Ask Foghorn: Do groups “tighten up” at longer distances?

Tyler writes:

Have you done any research on bullet stabilization? Some of the boys back home seem to think shot groups sometimes tighten up at some point downrange. Have you heard or seen such a thing?

I was going to hold off on this one until I finished up the silencer reviews from my trip to AAC but it’s been sitting at the top of my inbox and starting at me for days now, mocking me, calling for me to answer it. And so I will. Grab your protractors boys, it’s time for physics!

Devoted readers of my technical jargon will remember that I did a little bit on why people use cheap ammunition to practice. In that article I introduced a concept called the “cone of uncertainty.” I believe my exact words to describe it were:

If you were to shine four lasers from the end of your barrel and through the furthest apart holes in your target (up and down, left and right) you would see an ever-expanding cone formed by these lasers. That’s the “cone of uncertainty” for your firearm and your ammunition; every round you fire will fly within that cone until it strikes a target. That cone exists even with bench rest shooting (where the firearm is in a vice and doesn’t move) because the variation is not solely a factor of your own personal accuracy, but also that of the firearm.

It’s an over-simplification of the concept, as gravity and wind and a number of other forces acting on the bullet tend to pull it in a parabolic trajectory rather than an actual laser straight line, but it works for our purposes. The reason that bullets form this ever expanding cone was first observed by a man clocked in the head by an apple. You may remember this little ditty from High School:

Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

Or, in English, “a moving object will remain moving in a straight line unless another force moves it.” It’s Newton’s first law, one of the fundamental principles of physics.

When firing a gun, the expanding gasses of the gunpowder are the force making the bullet move. The barrel of the gun directs those forces in a straight line, usually towards a target of some sort. From the second the bullet leaves the barrel of that gun the shooter has no more influence on the path of the bullet, and it will continue in a more or less straight line until it hits something.

So what does that have to do with the question? If we apply Newton’s law, we see that there is no physical way for the bullets to suddenly “tighten up” at a further distance. The closest possible group you’re going to get out of a rifle is at the muzzle, and targets further away will always have larger groups. Always.

“But Foghorn,” I hear you cry like a high school student who thinks they’ve outsmarted the teacher, “other forces act on the bullet when it leaves the barrel! Couldn’t that change the trajectory?” Well Jimmy, they can and do alter the trajectory of the bullet — but they alter the trajectory in a uniform and consistent manner for each round fired. If one round you fire is pushed 5 inches left by the wind, the same wind is going to push the next bullet that much as well. In order for these external forces to “tighten up” a group at distance they would need to focus the bullets like a lens and affect them differently depending on their position, but instead they simply push everything equally.

So where does this myth come from? It’s possible that football (the American version) has an answer.

When the quarterback throws a football, you can sometimes see a bit of wobble as the ball starts its flight down field. The wobble disappears after a while, resolving into a nice spiral and landing exactly where he wanted it. When we say “a bullet flies like a football” we put that idea into shooter’s minds; that the bullet wobbles at the beginning of its flight. Which is not true.

The football wobbles because the force applied to the back of the ball is not uniform. As your hand releases the ball, the side of the ball with your fingers on it gets just a little extra “oomf” than the rest of the ball and causes the wobble. With a gun, the force applied to the bullet is constant and uniform thanks to the fluid-like gasses pressing on it from behind. When the bullet leaves the barrel there is no significant amount of wobble, and no time needed to stabilize in flight.

(As someone noted in the comments, bullets do in fact wobble when they leave the barrel. Slightly. This us usually due to concentricity errors made when loading the bullets, which increases the force on one side of the bullet in relation to the other side of the bullet and causes some minor wobbling. This wobble does alter the flight path of the bullet, but once it is corrected the bullet will not magically re-align with the point of aim. If there’s wobbling going on then the wobble will result in larger groups, not smaller ones, as the mean vector (the general direction in which the round is travelling) will not change. I didn’t want to go there, but as a commenter brought it up I thought I should mention it in the article proper. So there. I hope you’re happy.)

So, in summary, it is physically impossible for a group to “tighten up” downrange.

If you have a topic you want to see covered in a future “Ask Foghorn” segment, email guntruth@me.com.

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About Nick Leghorn

Nick Leghorn is a gun nerd living and working in San Antonio, Texas. In his free time, he's a competition shooter (USPSA, 3-gun and NRA High Power), aspiring pilot, and enjoys mixing statistics and science with firearms. Now on sale: Getting Started with Firearms by yours truly!

