Thoughts on Shooting at Extreme Ranges

21 June 2003

By
Jack D. (JD) Martin

**Table 1. Weight of Various Bullets for a Sectional Density of 0.253**

**Table 2. Weight of Various Bullets for a Volumetric Density of 0.821**

**Table 3. Common Rifle Sight-in Parameters**

**Table 4. Ballistics Program Input**

**Table 5. Selected Ballistics Program Output**

**Table 6. Ballistics Program Atmospheric Conditions**

1: Time-of-flight is the time from when the bullet leaves the muzzle until it reaches the target or designated range.

2: LOS is Line-of-Sight, which is horizontal in all cases.

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Summary

Some of the factors affecting hit probability for targets at extreme (>800 yards) ranges are discussed and some data comparing performance of several bullets are presented. The conclusion reached by the author is that a relatively small diameter bullet (6 to 7mm) with a high ballistic coefficient, pushed out the muzzle at higher-than-normal velocity (>>3000 fps) might very well be the best choice for extreme range shooting.

Discussion

Hitting a target at ranges over 800 yards is not easy! It requires a well tuned system consisting of a skilled shooter, a solid rifle and suitable cartridge. A deficiency in any element of the system will make hitting the target less likely. The three elements of the shooting system are discussed below.

For those who may not have experience shooting at such long ranges, 800 yards is just under one half mile (0.45 mile), while 1000 yards is almost six tenths of a mile (0.57 mile), and 1200 yards is about seven tenths of a mile (0.68 mile).

A "skilled shooter" can be defined as a shooter with the innate ability, will and dedication, and the practice required to consistently put the bullet where intended. In general, the shooter needs a rifle-cartridge combination that is inherently and consistently accurate. The exceptional shooter becomes almost one with their equipment and are able to make shots that border on miraculous. Unfortunately, the shooter is the only part of our shooting "system" that cannot be standardized like the rifle and cartridge can be.

It should be a given that a rifle can be built which will provide a good platform for any selected cartridge. What constitutes a "good platform" is a rifle, including telescopic sight, that repeatedly produces a tight shot grouping — less than one minute of angle (MOA) — with the selected, tuned cartridge, and that group is where the shooter aimed. Admittedly, one has to work the problems in extreme range shooting from both ends. That is, first select a cartridge that seems to fill the bill, then get a rifle chambered for that cartridge and thirdly load some (many?) rounds and fire them off to see how the shots are grouping. Getting the "ultimate" rifle/cartridge combination may require several iterations! That said, let's look at some of the factors about the cartridge that affect the ability to hit a target at extreme range.

The cartridge is a subsystem made up of four components. The components are:

1. case, or brass,

2. primer,

3. powder charge, and

4. bullet.

All four components affect the shot grouping to some extent. One can't put together a cartridge willy-nilly and expect good results! I'll stick to basics here, as there is plenty of other literature available about handloading for accuracy. To whit, the case must have enough, but not excessive, volume to hold the required powder charge, i.e., it should be an efficient powder burner. The primer must be one that properly ignites the powder charge. The powder charge must have enough powder with the right burning rate to achieve the desired muzzle velocity without exceeding safe chamber pressure. Lastly, and perhaps most importantly, is the bullet. Commercially available bullets come in a wide variety of calibers and a number of styles and weights for each caliber. Simply put, we would like to have a bullet which retains enough energy to do some damage at the maximum expected range, and is least affected by shooting conditions. (Ain't asking much, are we?)

There are many field conditions that affect the ability to hit the target. Weather conditions can only be corrected for on-the-spot, we can't do much of anything ahead of time to minimize that correction. Yes, some will argue that a heavy bullet is less susceptible to wind drift, but let's set that aside for the moment. One condition we can do something about ahead of time is to minimize the affect of the pull of gravity.

What can we do about gravity? Well, let's look at the physics of the problem. The downward velocity (v) of the bullet due to the
acceleration of gravity (g) is given by

v = gt ft/sec,

where: g = 32.16 ft/sec/sec and

t is the time-of-flight (TOF^{1}) in seconds.

This says that the longer the TOF the higher the downward velocity of the bullet! It's nice to known about the downward velocity, but
what about drop? Well, the bullet drop (d) from the extended bore centerline is the average downward velocity times the TOF, i.e.:

d = (v/2)t = gt^{2}/2 ft.

Wow, here the drop is a function of the square of the TOF! This suggests that anything that can be done to reduce the TOF is doubly beneficial in reducing the bullet's drop.

