Shot grouping

Two shot groupings obtained with different firearms at different distances.
The group on the left measures about 13 mm and was fired at about 45 meters, which equals 13 mm45 m = 0.29 mils (1⁄2 in group at 50 yards, approx. 1.047′×50/100 = 0.524′).
The group on the right measures about 7 mm and was fired at about 90 meters, which equals 7 mm90 m = 0.08 mils (0.3 in group at 100 yards, approx. 1.047′×0.3 = 0.314′).

In

accuracy

.

Tightness of shot groupings are calculated by measuring the maximum distance between any two bullet holes on the target (center-to-center) in length measurements such as

minutes of angle

(MOAs), which expresses the size of shot scatter regardless of the target distance. Thus, by using angular measurements, one can reliably compare the relative tightness of shot groupings fired at different distances.

Uses of the term

For firearms that shoot one round at a time, a shot grouping test can be used to measure the accuracy of the entire shooting system: the weapon's mechanical precision and the uniformity of the ammunition. The weapon is fixed into position on a test mount, and aimed at a target. Multiple shots using rounds from the same type and batch are fired to observe how the weapon groups the shots. If a person holds the weapon and shoots it, the grouping measures the combination of the person's skill and the weapon's accuracy.^[2]

In

shotshell, measured as the smallest circle containing all the shots on the target. The barrel of a shotgun is choked to deliver a wider or narrower scattering, depending on the expected use. Shooting at close range indicates a cylinder bore barrel to deliver a wide grouping, while for hunting at longer distances such as 50 yards or meters, a choke is recommended to constrict the scattering for a tighter pattern.^[3]

In archery, a shot grouping is the result of one person shooting multiple arrows at a target. A tight grouping indicates consistency in the archer's form.^[4]

Firearms

Mean point of impact (MPI) is the calculated center of the grouping, which is the average center of all the shots, and is not necessarily located at a hole in the target.

gunsight's point of aim to match the MPI is called sighting in or "zeroing" the gun. The size of the grouping is described as the diameter of the smallest circle that can be drawn to contain all the shots,^[5]

typically only measured from the center points of each impact (known as "center-to-center size").

A "flier" is a shot from the same shooting session that is distinctly farther from the general grouping, considered to be the outlier of the group. Such shots may be the result of trajectory deviation caused by unexpected changes in wind condition (known as a "wind shift" or "gust"), a muscular flinch of the shooter at the time of the trigger pull, a problem with the firearm mechanism, poor tuning of barrel harmonics, or inconsistency in the ammunition (e.g. bullet/pellet weight and aerodynamics, propellant load and efficiency, muzzle velocity).^[6] Infrequent single fliers may be discounted when evaluating large cohorts, but if random fliers occur often, then the problem is considered significant and should be traced to its origin.^[2]

While target shooting with a handgun, if a grouping is consistently off-center then the shooter is instructed to alter the body angle or the stance, rather than shifting the arm, wrist or hand, which should remain in position.^[7]

Metric units

When using the

rays

projecting from that center, the group size can be geometrically considered a very short length of arc, and the distance to the target as the radius.

By measuring the group size in

meters, the numerical conversion between radians and milliradians is cancelled out, and the angular measurement can be very easily calculated as a simple division

:

{\text{group size in milliradians}}={\frac {\text{group size in millimeters (mm)}}{\text{distance in meters (m)}}}={\frac {\text{group size in centimeters (cm)}}{\text{distance in meters (m)}}}\times 10

And conversely, the group size of 1 milliradian at 100 meters (the default metric sighting-in distance) can be determined just as easily:

{\text{1 milliradian at 100 meters distance}}={\text{100 millimeters}}={\text{10 centimeters}}

Since shot grouping are very small angles, the linear formula above can be used as an extremely good approximation for group sizes in milliradians. The error of assuming that 0.1 mil (the typical click value on mil-based adjustment wheels) equals "10 mm (1 cm) at 100 meters" is about 1×10⁻⁷% (or 0.0000001%).

Metric units can also be used to calculate group sizes in

minutes of arc, though this is mathematically inconvenient due to the need to convert between central angle and arc length, which involves multiplication with the irrational mathematical constant

π

:

{\text{group size in arcminutes}}={\frac {\text{group size in millimeters}}{{\text{distance in meters}}\times 1000\times \pi }}\times 10800={\frac {\text{group size in millimeters}}{\text{distance in meters}}}\times {\frac {10.8}{\pi }}\approx {\frac {\text{group size in millimeters}}{\text{distance in meters}}}\times 3.43774677

In the above formula, "1000" is the

conversion factor between meters and millimeters; "10800" is how many arcminutes are within a 180-degree semicircle, whose arc length

is "

π

× r" and "r" corresponds to the distance in meters.