31 Responses to Ask Foghorn: Do groups “tighten up” at longer distances?

  1. avatarChaz says:

    When the bullet leaves the barrel there is no wobble

    Be that as it may I know from my reloading that different loads for the same handgun and bullet punch different looking holes in the target e.g. cleanly round versus key hole. What is going on? I would presume it’s some kind of bullet wobbling or tumbling. Barrel twist rate, velocity and bullet characteristics probably come into play.

    Whatever this phenomenon represents I concede that extending the target distance is unlikely to shrink “the cone.”

    • There’s an ideal bullet weight for every rifling twist rate. If the bullet is too heavy or too light it will not properly stabilize in flight and start keyholeing or just plain disintegrate. Also, bullets travelling at different velocities and with different profiles make different sized holes.

      In short, changing the load will alter the physics and may make the bullet do strange things. Identical bullets out of the same gun, however, will always act identically.

    • avatarirock350 says:

      When I used crappy milsurp ammo the powder did not burn all the way, and it would drasticaly change the flightpath of the bullet. On several occasions my .303 looked like it wobbeld when it hit the target and keyholed the paper. Once I picked up a new box of first time reloads I noticed the groups tightened and the the round stopped keyholing the paper.

  2. avatartdiinva says:

    Perhaps the myth comes from how the sight picture changes with range. I know from experience that I shoot my tightst groups at an indoor range at about 20 yards. At shorter ranges I am lower and more spread out. Beyonf 20 yards the groupings spread out again. It’s not the ballistics, it’s how I see the target.

    • avatarirock350 says:

      It could be the trajectory of the bullets based on your sight plane. Depeding on the round and the gun and how high the sights are off the barrel the bullets arching trajectory will group high or low at different distances.

  3. avatarJoe Grine says:

    Hey Nick: Chris Dumm and I have been having an ongoing friendly debate about “keyholing” bullets and the effect that distance has on this phenomenon. As you know, barrels with longer twist rates may not be able to stabilize longer, heavier bullets. As an example, an older AR-15 with the “1 in 12” twist rate barrel cannot stabilize the modern 62 grain M-855 round. Chris seems to think that a bullet that is ballistically unstable as it exits the barrel may become somewhat more ballistically stable (i.e. “straighten out”) as it travels downrange. His evidence for this is that his test targets show greater keyholing effect at shorter ranges (25 yards etc) than at longer ranges 55-100 yards). My position is that once a bullet’s nose is traveling in any other direction other that straight forward, the bullet will start to act more like a wing, which will further destabilize the bullet and cause it to tumble. This is because the path that air has to take as it goes past the bullet will be different. Chris also pointed out that arrows tend to straighten out as they go downrange. True, but there are different forces working on an arrow, so that is not a good analogy (an arrow is long and flexible, whereas bullets are short and rigid). Unfortunately, I don’t think either of us have cracked a physics book open in twenty years. Your thoughts? By the way, we have seen a few internet commandos argue (in response to the CAI Tantal debacle) that the Russian 5.45 x 39 (7N6) bullet is SUPPOSED to tumble through the air as it travels to its target. That argument, of course, is pure nonsense. The tendency of the 7N6 bullet to yaw only occurs AFTER it hits soft tissue.

    • I get the feeling the “5.45 is supposed to tumble” argument came up sometime around when CAI started installing 5.56 barrels on their 5.45 Tantal rifles. My friends and I scratched our heads for a while after a brand new one we had was keyholeing at 10 yards. The logic probably went “This is new, and I only buy good things, so it must be designed to do that!” Mmhmm, you keep thinking that Mr. Mall Ninja. I’ll be at the 600 yard line if you need me.

      1:12 should under stabilize the bullet, not giving it enough spin to stay facing forwards. 62+ gr bullets need a 1:9 or better to stabilize properly, spinning it a bit faster. I don’t have a degree in fluid dynamics or anything, but I would be willing to bet that the 50 yard difference is enough to spin the bullet completely around so it’s travelling ass first, and would not show up as a keyhole.

      Arrows have the same issues as footballs, with a little bit of force applied on one side and not the other upon release. That causes the wobble, and the spin stabilizes it.

      • avatarChris Dumm says:

        Joe and I have several pictures (and some rather long-winded videos) of targets we shot at 25 and 50 meters with his HK93. With its favored 55-grain ammo, that HK is a tackdriver until you overheat the barrel, but it just can’t stabilize Radway 62-grain bullets with its slow-twist barrel.

        At 25 meters the paper target showed conspicuous keyholing and poor accuracy. At 50 meters the bullet holes are almost perfectly round (almost no keyholing) but the groups were even worse.

        My suspicion is counter-intuitive, but I think this controlled experiment (same ammo, same rifle, same shooter, same day) shows that under-stabilized bullets can wobble and keyhole at closer ranges but can eventually stabilize themselves in flight.

