I didn't read Dr. Drew's links, but we are more interested in pattern percentages at different ranges with different chokes, than we are in the pattern diameter. So far, I think we have to go back to shooting 30" patterns and counting holes. Wow, haven't done that for a while. Drew's Field and Stream charts give us all we really need, without counting holes. Thanks, Drew. On a similar subject, I once had a bunch of 1 1/4 ounce lead fours loaded in AA compression formed hulls, ahead of heavy charges of Unique. I shot them at 40 yards out of a heavily choked Sterlingworth and was amazed at how thick the pattern was. I decided to try the same combination at 60 yards, and found that, even though there aren't a whole lot of shot in a load of 1 1/4 ounces of #4, a teal would have had a hard time getting through that pattern. I can't remember the percentages without looking at the pattern sheets, but they were over the top. I was rather amazed. I kept the pattern sheets and still have them thirty years later. Long story short, I sold the Sterly to a friend who shoots ducks, thinking he would put it to good use. He drilled out the chokes and gave the gun to his son to shoot clay targets. I guess we can't save them all.

Damn .............

Thirty years later, I still have a few of the lead #4 loads. I also have a few HE Grade Fox shotguns. Maybe I should shoot some patterns and compare them to the Sterlingworth 60 yard patterns.

See if you can find this: 3/31/2017 Shotgun Sports | Pattern Analysis For Busy Sportsmen by Ron Jones (https://shotgunsportsmagazine.com/archive/mar13/story0313.html) Cites Oberfell and Thompson, The
Mysteries of Shotgun Patterns (Oklahoma State University Press, Stillwater 1957). Here is a table from the book:

Pattern Percentages for All Degrees of Choke for All Distances
Pattern Percentages Distance in Yards 15 20 25 30 35 40 45 50 55 60
Choke Full 100 100 100 96 82 70 58 48 39 32

Modified 100 100 96 83 71 60 49 39 32 26
IC 100 96 83 71 60 50 41 32 26 21
True Cylinder 98 83 71 59 49 40 33 26 21 17

Rough approximation is you lose 10% every 5 yards after 25 yards.

Thank you for posting that link. Here are the charts, which are a bit easier to interpret





I don't have Oberfell & Thompson, but it appears that the data is calculated using mathematical formula rather than having been measured, as is likely the shot spread data I posted.

Compton's study (linked above) discusses 3 dimensional representations of shot cloud phenomena starting on p. 155; and his conclusion:
"It has emerged clearly from this work that it is not possible to produce a satisfactory theory which can predict the downrange behaviour of shot clouds from the muzzle condition in sufficient detail to render practical measurement superfluous. Ballistics therefore have to remain very much an experimental science. Also further work is required to understand the full effects of choke constriction and choke profile on shot clouds."

Oh well - still fun to talk about

I agree that data is not based on real patterns but most likely close enough to be within five yards of real life. From that chart it seems IC at 30 yards would be just as effective as a Full at 40, perhaps more so as 30 yard retained energy is greater. But few seem to know what 40 yards is in shooting situations.

In the world I shoot in most shooters have a very poor ability to accurately estimate ranges. Most reported 45 yard shots are much closer to 30-35 yards. So IC or Mod might be a better choice for most. The few people who can correctly estimate range and correct leads can make shots long past 40 yards. It’s just that 3/4 of them think they can do it, but in reality can’t.

If you are deeply interested in patterns, read Dr. Andrew C. Jones's book, "Sporting Shotgun Performance - Measurement, Analysis, Optimisation." Dr. Jones deals with statistically viable data. Data is obtained by feeding a computer program digital photos of patterns. One of the most enlightening findings is that patterns have so much variability that one must have ten (10) patterns with the same factors to get reliable data. This sort of data is capable of predicting "X" hits on a target at given range. Now that is a true prediction of performance.

Rifle fire uses the same type of statistics. Should you shoot 3 shot groups? 5? 10? How about 600! (sounds suspiciously like a shotgun pattern, no?)

I have no idea why O & T did all that work and then fell flat with their analysis.

DDA

Don, to play the devil's advocate, do you have any idea why Jones fell upon the number 10?

Yes, Stan. In statistics there are equations that predict how confident you may be in conclusions based on the variability of data and how much data you can gather. One such equation is "R-squared." It is a good predictor of how much data you need. For example, my little MOI machine has "R-squareds" of , usually, better than 99.9%. In said case, I would be safe with one data point. Note that the weight, balance, and MOI of any single gun does not vary. The only significant source of variability is bearing drag or weather vaneing in a strong air draft. With patterns there are many variables that may/may not be significant. I would take a SWAG that Jones used R-squared in his decision as to the number of data points required.

DDA

That's about as good an answer as I can understand, Don. Thanks!

IMO, a lot of misinformation has been passed to shooters over the years. O&T should have understood what was required for proper analysis. I guess they were unable/unwilling to invest the resources to do it manually, even with semi-slave student labor, like Jones and his trusty computer do it.

I'm aware of master barrel borers shooting patterns and "tinkering" with the choke until they got the pattern they/the customer desired. Never heard of anyone firing nine more patterns for verification.

I have fired scores of patterns (not thousands) at paper and my grease plate over the last 40 years or so. I have never found the need for statistical analysis of shotgun patterns. Not saying there isn't a need, just that I have not had one. My main purposes for patterning a shotgun are:

1) to determine if a doublegun's patterns are regulated, and to determine to what extent they shoot to point of aim
2) to determine what load they are regulated for
3) to determine the approximate percentage of the pattern of a certain load

Beyond that it is is "too much sugar for a dime", for me. Once regulation is determined, and the best load for the gun and purpose, I just need to shoot it, because at that point I have confidence in the gun and load. And, it's hard to overstate the importance of that, IMO.

#1, absolutely. #2 & 3, not, IMO. You are drawing a conclusion about a choke/load/distance/target area based on much too limited data. The ten patterns to draw valid conclusions still applies, IMO. Conclusions based on statistical unreliable data are, well, unreliable. IMO.

DDA

How can you disagree with #2 and #3 Don, when they make no hard statement about any general principle? They are two of MY purposes for patterning a shotgun. If you read closely you will see that neither make a broad, sweeping statement about patterning, in any way. They are MY purposes. You may not agree with my reasoning for having these purposes, but you can't reasonably disagree with my opinions for myself. You can state that my principles are at fault, but my decisions on the level of accuracy necessary for me are mine. I have killed a limit of doves without a miss, a limit of 6 ducks with 6 shells, and have shot two 100/100 on sporting clays courses. Do I have to do each 10 times to have a valid statistical reference about my loads in each circumstance? I guess the answer may be "yes", and that without 10 replications it means nothing.

I just cannot see how determining the APPROXIMATE percentage of a load requires 10 shots, over 5? Remember, I said approximate. (The expectations here are the key. Actually, the expectations are the real reason for choosing 10 over other lesser numbers, are they not?)

Re Dr. Jones, I recall that he came to some conclusions about skeet and single pellet breaks that, I think, pretty much surprised skeet shooters. Jones' analysis concludes that they're relatively common. Personally, that caused me to wonder whether maybe he needed to walk away from his computer, stroll around on a skeet field, and see how many unbroken targets he could find with holes in them. Plenty with one hole . . . some with even more than one. While his analysis might predict the likelihood of single pellet hits, can it predict the likelihood of single pellet breaks? The simple exercise of examining unbroken targets clearly shows that single pellet hits often fail to produce single pellet breaks.