Recently a news story has been doing the rounds regarding a world record shot made by a Canadian Sniper. The story suggests the sniper made the shot at 2.2 miles. Some stories differ on the exact range but most seem to agree on 3540 meters. This article discusses the ballistics involved in making such a shot. I work as a Ballistician for a defence contractor and I shoot ELR (Extended long range) reguarly in calibers up to .50BMG. The article is not trying to prove or disprove anything. Some of the variables are unknown and It serves only as an interesting discussion.
The shot was made with a Mcmillan Tac50 bolt action rifle. The rifle is chambered for .50BMG which is a heavy hitter but perhaps not the best caliber for extreme long range. There are multiple calibers which are better suited and one only has to look at competitions such as “The king of 2 miles” to see that few of the top shooters are using .50cals. The rifle itself is fantastic and capable of extreme accuracy. In the right hands with the right ammunition it will print 0.5MOA 3 shot groups consistently. The Canadians fit their rifles with S&B 5X25 PMII scopes. S&B make quality optics which have been proven in both battlefield and competition for many years. The scope mount is one of the unknown varibles. As standard the rifle has a canted rail offering 30MOA of elevation built in. I have read that the Canadians were using either a specialised rail or mount for increased elevation capability. I would hazard a guess that they were using an adjustable mount which offers up to 120MOA of elevation. This would allow them to drop back down to the standard 30MOA for standard distances and zeroing. As far as I am aware that is the max elevation available for rail/mount unless they had a custom canted rail made which I very much doubt.
The ammunition used was said to be Hornadys 750gn Amax factory load. Although this is not a bad choice it isn’t the best either. There are loads with a higher ballistic coefficient, faster muzzle velocity and lower standard deviation.
Of course we take for granted that both SF sniper and spotter are experts in their field.
I have used the Applied Ballistics Analytics software. For those unfamiliar with the software I should probably explain it a little. First off it works as a very accurate ballistic calculator. The user inputs variables regarding weapon, ammunition and environment and the software will produce a drop table. It is able to compute factors such as coriolis, spin drift, aerodynamic jump and powder temperature sensitivity. I have used it with great success as have many top end long range shooters including team Applied Ballistics.
The second and I think most interesting part of AB Analytics is the ability to predict hit percentage based upon known errors. For example a shooter or spotter must make a wind call. Even with a Kestrel Anenometer and an experienced wind reader it becomes very tough to make accurate calls with shots at 1500m+. AB can compute all kinds of errors which can be entered as +_ values.
The rifles barrel length and twist are known variables as is the form and muzzle velocity of the Hornady ammunition. You can see the input fields in the screenshot above. The are some fields which are not quite as straightforward. I have taken the weather data from the recorded conditions in the capital on the given day. These may or may not match the exact weather conditions when the shot was taken. The same goes for shooters position. I have been kind in these regards and entered data which in shooting terms is considered fairly standard defaults.
As we can see the drop table makes for interesting reading. The most relevant factor for me is the speed of the projectile. When bullets move from supersonic to transonic and finally become subsonic they become unstable. The transonic zone is considered by many to signal the rounds max effective range as shots beyond this become hard to predict. Those of you who shoot standard milsurp 5.56mm at ranges beyond about 800m may have noticed the group becomes erratic and disperses far enough that you cannot consistently strike a man size target. The 750gn Amax reaches the transonic zone at about 2000m leaving a further 1540m to travel at Subsonic speed. Bear in mind that any slight deviation in trajectory becomes magnified at increased range. The heavy bullet does retain lethality even at these speeds due to weight.
Lets take a look at elevation. 1 MOA at 3540m works out equating to 40.54 inches. We can see that the shooter would require 278.39MOA to have the bullet strike a target that far away. This would equate to 11307.3 inches. Lets be kind and say the shooter has 120MOA in the mount + 30MOA in the rail + another 97MOA in the turret. Added together we have a total of 247MOA. This would leave the shooter with a 31.39MOA holdover or 1272 inches. It is not uncommon for FFP scopes to have up to 8Mil or 30MOA in the reticle which could be used for a holdover.
In terms of wind I have again been conservative and input a 2mph full value crosswind. For now we will assume it is constant. The shooter would need 10MOA of windage correction if one were to include Coriolis and Spin Drift. Missing these from the equation would result in a huge miss.
We can see that it is technically possible to make the shot if all variables are favourable. It is when we begin to examine the sensitivity of each variable that things become more interesting. For this section I have made the target a man sized rectangle of 72″ x 24″.
The wind is the bane of all shooters. If our guy were in a windless void (never going to happen) then he would actually stand a reasonable chance of making a hit (just under 30%). Just 1mph of error in wind estimation results in a dramatic drop in hit probability to around 3.5%! Even highly experienced shooters using a Kestrel can only call the wind that the Kestrel detects or that they can see. The margin of error on such a long shot is more likely to be at least +/-2mph. Undulations in terrain and environmental factors would require almost superhuman judgement at this range. That is why the ELR sport shooters tend to use multiple windstations and it still takes them multiple rounds to make 1 hit on a 2m square board.
We can see just how big a factor wind is by looking at horizontal uncertainty in AB Analytics. Wind at even +/- 1mph gives over 80″ error and dwarfs the other variables. Tightening rifle accuracy or MV spread of ammunition would yield no noticeable benefit in comparison. Increasing MV by about 2000fps might be useful but also impossible!
While MV spread might not be much of an issue for horizontal error it dominates in the vertical plane. A figure of +/-10fps is a possibility for extremely good factory ammunition. You will not find mass produced ammunition from automated production gets much better than this and is often a lot worse. That is due to automated powder dispensers which are unable to meet the tight tolerances a skilled handloader could. The MV spread gives over 80 inches of vertical error at 3540m. Small miscalculations in temperature, pressure, inclination and range all produce enough vertical error to miss the chosen target. Estimating range at this distance can be tough even with the latest equipment. High end GPS or LRF systems will in absolutely ideal conditions give about +/-1m. Of course the target could also move which to be honest adds such a level of complexity and fast calculation that the shot would become nothing other than pull the trigger and hope it hits something.
Even if we could perfectly predict every variable involved there is still one big problem – flight time. The projectile will be in the air for over 9 seconds after the trigger has been pulled. The shooter/spotter would then just have to hope none of the variables change at all. If they do then the likelyhood is they miss the target by a huge margin.
I have not written this article to call anyone out or belittle the professionalism of anyone serving. What I do hope is that it educates people a little in terms of what a modern sniper system can and can’t do. Above we can see the best case scenario only gives a hit probability of just over 3%. I also hope it shows shooters how useful Applied Ballistics Analytics can be when assesing the importance of each variable. Do you benefit from spending 10k on a 0.25MOA rifle or would it be better to handload your own ammunition for more consistent MV spread. Calculating such factors can save the shooter a lot of time and money. Was this system the best tool for the job? No, not by a long shot (groan..) If you absolutely had to use a rifle then it would ideally be a caliber which is better suited for extreme range.
Check out the Applied Ballistics App here: