# Difference between revisions of "What is Precision?"

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* Ammunition: Irregularities in its dimensions and their fit to the gun's chamber can introduce yaw moments that begin as soon as the bullet starts to move. Variations in powder charge and burning can affect muzzle velocity and introduce dispersion in barrel harmonics. Sample imbalances and dimensional variation in the bullets themselves can affect their trajectory. | * Ammunition: Irregularities in its dimensions and their fit to the gun's chamber can introduce yaw moments that begin as soon as the bullet starts to move. Variations in powder charge and burning can affect muzzle velocity and introduce dispersion in barrel harmonics. Sample imbalances and dimensional variation in the bullets themselves can affect their trajectory. | ||

* Shooter: An ideal shooter can sight the gun to the exact same point each shot, and can apply the same forces to every point of contact. Any deviation from this ideal shows up as added shot dispersion. | * Shooter: An ideal shooter can sight the gun to the exact same point each shot, and can apply the same forces to every point of contact. Any deviation from this ideal shows up as added shot dispersion. | ||

+ | |||

+ | Note that error propagates through the system, and in general we expect Variance<sub>System</sub> = Variance<sub>Gun</sub> + Variance<sub>Ammunition</sub> + Variance<sub>Shooter</sub>. | ||

= Reference Values = | = Reference Values = |

## Revision as of 16:39, 22 April 2015

# Precision vs Accuracy

Before going any further we need to distinguish precision from accuracy, and show why we care so much about the former, but won't be dealing with the latter at all. Note that here we use the specific statistical meaning of these terms, even though in casual usage they are often sloppily interchanged.

**Accuracy** refers to how well shot groups are centered on a target, and is essentially a problem of sighting-in a shooting system. **Precision** describes the spread of individual shots about the center point of a shot group. A precise shooting system will, over many shots to and from the same points, produce a tight shot group with *smaller* distances between individual shots than a less precise system. If the shot group doesn’t center on the desired target the gun merely needs to have its point of aim adjusted. I.e., *accuracy is dialed in*. But you can't just dial more precision into a shooting system.

(NB: At longer distances wind can introduce errors in both accuracy and precision. Shooters who can compensate for wind will apparently have higher precision, but we prefer to say they are reducing the error term that the wind adds on top of the intrinsic precision of their system, which is independent of the distance shot.)

Note also that precision shooters will often intentionally align their sights so that groups do *not* center on their aiming point so that their aiming point isn't degraded or "shot out" for subsequent shots. For example, a common load development target is the one shown here on the left: The shooter aims for the bullseye, but sights the rifle high so that impacts are in the square box above it.

# Precision in Shooting

When we talk about shooting systems and their precision we may be talking about a gun, ammunition, shooter, or a combination of all three. On one extreme are devices like rail guns, which are little more than barrels clamped in a rigid machine rest, and which are typically built to such fine tolerances that their extraordinary shooting precision is determined primarily by the quality and fit of ammunition. More common firearms can exhibit variability in production and operation that outweigh the dispersion inherent in high-quality ammunition. An inexperienced shooter, or even an experienced shooter who has to fire from an unsupported position, will typically add dispersion to the shot pattern greater than that produced by a good gun or ammunition. Finally, distance to target can introduce significant error sources like wind and mirage that aren’t a factor at short or indoor ranges.

Therefore, when we talk about precision it is important to qualify the system being tested: If it’s a competent shooter with a good sight shooting from his preferred supported position the dominant factor will probably be the gun and ammunition. If ammunition is match-grade factory or, better yet, custom-loads tuned to the gun, then the gun is probably the limiting factor in precision. On the other hand, precise guns are often handicapped by the quality of ammunition fed to them. Finally, if instead of shooting 100-yard targets on a calm day the target is shot at 1000 yards with significant winds then the shooter’s ability to read wind may be the dominant source of precision.

An ideal shooting system would have zero dispersion, or perfect precision. In reality, when shooting from a fixed position at a fixed target we will observe dispersion, significant sources of which include:

- The gun: from irregularities in how it reacts to firing stress to how consistently it stabilizes and points the bullet from the muzzle. Defects in its sighting system can also contribute to dispersion.
- Ammunition: Irregularities in its dimensions and their fit to the gun's chamber can introduce yaw moments that begin as soon as the bullet starts to move. Variations in powder charge and burning can affect muzzle velocity and introduce dispersion in barrel harmonics. Sample imbalances and dimensional variation in the bullets themselves can affect their trajectory.
- Shooter: An ideal shooter can sight the gun to the exact same point each shot, and can apply the same forces to every point of contact. Any deviation from this ideal shows up as added shot dispersion.

Note that error propagates through the system, and in general we expect Variance_{System} = Variance_{Gun} + Variance_{Ammunition} + Variance_{Shooter}.

# Reference Values

At National Bench Rest competitions it is common to see rail guns, which practically remove shooter error from the equation, shoot 10-round groups measuring less than .3MOA in diameter, and bench-rest rifles with custom loads handled by experts shoot 5-round groups with the same precision.

The requirement for the U.S. military’s Precision Sniper Rifle is fifty 10-round groups, 80% of which must show less than 1MOA vertical spread at 1500 meters, and none of which may show more than 1.5MOA vertical spread.

Federal specifies that its XM193 ammunition exhibit three 10-round groups not to exceed 4.00” mean radius maximum average at 200 yards.

Next: Describing Precision