Geckgo
Member
Hello all, haven't been shooting long, but I'm sick of seeing these threads. Maybe if I'm lucky the mods will sticky this, but it needs a writeup.
As a physicist, this is an attempt to describe how shotgun patterning tends to work, and why all of us are wrong whether we say shotgun barrel length does or doesn't matter.
The people who say it doesn't matter are generally referring to the fact that it doesn't matter that much, when not accounting for a built in choke, but straight cylinder bores.
The people who say it does fall into many categories. Some are concentrating on the minute differences in the above scenario, and admit that it isn't much. Others are pointing out that you remove the permanent choke of the shotgun by sawing it off. Others live under some delusion that because the barrel is shorter it is less acurate, thus the shot will spread "faster". Anyways, here are my thoughts, speaking purely as a physicist and not neccessarily as a shotgun expert.
First, there are a couple things that I'm taking for granted, number one is a perfect shot cup that for the velocites we are discussing, will perform as it should. It will carry the shot to the muzzle and then drop away. I'm also not going to bring up pellet deformation, as in cylinder chokes, it really doesn't have any real effect. Third assumption is for the same ammo from cyclinder chokes of different lengths, as this is the "meat" of this argument.
For the sake of argument, I will talk about spread at a distance from the muzzle of the shotgun, not from the action, so the little arguments about "it has a foot or two more room to expand" can be ruled out. This is true, but it's academic.
So, we have two loads, we'll say one from a 36" cylinder bore and one from a 24" cylinder bore. When fired, we'll say the 36" has a velocity of 1500 fps, and the same load in the 24 will be 1100fps, just for the sake of argument, invent whatever kind of powder/primer load you want to fix this. When measured from the muzzle, I argue that the 24" barrel will account for a larger spread (not much) than the 36" barrel, the reason is this:
At 10 yards, we check the pattern from our 36" barrel and get a 5" diameter, again, for the sake of argument (this is from the muzzle), we can assume that we are pretty close to muzzle velocity to keep the equations from getting too big (no need to post the actual equations, I think everyone will see my point without them). At 1500fps, it takes the shot .02 seconds to reach the 10yrd target, and begins with a diameter of around .75 inches. So the shot is expanding at (5-.75=4.25inches, 4.25/0.02=~212in/sec),, We can hold this as a general rule of thumb for the expansion of the shot pattern. Using the same expansion vs time, the 24" barrel would make a pattern at 1100fps of about 5.78 inches. At the next interval, the velocity drops a bit and the pattern increases a little more...
36" :~1450fps now form 10 to 20 yards = 9.39" pattern at 20 yrds
24" :~1070fps now form 10 to 20 yards = 11.72" pattern at 20 yrds
I'm sure everyone by now can see where this is going. All other things being equal, the shorter barrel is going to produce a larger pattern because while the expansion of the shot remains the same versus time, the shorter barrel releases it at a slower velocity, impating the pattern at range.
Seems like a lot of difference at the moment, but there is (among the millions of variables out there) another point to be made, that the faster moving shot will be a bit more unstable when it fires from the muzzle, due to higher energy and more "shock" from the transition from tube and cup to open air, and will have a higher rate of spread, maybe 220 instead of 212 or something similar, I haven't measured these directly so it's just a for-instance, but more velocity=more instability=faster rate of spread. This will allow the 36" barrels pattern to be a bit larger than the above calculation perscribes, and thus the actual patterns will be a bit closer to eachother then the calculation predicts.
This speed difference is also the reason that shotgun patterns tend to "fan out" at larger distances rather than being related linearly as pattern vs distance. As the pellets slow down, it takes them longer to cover the same distance and they have more time to expand.
I already know there's going to be a billion know-it-alls out there, and this simple model does not cover everything pertaining to shotguns, there are many other variables, but these are the big ones that will have the most influence.
Hope this clears the issue up for most people.
lol, told you I would write it up one day, cheers!
As a physicist, this is an attempt to describe how shotgun patterning tends to work, and why all of us are wrong whether we say shotgun barrel length does or doesn't matter.
The people who say it doesn't matter are generally referring to the fact that it doesn't matter that much, when not accounting for a built in choke, but straight cylinder bores.
The people who say it does fall into many categories. Some are concentrating on the minute differences in the above scenario, and admit that it isn't much. Others are pointing out that you remove the permanent choke of the shotgun by sawing it off. Others live under some delusion that because the barrel is shorter it is less acurate, thus the shot will spread "faster". Anyways, here are my thoughts, speaking purely as a physicist and not neccessarily as a shotgun expert.
First, there are a couple things that I'm taking for granted, number one is a perfect shot cup that for the velocites we are discussing, will perform as it should. It will carry the shot to the muzzle and then drop away. I'm also not going to bring up pellet deformation, as in cylinder chokes, it really doesn't have any real effect. Third assumption is for the same ammo from cyclinder chokes of different lengths, as this is the "meat" of this argument.
For the sake of argument, I will talk about spread at a distance from the muzzle of the shotgun, not from the action, so the little arguments about "it has a foot or two more room to expand" can be ruled out. This is true, but it's academic.
So, we have two loads, we'll say one from a 36" cylinder bore and one from a 24" cylinder bore. When fired, we'll say the 36" has a velocity of 1500 fps, and the same load in the 24 will be 1100fps, just for the sake of argument, invent whatever kind of powder/primer load you want to fix this. When measured from the muzzle, I argue that the 24" barrel will account for a larger spread (not much) than the 36" barrel, the reason is this:
At 10 yards, we check the pattern from our 36" barrel and get a 5" diameter, again, for the sake of argument (this is from the muzzle), we can assume that we are pretty close to muzzle velocity to keep the equations from getting too big (no need to post the actual equations, I think everyone will see my point without them). At 1500fps, it takes the shot .02 seconds to reach the 10yrd target, and begins with a diameter of around .75 inches. So the shot is expanding at (5-.75=4.25inches, 4.25/0.02=~212in/sec),, We can hold this as a general rule of thumb for the expansion of the shot pattern. Using the same expansion vs time, the 24" barrel would make a pattern at 1100fps of about 5.78 inches. At the next interval, the velocity drops a bit and the pattern increases a little more...
36" :~1450fps now form 10 to 20 yards = 9.39" pattern at 20 yrds
24" :~1070fps now form 10 to 20 yards = 11.72" pattern at 20 yrds
I'm sure everyone by now can see where this is going. All other things being equal, the shorter barrel is going to produce a larger pattern because while the expansion of the shot remains the same versus time, the shorter barrel releases it at a slower velocity, impating the pattern at range.
Seems like a lot of difference at the moment, but there is (among the millions of variables out there) another point to be made, that the faster moving shot will be a bit more unstable when it fires from the muzzle, due to higher energy and more "shock" from the transition from tube and cup to open air, and will have a higher rate of spread, maybe 220 instead of 212 or something similar, I haven't measured these directly so it's just a for-instance, but more velocity=more instability=faster rate of spread. This will allow the 36" barrels pattern to be a bit larger than the above calculation perscribes, and thus the actual patterns will be a bit closer to eachother then the calculation predicts.
This speed difference is also the reason that shotgun patterns tend to "fan out" at larger distances rather than being related linearly as pattern vs distance. As the pellets slow down, it takes them longer to cover the same distance and they have more time to expand.
I already know there's going to be a billion know-it-alls out there, and this simple model does not cover everything pertaining to shotguns, there are many other variables, but these are the big ones that will have the most influence.
Hope this clears the issue up for most people.
lol, told you I would write it up one day, cheers!
You state that the rate of expansion is constant...but how do you know this?