Two things can be done to minimize the TOF. They are: 1) maximize the muzzle velocity, and 2) minimize the drag on the bullet, i.e.,
use a bullet with the highest ballistic coefficient (BC). Let's ignore the BC for now and just look at muzzle velocity. Both the Army
and Marine Corps sniper rifles, M24 and M40A3 respectively, use the NATO 7.62 x 51mm case (aka Winchester 308) custom
loaded as "Match Grade" cartridges. Muzzle velocity for these loads is about 2800 ft/sec. If that velocity could be retained
throughout the flight to 1000 yds, the TOF (t) would be

t = D/V secs,

where: D is the distance traveled and

V is the muzzle velocity (D and V in consistent units).

So, for the case at hand

t = 3000/2800 = 1.07 sec,

giving a drop of

d = 32.16 x 1.07^{2} x 0.5 = 18.4 ft,

which is the least possible drop we can expect for that cartridge. If we could get, say, 4000 ft/sec muzzle velocity, the TOF would be

t = 3000/4000 = 0.75 sec,

so the absolute minimum drop would be

d = 32.16 x 0.75^{2} x 0.5 = 9.045 ft,

which is slightly less than half as much drop for only 1.43 times the previous velocity! Over simplified comparison, maybe, but it sure
points out the importance of achieving the highest reasonable muzzle velocity to reduce the drop. And, a reduced TOF also gives less
time for any wind to modify the bullet's path.

Now let's take a look at the ballistic coefficient (BC). The BC is a simplified way of accounting for the drag on a bullet as it goes through the air, with a higher BC meaning a lower drag. To reduce the TOF, we want a bullet with a high BC. More recently designed bullets having long pointed noses and long boat tails have higher BC's than the more traditional spire point boat tail bullets of the same weight. Generally speaking, for bullets of the same caliber with similar profiles, the heavier bullet will have a higher BC, which is at least partially because the drag energy consumes a smaller percentage of the bullet's kinetic energy (I said I'd get back to bullet weight). Since there are so many different caliber bullets with several styles and weights, how do we begin pinning down a specific bullet?

At first blush, it would seem that having bullets with the same sectional density would be a good basis for comparison. Sectional
density, SD, is defined as

SD = w/kD^{2} lbs/in^{2},

where: w is the bullet weight, in grains,

k is 7000, grains per pound, and

D is the bullet diameter, in inches.

Using the 168 grain bullet for the 7.62 x 51mm as a standard, we start with a SD of 0.253 and then calculate the bullet weights for several calibers as given in Table 1.

D - inch | 0.224 | 0.243 | 0.257 | 0.264 | 0.308 | 0.338 |

w - grains | 88.9 | 104.6 | 117 | 123.4 | 168 | 202.3 |

Using constant sectional density as the criteria for selecting a bullet weight doesn't seem to work as the weights for the smaller diameters are too high and that for the larger diameter seems too low. Let's try something else as the criteria.

Let's define a new density factor that I call the volumetric density, DV, calculated by

DV = w/kD^{3} lb/in^{3},

where the terms are as previously defined. The 0.308 inch diameter 168 grain bullet then has a DV of 0.821. The bullet weights for
other calibers having the same DV are given in Table 2.

D - inch | 0.224 | 0.243 | 0.257 | 0.264 | 0.308 | 0.338 |

W - grains | 64.6 | 82.5 | 97.6 | 105.7 | 168 | 221.9 |

This seems to give more reasonable bullet weights, but they should probably be considered as minimum weights since we're looking to maximize the ballistic coefficient.

Now lets look at the ballistics, particularly drop, for several cartridges. Let's do a comparison between the military 7.62 x 51mm sniper round and some hypothetical rounds based on selected web-published data. The parameters common to all rounds are given in Table 3. The individual inputs to the ballistics program are tabulated in Table 4, and results from the program are shown in Table 5. For those interested in reproducing these results, the atmospheric conditions used are given in Table 6.

Parameter | Value |
---|---|

Sight Height (above bore) | 1.50 inches |

Zero Range | 250 yards |

The Sight Height given in Table 3 is pretty standard. The Zero Range was arbitrary and perhaps should have been set farther out since we are talking about extreme range shooting. However, we're still comparing apples to apples.

For the Table 4 input, the 7.62 x 51mm bullet is assumed to be similar to the Speer 0.308 168 grain Match BTHP bullet. The bullet data for the Specials are those published by Lost River Ballistic Technologies for their J36 Hunting or J40 Match bullets. For those that prefer "caliber" designation rather than the metric designation: 6mm = 0.243, 6.5mm = 0.264 and 8.6mm = 0.338. I'll use the metric designation in the following discussion.

