In physics, an inverse-square law is any physical law stating that some physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. Sounds like a mouthful don't it!
This law, fortunately not made by morons in Washington, D.C. is actually easily applied to shotgun patterns.
In an example that will help explain why it is so much more difficult to kill a crow at 60 yards, compared to 30 yards, we will use 1 1/8 oz. of shot as the physical quantity, and 30 yards as the distance. If a pattern covers 30" in diameter at 30 yards, or 707 square inches, we would intuitively conclude that the pattern would cover 1414 square inches at 60 yds. And our pattern density would be one-half at sixty yards, what it is at 30 yds. Wrong.
The actual pattern area at 60 yds. would be 2828 square inches. This is because the pattern doubled, or enlarged, in the horizontal AND vertical dimensions. Therefore, the shot must cover FOUR times the area at 60 yds. as it does at 30 yds. A shot pattern at 60 yds. is actually only 1/4 as dense at 60yds as at 30 yds. It would therefore take at least FOUR loads of 1 1/8 of shot, to produce a pattern as dense at 60 yds. as at 30 yds.
In reality, four loads of shot at 60 yds, would not produce a pattern just as dense as at 30 yds. Why? Because all shotgun loads are damaged to some degree, as the pellets scrape down the barrel, and as they crunch through the choke, and some pellets end up with flat spots on them. Some of these pellets become flyers, causing scattering, and are useless, as the pellets fly to the target.
This loss of pattern density, easily explained by an inverse square law, is just one of the evil gremlins that rear their head to defy us of making a kill on a flying bird. There are many others.
Me? I'll stick to No. 7 1/2, or 8 shot, shoot at crows which I THINK are in range, under 40 yards, and not worry one bit if my shotgun had an extended choke tube, would be more effective than a medieval trebuchet.
I like your post. I had a guy tell me once that he was getting a very dense pattern at 50 yards. When at his house, I asked where he shot 50 yards to the target, he showed me and I paced it out. I paced it to 35 yards and then "shot" with my laser range finder and it was 34 yards. He was "positive" that it was 50 yards.
Ken, do you think the pattern holding together would be any different with hardened or magnum shot, as compared to the softer shot in the lighter target loads ? (less damage to the shot going thru barrel & choke)
Your thinking is very correct. I have proven that hard, magnum, shot definitely hold a tighter pattern, at any range, with less flyers, than chilled shot, if all other things are equal. Magnum, target, or hard shot, usually have 4-6% antimony in them, which makes the shot harder, and less susceptible to deformation than chilled shot. But remember, some, maybe all, of the lighter high quality TARGET loads, are also made with hard shot, and are very useful if you are recoil sensitive, or if more powerful shells are not needed.
Cheaper shells, made with chilled shot, containing about 2% antimony, have their place in hunting and target practice. An example of this is when hunting quail, where shots are usually close, the cheap shell would produce a slightly wider pattern than a high quality, expensive competition target shell. But the choke has much more influence on the pattern density, regardless of the shot.
Ken; if I remember correctly antimony runs between 2 & 6% depending on the quality of the load. For example some of the cheaper 4packs are at about 2% while loads like AAs are at 6%. Also I think antimony becomes less important in shot sizes 6 & larger as they don't deform as bad as some of the smaller sizes. Jerry