And conversely:

{\text{1 arcminute at 100 meters distance}}={\frac {100\times 1000\times \pi }{10800}}={\frac {\pi }{0.108}}\approx 29.08882\approx {\text{29 mm}}

Therefore, at 100 m, a 1 MOA group can be represented approximately by a 29 mm circle, slightly smaller than a half dollar coin.

Imperial units

When using

semi-circle

always has 10,800 arcminutes.

By measuring the grouping size as a short

arc (measured in inches) on a circle whose radius corresponds to the distance to target (measured in yards), the angular measurement can be calculated using simple geometry

:

{\text{group size in arcminutes}}={\frac {\text{group size in inches}}{{\text{distance in yards}}\times 36\times \pi }}\times 10800={\frac {\text{group size in inches}}{\text{distance in yards}}}\times {\frac {300}{\pi }}\approx {\frac {\text{group size in inches}}{{\text{distance in yards}}\times 0.010472}}

In the above formula, "36" is the

conversion factor

between yards and inches.

Conversely, the group size of 1 arcminute at 100 yards (the most commonly used sighting-in distance in North America) can also be calculated:

{\text{1 arcminute at 100 yards distance}}={\frac {100\times 36\times \pi }{10800}}={\frac {\pi }{3}}\approx 1.04719755\approx {\text{1 inch}}

The linear formula above for measuring group sizes using arcminutes with imperial units is less precise than using milliradians with metric units, but can still be a good approximation depending on the demands for precision. When shooting at a target 100 yards away, a 1 MOA group is a circle of approximately 1.047 inch diameter,

coincidentally can be rounded down to just 1 inch, and the round-off error

of assuming 1 MOA equals "1 inch at 100 yards" is about 4.5%, which is considered acceptable in most shooting applications.

Benchmarks

A

match-grade pistols demonstrate a higher accuracy than normal handguns, capable of groupings of 1.25 inches at 25 yards, which is about 5 MOA (equivalent to about 30 mm at 25 meters, which is 1.2 mil).^[10]

Archery

With the increased element of human skill in archery, a grouping on target is more a measure of the archer's skill. If an archer is not getting a consistent grouping, then their basic form needs work. If an archer's arrows are grouping on target but off center, this shows consistent basic form, with better results achievable after slight adjustments.^[4]^[11]

On the equipment side, bow stabilizers have been used since the 1960s by tournament competitors and by bow hunters to counteract the torque of shooting the arrow. A tighter grouping may be achieved with such a stabilizer, which adds mass extending outward on a moment arm, usually mounted perpendicular to the bow riser, aligned with the arrow path.^[12]^[13]^[14]

Example groupings

Handgun and paper target showing grouping of ten shots
A grouping made with a five-shot revolver
Eight-shot grouping
Multiple shots from a semi-automatic handgun
Arrow grouping with fairly consistent results but slightly off center
Long Range Sniper Rifle Grouping

References

^
ISBN 978-0-9722804-2-6
.

^
ISBN 978-1-4402-3897-0
.

^ Moller, Cliff. "Understanding Shotgun Chokes, A brief explanation by Briley". Briley Manufacturing. Archived from the original on July 29, 2015. Retrieved August 10, 2015.
^
ISBN 978-0-7360-5501-7
.

ISBN 978-0-9707493-9-0
.

ISBN 9781628733006
.

ISBN 978-1-60239-086-7
.

^ Dexadine Ballistics Software - ballistic data for shooting and reloading

ISBN 978-0-89689-938-4
.

ISBN 978-0-89689-684-0
.

ISBN 978-1-4504-4468-2
.

ISBN 978-1-62873-012-8
.

^ Haywood and Lewis 2013, p. 15.

ISBN 978-0-7360-4634-3
.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Shot_grouping&oldid=1212209918"

[Matunas2003-1] 
ISBN 978-0-9722804-2-6
.

[Watson2014-2] 
ISBN 978-1-4402-3897-0
.

[3] Moller, Cliff. "Understanding Shotgun Chokes, A brief explanation by Briley". Briley Manufacturing. Archived from the original on July 29, 2015. Retrieved August 10, 2015.

[Engh2005-4] 
ISBN 978-0-7360-5501-7
.

[5] ISBN 978-0-9707493-9-0
.

[6] ISBN 9781628733006
.

[7] ISBN 978-1-60239-086-7
.

[8] Dexadine Ballistics Software - ballistic data for shooting and reloading

[9] ISBN 978-0-89689-938-4
.

[10] ISBN 978-0-89689-684-0
.

[11] ISBN 978-1-4504-4468-2
.

[12] ISBN 978-1-62873-012-8
.

[13] Haywood and Lewis 2013, p. 15.

[14] ISBN 978-0-7360-4634-3
.

[2]

[3]

[4]

[5]

[6]

[7]

[10]

[11]

[12]

[13]

[14]