Parameter | 7.62 x 51mm | 6mm Special | 6.5mm Special | 8.6mm Special |
---|---|---|---|---|

Muzzle Velocity - ft/sec | 2800 | 3850 | 3300 | 3000 |

Bullet Weight - grains | 168 | 100 | 120 | 225 |

Ballistic Coefficient | 0.450 | 0.665 | 0.687 | 0.617 |

Drag Function | G5 | G7 | G7 | G7 |

The "Specials" are as yet fully defined cartridges, as right now we're just comparing the bullet performance, not trying to define how we get that performance. Muzzle velocities for the Specials were based on those claimed by various wildcat and magnum cartridge producers. The velocities may be a bit optimistic, but given the right case, powder charge and barrel length, should be achievable. However, throat burnout could be a problem, although I've read that throat burnout is no longer a problem for the 220 Swift with the newer barrel metals. There is always a trade-off between bullet weight and attainable muzzle velocity, and between muzzle velocity and throat burnout. Oh well, who ever said that life is supposed to be simple?

The results in Table 5 shouldn't be too surprising, given the input data. The 6 and 6.5mm bullets give similar down-range performance, while the 7.62 and 8.6mm bullets lag behind as far as drop goes. All of the bullets will probably shoot flatter on the range, i.e., have a shorter TOF than the table indicates, particularly the Specials. However, the software indicates all of the bullets retain supersonic velocity and adequate energy at 1000 yards. The 6mm Special looks especially promising, having about the same drop at 1200 yards that the 7.62 x 51mm has at 800 yards. (NOTE: Conclusions are given after Table 5.)

Output | Parameter | 7.62 X 51mm |
6mm Special |
6.5mm Special |
8.6mm Special |
---|---|---|---|---|---|

At 800 Yards | TOF - seconds | 1.037 | 0.679 | 0.797 | 0.892 |

Bullet Velocity - ft/sec |
1908 | 3243 | 2747 | 2416 | |

Remaining Energy - ft-lbs |
1358 | 2336 | 2011 | 2915 | |

Drop - inches (from LOS ^{2}) |
132 | 56 | 79 | 99 | |

Drop - ft-in. | 11'-0" | 4'-8" | 6'-7" | 8'-3" | |

At 1000 Yards |
TOF - seconds | 1.369 | 0.868 | 1.021 | 1.147 |

Bullet Velocity - ft/sec |
1711 | 3098 | 2616 | 2280 | |

Remaining Energy - ft-lbs |
1091 | 2130 | 1824 | 2597 | |

Drop - inches (from LOS) |
245 | 101 | 141 | 177 | |

Drop - ft-in. | 20'-5" | 8'-5" | 11'-9" | 14'-9" | |

At 1200 Yards |
TOF - seconds | 1.740 | 1.067 | 1.256 | 1.418 |

Bullet Velocity - ft/sec |
1531 | 2954 | 2489 | 2149 | |

Remaining Energy - ft-lbs |
874 | 1938 | 1650 | 2307 | |

Drop - inches (from LOS) |
405 | 159 | 222 | 282 | |

Drop - ft-in. | 33'-9" | 13'-3" | 18'-6" | 23'-6" |

One caliber not examined for ballistics is the 0.257, which should fall between the 6 and 6.5mm bullet's performance. The bullet is 0.014" larger in diameter than the 6mm and only 0.007" smaller than the 6.5mm. Could be a good trade-off to get a higher muzzle velocity than can be obtained with the 6.5mm, especially since the 25-06 is a production cartridge and there aren't any production cartridges in the 6mm or 6.5mm class that can achieve the desired muzzle velocity.

Conclusions

The results given in Table 5 indicate that a smaller caliber (6 to 7mm) cartridge providing a higher than normal muzzle velocity for a bullet with a high ballistic coefficient may be the best choice for extreme range shooting. This conclusion is further supported by the match data and summaries given on the North Carolina 1000 Yard Benchrest Association's web site. The cumulative summary of the calibers used during the 2000, 2001 and 2002 seasons indicates a decided trend toward increased use of 6.5mm cartridges. The cases (brass) used ranges from those based on the Winchester 308 to belted magnum. During the 2002 season, a shooter in the Light Gun (<17 pounds) category set a club, and possibly international, 5-shot group record of 1.561" using a "6.5 Super" – whatever that is. However, the 0.243" and 0.308" based cartridges continue to win matches either on score or on group size. As-manufactured rifles have done reasonably well in these matches, although undoubtedly using handloaded, tuned ammo.

Parameter | Value |
---|---|

Temperature | 72.0 °F |

Barometric Pressure | 29.92 in Hg |

Relative Humidity | 20.00% |

Altitude | 0 feet |

Air Density | 97 % of Sea Level |

Notes

1: Time-of-flight is the time from when the bullet leaves the muzzle until it reaches the target or designated range.

2: LOS is Line-of-Sight, which is horizontal in all cases.

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