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Applied Ballistics For Long Range Shooting
Itís very important to remember that this analysis assumes that all of the deterministic variables are accounted for. If the rifle is slightly canted, spin drift unaccounted for, shot taken from a poorly supported position, sights not properly calibrated and adjusted, zero not accurately set, etc etc, the impact zone will be the same size, but it will not be centered on the aim point which will likely result in a miss. Figure 15.2 shows the likely impact zone from the previous example and its relative size on the vital area of a deer; as well as the effects of having an unaccounted for deterministic variable.
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As illustrated in Figure 15.2, if all the deterministic variables are accounted for, then the uncertainty introduced by the muzzle velocity variation and wind uncertainty isnít enough to cause a miss on a typical white tailed deer at 500 yards (left). However, if the deterministic variables are not perfectly accounted for, the impact zone can be offset from the aim point and result in a miss. The example in Figure 15.2 has the impact zone shifted by about 15 inches. At 500 yards, if the rifle is canted by just 5 degrees, it will cause the point of impact to shift laterally by 4.3 inches in this example. In contrast, spin drift is only worth about 1.4 inches at this range. The most likely cause of offsetting the aim point in a hunting situation is the combination of not having a perfectly steady platform to shoot from, and being excited about the shot. These real world effects can easily compromise shot placement as much as any other variable.

Applied Ballistics For Long Range Shooting
Figure 15.2. If all of the deterministic variables are accounted for, the impact zone will be centered on the aim point. However if the deterministic variables are unaccounted for the impact zone will be offset and a miss can result.

In the above analysis, the ballistic performance of the rifle/bullet comes into play in the step where you translate the non-deterministic variables into physical displacement on the target. The better the ballistic performance of your bullets, the less wind deflection you will incur from a given uncertainty of crosswind speed. Seeing as how wind is usually the greatest non-deterministic variable, ballistic performance turns out to play quite an important role in the size of the expected impact zone. Furthermore, improved inherent precision of the rifle and more consistent muzzle velocities will serve to further shrink the size of the expected impact zone. However, taking another look at Figure 15.2 for the 500 yard shot on a deer, itís clear that the impact zone is small enough to insure a pretty reliable hit on a deer sized target. Therefore, the reasons for missing a deer at 500 yards will likely have more to do with improperly accounted for deterministic variables and/or poor shot execution.

The conclusion to be made about hit probability in hunting situations is very similar to the conclusion made in the last chapter on score shooting. Improving the ballistic performance of your equipment can increase the margin of error for a given shooting objective, but success is very dependent on the ability of the shooter to judge wind and execute well placed shots.

The stated objective of this book is to promote successful long range shooting by establishing a strong understanding of external ballistics. Part of understanding external ballistics is knowing its relative importance in the big picture. Successful long range shooting does require a working knowledge of external ballistics, but thereís much more to it than that. If youíre serious about achieving success at any long range shooting objective, itís important to have a well rounded understanding of all the aspects related to your chosen shooting objective including the ballistics, special skills required to handle the elements present like keeping your scope from fogging in cold weather or preventing the grease from freezing in the firing pin spring and causing a misfire. You also have to know your body and its effects on your shooting objective. How fast can you calm your heartbeat if you have to stop hiking and settle in for a long range shot? Do you have a plan for keeping the sweat from running in your eyes and compromising the sight picture? You need to have a basic understanding of the instruments you use to measure all the variables in the field. You should know the effects of moisture and temperature on the performance of your rangefinder. You need to make sure you have your weather reading instrument calibrated so youíre getting accurate measurements of temperature, humidity and pressure.

Successful long range shooting is dependent on so many things. Again, external ballistics is an important subject to study because it can help you make decisions about the best equipment for your application and allow you to make accurate corrections to your sights in order to hit targets. Keep in mind there are many other subjects that are equally critical to successful long range shooting, and donít think you can do it all just because you read this book.

The final example in this chapter will be a little more humbling than the first. Weíll consider the effects of the non-deterministic variables involved in taking a shot at the same deer sized target at 1000 yards.

Weíll consider the ballistics of a 7mm Remington Magnum with the heavy 180 grain Berger VLD hunting bullet at an average 3000 fps muzzle velocity, with a standard deviation of 10 fps.

According to the lethality charts in the previous chapter, a large capacity 7mm cartridge with these bullets is lethal on 150 lb game up to 1225 yards, and up to 850 yards on 300 lb game. Considering the size of an average deer to be around 225-250 lb, this combination of rifle and bullet should be lethal on this game at 1000 yards. The rifle is a typical hunting rifle, capable of 1Ē groups at 100 yards. The times of flight for this bullet are 0.1024 seconds and 1.3157 seconds at 100 and 1000 yards, respectively. That means the smallest groups we can expect at 1000 yards are: 1 inch times 1.3157/0.1024 = 12.9 inches. Over 1000 yards, the wind will be harder to judge than over a short range, possibly blowing with different speed and direction at several points between the shooter and target. Weíll assume +/- 4 mph of crosswind uncertainty for this example. Iíll skip the component build up this time and go straight to the impact zone probability contour.

The top of Figure 15.3 shows the size and shape of the impact zone and the probability rings. As you can see, the innermost ring is about 15.4Ē wide and 5Ē tall. Thatís already bigger than the vital area of the deer and thereís only a 67% chance of hitting in that ring! The bottom half of Figure 15.3 shows the 99% ring which is 46Ē wide and over 15Ē tall. Remember that this picture is for a rifle/bullet combo that has way above average ballistics and is meant for long range shooting. If the rifle were a .308 Winchester with 168 grain bullets, the impact zone would be much larger. Even with the terrific ballistic performance of the 7mm Remington Magnum with super high BC bullets and relatively low variation in both muzzle velocity and wind uncertainty, thereís still a good chance you miss will the deer completely or hit it in a non vital area, wounding the animal.

Also remember that this analysis assumes that all of the deterministic variables are completely and accurately accounted for. At this range, if the sights are canted by 5 degrees, the entire impact area will be shifted over 21Ē to the side! Thereís also over 5Ē of spin drift, and donít even think about shooting from a less than a rock solid supported position.
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Iím not presenting these sobering facts about the realities of long range hunting to discourage you from trying it, but to illustrate the need for complete attention to detail. If the loads for the 7mm Remington Magnum were refined a little more to reduce the muzzle velocity variation and improve the accuracy; shots were only taken in no wind or very low wind scenarios; all of the other deterministic variables were perfectly measured and accounted for; and the shot perfectly executed, it is possible to hit deer sized targets at 1000 yards on the first shot. However, you had better know what youíre doing, and put in the time on the range practicing and learning about all the variables if you expect to make successful shots on game at 1000 yards. It is possible, but itís not a stunt and you shouldnít risk making a shot that might wound the animal if itís beyond the range youíve practiced at and are comfortable shooting.

Applied Ballistics For Long Range Shooting
Applied Ballistics For Long Range Shooting
Figure 15.3. Impact area under only the influence of the non-deterministic variables.

Bryan Litz majored in Aerospace Engineering at Penn State University and worked on air-to-air missile design for 6 years in the US Air Force before taking a job as Berger Bullets Chief Ballistician in November 2008. Bryan is now 29 years old, and has been an avid long range shooter since the age of 15. In particular, Bryan enjoys NRA Long Range Prone Fullbore/Palma competition and is the current National Palma Champion. Bryan is also a husband and proud father of 3.

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