I’ve been trying to figure this one out for a while, and I think I’ve forgotten too much trigonometry to solve it.
Large targets will appear smaller at longer distances. An error in aiming of a constant angle (you pointed the thing one minute-of-angle to the left of where it shoulda been) will result in a larger miss at longer distances (you missed the turkey at 50 meters but you woulda hit him at 20 meters).
Okay, so a shot load will begin spreading out when it exits the barrel. This is why people always argue about whether it’s easier to hit something at long range, or at short range with a shotgun. At short range it doesn’t spread much, but at long range the target is smaller.
I was wondering what degree of shot spread, if any, would be required to have an equal chance of hitting a target at all ranges. This requires a few counterfactual assumptions, namely, that the shot spread triangle has straight sides, that the spread travels out at a constant velocity (never runs out of energy and hits the ground), and that you don’t get any special problems aiming at a long-range target.
So really, it’s not about hunting but about geometry: how does this work? Is there a constant-hit spread angle?
I’m no math expert, but i have shot guns all my life, and i’ve used plenty of shotguns shooting skeet and hunting. There are 2 things you must understand about the shot pattern. First, when the shot stream leaves the barrel, it is like a big cigar shape. The ammount of spread you get is determined by the choke tube you have in the barrel. If you use a really tight choke, you get a tighter pattern. A more open choke, more open pattern. The second thing to understand is that, the target runs into the shot, not vice versa. You have to lead your target considerably with a shotgun, and put the shot in the correct place when the target gets there. So, i don’t think there is one universal optimal distance for all situations. The best rule is that if you are really accurate and want to shoot stuff at long distances, use some 12 gauge 7 1/2 (shot size, not shell size!) high brass shells and some tight choke tubes. You will be able to hit stuff acurately and with considerable power at long distances. However if you can’t aim, get really close with some 9 shot and some open chokes.
“Oh dreadful angel of mine, enrich me with the vastness of your being…”
The answer you seek does not exist beacuse the logic doesn’t work with shotguns. You picture an expanding cone of shot that helps your chance of a hit. The problem is at long range when the shot pattern is too dispersed to ensure that enough pellets hit the target to do the job. It’s unethical to take a shot that is likely to only wound and animal and not get a clean kill. Choke and load should be chosen for an optimum pattern at the ranges you expect to shoot.
Flashlight. Let’s say you’ve got a flashlight, and you want it to illuminate a guy from shoulder to shoulder. Is there a cone shape which would illuminute this dude shoulder to shoulder, no more no less, at all ranges? My last round of counterfactual assumptions didn’t really hit home, but let’s just say it doesn’t matter how brightly this guy reflects, just that the light hits him.
At all ranges? I would say it’s impossible. Unless you have an infinite number of pellets, then they will constantly be spreading. Ergo, the space between them is getting larger and the chance of something passing between the pellets gets larger.
I’m not an astrophysicist, but IIRC correctly from college, there is a physical law that light will always disperse over a wider area as it travels in a straight line.
If the shot does spread out in a perfect cone pattern then it doesn’t matter what distance you are from the target. The cross sectional area of the target decreases with the square of the distance and the spread area increases with the square of the distance.
In real life the shot will not spread out like a cone. It will probably have a maximum width. That means it’s easier to hit a non-moving target when you’re close to it.
Don’t worry, I’m just insane. I was trying to set it up so, if the target were untouched between shotgun pellets, that would still be considered a hit.
Basically, it was a geometry problem that turns out be tautological. A cone with an angle of such-an-such will compensate for errors in aiming of that angle. Both of them are angles. I don’t know why I thought this was a problem; I was imagining some exotic calculation.
Yep, with a cone this is impossible, but you could try a collimated laser beam… (I think that’s that the right term; it’s been a few years.) You’d need a pretty big lens to do it, but the dispersion should be minimal.
Of course shotguns don’t work like lasers. Try using slugs instead.