        ‘Stabilized’ only means that they’ll eventually end up flying nose-first through the air instead of sideways. It *doesn’t* mean they become accurate again. If they’ve wobbled and keyholed, their point of impact becomes much more random. You’ll have nice round bullet holes, but they’ll be all over the place.

        • I don’t think that’s what’s going on. Once a bullet starts to tumble and keyhole nothing in the world is going to put it right again, it’s not magically going to start flying nose first because it suddenly “stabilizes.”

          It is, however, entirely possible that the bullet decided to fly backwards and straightened out that way. If you look at wound channel analysis from when bullets hit tissue, you’ll notice that the bullet “de-stabilizes,” turns, and then proceeds backwards for a while. This might be what’s going on, and in that case the increased air resistance and non-uniform face are going to significantly hurt accuracy and distance.

    • avatarRebecca says:

      I’m no expert, but I submit that a bullet travelling 1000 fps is going to “see” the air more like fluid (i.e., water) than as air. I think your argument – that if the bullet isn’t stable coming out of the barrel, it is never going to stabilize – is more plausible than the Chris’. What he may be seeing – *may* being the operative word – is that at longer ranges, the bullet tumbles to a point where it looks like it goes through the target properly. Kind of a harmonics thing. I’m probably wrong on this, but that’s my thinking right now.

    • avatarChaz says:

      there are different forces working on an arrow… (an arrow is long and flexible, whereas bullets are short and rigid)

      Also arrows, throwing darts, badminton shuttlecocks, etc. have stabilization fins.

  4. avatarCoyote Gray says:

    “When the bullet leaves the barrel there is no wobble”

    From what I understand, and from what various ammunition makers will state, bullets do indeed wobble, “ever so slightly”, when leaving the barrel, and then stabalize; A phenomenon referred to as “going to sleep”.

    ” it will continue in a more or less straight line until it hits something”.

    Yes, and no. Bullets travel in a arc, because at distance, the barrel of a rifle is usually higher then the target, to compensate for the effect gravity has on a trajectory. Which is why we have to compensate for muzzle elevation when using higher velocity ammunition VS lower velocity ammunition. Higher velocity ammuntion has a “flatter” trajectory then low velocity ammunition at long distances.

    As the bullet starts its descent on its trajectory arc, it again begins to tumble. Some bullets do this by design, when the tumbling or yawwing on impact is key to its ability to”incapacitate”.

    Still, this does not support the idea that groups “tighten” as you move down range; instead suggesting there is likely a “sweet range” when shooting for pin-point accuracy.

    • avatarirock350 says:

      +1 Exactly what I was thinking.

    • I didn’t really want to get into concentricity issues and the finer points of bullet flight, but sure. I’ve edited the article to include a bit on the wobble. As I say, once the wobble is gone the bullets do not magically re-align with the original point of aim, so the original idea that groups tighten up downrange is still impossible.

      My main point was that the final destination of the bullet is set as soon as it leaves the barrel, and no amount of black magic can alter it.

      Bullet tumbling is always a bad thing, except AFTER they hit the target. A head-on impact is key for initial penetration, putting as much mass and momentum behind a small as possible surface area. I’d much rather be hit with a keyholeing .223 than a properly stabilized .223 any day of the week.

      • avatarCoyote Gray says:

        Sure, there is only so much physics you can squeeze into a piece, with out losing a majority of the audience; so I understand.

        Of course your correct…groups tightening up down range…says more about the shooter or the rifle elevation and windage in question, than it says about the general trajectory of a bullet.

  5. avatarTyler Kee says:

    Nick,

    Thanks so much. I will educate the boys back home.

    -Tyler

  6. avatarSid says:

    Well, the Zorg ZF-1 seems to have a tighter group as the bullets move further away, but only if you engage the “replay” function.

    http://www.youtube.com/watch?v=9pxjnl1yuXk

  7. avatarChris Dumm says:

    Hold The Presses!

    If you approach this question as an optics problem instead of a ballistics problem, the answer is “Yes, a scoped rifle can exhibit poor accuracy at short range and good accuracy at a longer range.”

    How? Parallax. If your scope is set to be parallax-free at 100 yards, the size of your groups at 100 yards will depend only on your skill, your rifle and your ammunition. It won’t matter where your eye is located behind the scope as long as the crosshairs line up with the target.

    Shoot the same gun at 40 yards with a poor cheek-weld, however, and the crosshairs won’t necessarily be pointing at your intended aiming point. Even if you line up the shot and break the trigger perfectly, you won’t actually be aiming where you think you’re aiming.

