2707 yard shot in Afghanistan by the numbers

I think I first saw it at Ry’s place. But others have mentioned it too. People at work have been asking about it too. It’s time I made a blog post about it.

According to the news reports a British sniper made three consecutive shots which were measured, via GPS, to be at a range 8120 feet. This is about 2707 yards which is the number I used with Modern Ballistics. I have uploaded the data file here if you want to tweak a few numbers and see what happens for yourself.

I used a high end 300 grain bullet with a BC of 0.785, a muzzle velocity of 2750 ft/sec, a muzzle velocity standard deviation of 10 fps and the inherent accuracy of the cartridge, gun, and shooter was 0.25 MOA. I assumed zero wind at 10,000 feet above sea level, and a temperature of 59 F. All are a bit on the optimistic, but plausible, side of “excellent” conditions.

The first thing that struck me about the situation was that with a 32-power, mil-dot reticle, scope the target was quite visible (the rectangle target is 18″ x 24″):

Even a 16-power scope gives a usable sight picture:

The sight angle to not require hold-over is 122 MOA. For best results a no hold-over shot is required.

Long range Leopold scopes give 70 MOA of adjustment so a shim of 52 MOA would be required for a no hold-over shot. This is not likely.

Some Nightforce scopes have 110 MOA of adjustment which would require a shim of 12 MOA. This would result in the closest range the rifle could be zeroed at under standard conditions to be about 460 yards. This seems plausible.

The articles claim a three second time to target but I come up with 4.9 seconds. My guess is whoever did the calculation assumed the bullet did not lose any velocity on it’s way to the target. Working backward we come up with about 2700 fps for a muzzle velocity.

The velocity of the bullet at the target is about 1043 fps. With a 300 grain bullet this corresponds to an IPSC “Power Factor” of 313. A 124 grain 9mm bullet at the muzzle is in the neighborhood of a PF of 135 so the sniper still had a lot of “stopping power” at this range.

On the average you would have to shoot 83 (the correct number is 4.9, apparently something hadn’t been updated properly in my simulation when I pulled the 83 off) three-shot groups to get one which was less than or equal to 1 MOA (about 30 inches). Only about 30% of the shots will hit a 18″ x 24″ target (1000 shot simulation):

My conclusion is there was some luck involved but it is plausible the event took place essentially as reported.

Update: I have rerun some of the simulations with what is believed to be the cartridge used by the British.

8 thoughts on “2707 yard shot in Afghanistan by the numbers

  1. ‘Course the probability that there’d be constant wind (no direction changes or variations) along that bullet path is quite low. Still, the shots lie within the possible as you say.

  2. “Harrison killed one machinegunner with his first attempt and felled the other with his next shot. He then let off a final round to knock the enemy weapon out of action. ”

    3 shots, 3 hits on target at that range?

    I don’t think so.

  3. Improbable, but possible. Right after I got the news that my brother’s fifth daughter was born, I thought aloud; “What are the chances of that?” I then flipped a penny and got heads five times in a row, right then and there. Answer; the chances are slim, but not zero.

    There’s also an x factor, for which I have no name but have experienced maybe two or three time in my 52 years. Many people who’ve done some something for a long time about which they are passionate will tell you similar stories, from a musical performer who’s playing for thousands of people and “sees” himself “from a distance” playing, to the carpenter who gets lost in the work and loses track of several hours of time, to the football player who makes an amazing play and then is genuinely confused, wondering what all the fuss is about when people are cheering and yelping (he just did what needed done at the time), to the shooter who makes not one, but three amazing shots in a row. It’s a state of total concentration wherein the ego completely lets go and the brain/body does things not ordinarily thought possible for mere mortals. The equipment, the practice, the situation, the load, the weather, and that x factor can sometinmes all converge on the same moment.

  4. No mention of mirage? Even if the winds were dead calm, there would be mirage. Even in extremely dry situations, there is some mirage. A target that size would bob and weave, especially at that kind of magnification.

    I have vehemently argued elsewhere that some of these guys are very good, and that all kinds of incredible shots are possible under the very real exingencies of war.

    This, though, seems a little to perfect.

    That said, luck happens when preparation meets opportunity!

  5. Bill,

    I haven’t done as much long range shooting as you so I’m asking…

    Aren’t there times when there is no mirage? When it’s cloudy and/or cold? Or maybe when you are looking through air that is high above the ground?

    I have only shot at 1000 yards a handful of times but I don’t recall mirage in all instances.

  6. Joe,

    There may be some condition without any mirage, I just haven’t ever seen it. It gets worse with increasing magnification, at least in my experience. There have been times when I actually went to 20 power from 42 on my Nightforce, because the mirage was confusing me as to true point of aim.

    I’ve shot in 20 degree, dry, calm conditions and seen mirage, I’ve shot in high wind conditions and seen mirage (Yep, especially at Boomershoot!) and I’ve shot in hot, dry, calm or windy, and I’ve always seen mirage, worsening at high power. It’s worse with humidity, too, though I suspect that isn’t an issue in most parts of Afghanistan!

    I haven’t shot at altitudes above those at Boomershoot, so I can’t make a comment there. I also haven’t ever shot across a canyon, from one high point to another, where the line of sight is significantly above ground level, so I can’t make any assertions there.

    I do know a recently returned Army sniper who served in Afghanistan, though, and I’ve asked him for his thoughts on those conditions and the mirage issue, as well as the holdover issues. The drop at that range is almost impossible to figure, because I don’t know of any military rifles set up with more than 20MOA rails, and realistically, I’m not sure that many have those. Since we don’t use the Lapua .338 much in the US for snipers, it is entirely possible that GB is, however. Certainly the Leupolds are out of the question, since 52 MOA isn’t realistic. 12 MOA is doable, but that assumes that the scope is completely bottomed out prior to installation and that you have all 110 MOA available, as you know. Seems pretty unrealistice to me, also.

    Possible, yes: plausible, yes: likely, no. But as I said before; Luck is what happens when preparation meets opportunity!

  7. Well, consultation is always good. My sniper friend says that he has encountered situations with little to no mirage at extreme ranges.

    That takes out one factor that I would have believed to be very significant.

    He also agrees that 3 consecutive hits on targets at that range and of that size was incredible.

  8. Just a little about the equipment: the rifle used was a L115A3 system, which is nothing more than a Accuracy International AWM rifle caliber .338 Lapua Magum with a 27″ barrel (part #2534), using a Schmidt und Bender MILITARY MKII 5-25x56mm with 0.1 MIL RAD double turn turrets and parallax/illumination controls (part #5848), mounted on a 45MOA mount/rail (part #5655), and shooting Lapua B408 ammo (part #4318033) loaded to 66,000 psi as ordered by British MoD.

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