    Because of parallax, a 2 MOA gun (at 100 yards) can be a 5 or 10 MOA gun at 35 yards if you don’t have a 100% consistent shooting stance.

  8. avatarMagoo says:

    Chris Dumm says: “Because of parallax, a 2 MOA gun (at 100 yards) can be a 5 or 10 MOA gun at 35 yards if you don’t have a 100% consistent shooting stance.”

    No, it’s still a 2 MOA gun by any sensible definition. It’s only being sighted improperly. There is nothing that will allow a firearm to group tighter at distance than at close range. As Leghorn noted, once the bullet leaves the muzzle, its trajectory cannot correct en route.

    • avatarJoe Grine says:

      Magoo, your point is well taken, but it does seem fairly obvious from the context of Mr. Dumm’s statement that he was refering to practical accuracy, which may have little to do with the inherent accuracy of the firearm.

      • avatarMagoo says:

        Understood. I am only noting the gun is 2 MOA. It’s not really 5 or 10 MOA. It’s being aimed improperly.

  9. avatarDaniel Williams says:

    Differant bullets have differant ballistic coefficients at differant velocities… what does this mean? This means that a bullet meets varying degrees of resistance from the air depending on its velocity… for instance I handload my rounds for .308… if I fire a handload that generates a velocity of over 2950 fps or so my groups get about 2 to 3 inches wide and the faster i get the worse it becomes… but if i stay around 2600 fps i get nice sub moa groups… my thoughts on this? sound does not like to transfer from one travel medium to the next… that is why if you are in the water next to an explosive device getting ready to go off you can float on your back on the surface just a few feet from the explosion and survive (mythbusters episode). so when a bullet that is traveling 2600+ fps meets the air, within the first few feet of the muzzle it has the greatest effect on the bullet impact… when it suddenly contacts the air the bullet the aerodynamic properties of the bullet push the air around the outside body of the projectile… it takes several feet for the turbulence to stabilize causing the projectile to vary impact points ever so slightly… think of how when you flush your toilet and at first the water floods the bowl in a random way, then it starts to swirl… this is what causes the round to have a slightly differant point of impact on a microscopic level… just my theory take it for what it is… but back to the ballistic cooefficient, the velocity will cause projectiles to fly straight or wierd, ask and handloader what happens to their groups when the velocity is too high… the bullets seem to fly straighter at lower velocities… but the problem is bullet drop… not enough velocity too much bullet drop etc…

  10. avatarDaniel Williams says:

    It called the epicyclic swerve… I just found it… It says that a bullet flies in a corkscrew motion… http://Www.appliedballisticsllc.com/index_files/epswerve.html

  11. avatarIn Box 485 says:

    Late comment, but this was linked from a recent article.

    My take on this theory is that it is a 100% mental effect that takes place when aiming for a more distant or otherwise smaller point. It is the “aim small hit small” concept. If you are shooting at a 3″ circle at 100 yards, then aim for that same 3″ circle at 300 yards, it is entirely probable that many shooters would see the group shrink considerably at the target size becomes closer to the size of the limit of what can be focused on at the tip of the front sight or behind the crosshairs.

    The reason shooters that have had marksmanship training might scratch their heads at this theory is that unless you are balancing time against precision, you are aiming at a point that is literally as small as you could aim for with your sight system even if it is a point within a larger target. But just as aiming for the second button down on a target tightens the group vs aiming for somewhere torso-ish backing the target up could have the same effect on measured group size.

    Just my theory.

  12. avatarLabman says:

    Hey Nick,

    Just found this site. Great conversations and lots of good info from your contributors. I shoot mostly .223/5.56 (Bushmaster Varminter w/24″ fluted barrel, comp 2-stage trigger, 6-18 Leupold VXII w/Factory target turrets), .308 (One competition and one hunting), .270 and 10/22. I handload for all but 10/22 which has a 16 inch bull-barrel, target trigger, Hogue stock (floated barrel) and a red-dot (great fun and cheap to shoot). All the hi-power guns shoot extremely well (.270 and .308′s are well under an inch) with Varminter having a best group to date of 6 shots into .29 inches at 100 yds w/sandbags off the bench . Great fun on “dogs” at 200-300 yds!

    Now that I’ve found your site, I’ll be back. Jim

  13. avatarMarta frawley says:

    I just found “Ralph’s” review of the of the sig sauer p290. It was incredibly informative as well as very humorous. I noticed that it was dated 2011…..really… Are you guys dead? Does the website still publish? In particular, is Ralph dead? Would like to see more posts. Pls. Let me know.

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