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shooting sports Shooting sports is a group of competitive and recreational sporting activities involving proficiency tests of accuracy, precision and speed in shooting — the art of using ranged weapons, mainly small arms (firearms and airguns, in forms such ...
, a shot grouping, or simply group, is the collective pattern of projectile impacts on a target from multiple consecutive shots taken in one shooting session. The ''tightness'' of the grouping (the proximity of all the shots to each other) is a measure of the precision of a weapon, and a measure of the shooter's consistency and skill. On the other hand, the grouping ''displacement'' (the distance between the calculated group center and the intended point of aim) is a measure of 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
millimeter file:EM Spectrum Properties edit.svg, 330px, Different lengths as in respect to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 meter to 1 millimeter. The millimetre (American and British Eng ...
s or
inch Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelft ...
es. Often that measurement is converted into angular measurements such as milliradians ("mils" or "mrads") or 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. In shotgun shooting, the grouping is also called the ''pattern'' or "''spread''". The pattern indicates the extent of scattering by shots from a single 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. 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 Form is the shape, visual appearance, or configuration of an object. In a wider sense, the form is the way something happens. Form also refers to: * Form (document), a document (printed or electronic) with spaces in which to write or enter dat ...
.


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. The process of mechanically readjusting the 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 A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...
that can be drawn to contain all the shots, 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 Gust may refer to: People Given name * Gust Avrakotos (1938–2005), CIA case officer known for the arming of Afghanistan's Mujahideen against the Soviet invasion under Operation Cyclone * Gust Hagberg (19th-century–20th-century) * Gust Kunde ...
"), 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 A bullet is a kinetic projectile, a component of firearm ammunition that is shot from a gun barrel. Bullets are made of a variety of materials, such as copper, lead, steel, polymer, rubber and even wax. Bullets are made in various shapes and ...
/ pellet weight and aerodynamics, propellant load and efficiency, muzzle velocity). 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. While target shooting with a
handgun A handgun is a short- barrelled gun, typically a firearm, that is designed to be usable with only one hand. It is distinguished from a long gun (i.e. rifle, shotgun or machine gun, etc.), which needs to be held by both hands and also brac ...
, 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.


Metric units

When using the SI or metric units, shooting accuracy is more easily measured in milliradians ("mil" or "mrad" for short), which is an arc-based angular unit corresponding to 1/1,000th of a radian, and mathematically a direct ratio between the length of a circular arc and its
radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
. When imagining the shooter as the center of a
two-dimensional In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise ...
circle, and his lines of sight as
ray Ray may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), a bony or horny spine on a fin Science and mathematics * Ray (geometry), half of a line proceeding from an initial point * Ray (g ...
s 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
millimeter file:EM Spectrum Properties edit.svg, 330px, Different lengths as in respect to the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 meter to 1 millimeter. The millimetre (American and British Eng ...
s (or in centimeters and then
multiplying Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition ...
by a
conversion factor Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Overview The process ...
of 10) and the distance to target 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 = \frac = \frac \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 = \text = \text 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 An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistic ...
of assuming that 0.1 mil (the typical click value on mil-based adjustment wheels) equals " at 100 meters" is about % (or %). 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 ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services ...
, which involves multiplication with the irrational mathematical constant : :\text = \frac \times 10800 = \frac \times \frac \approx \frac \times 3.43774677 In the above formula, "1000" is the
conversion factor Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Overview The process ...
between meters and millimeters; "10800" is how many arcminutes are within a 180-degree semicircle, whose
arc length ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services ...
is " × r" and "r" corresponds to the distance in meters. And conversely: :\text = \frac = \frac \approx 29.08882 \approx \text 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
imperial units The imperial system of units, imperial system or imperial units (also known as British Imperial or Exchequer Standards of 1826) is the system of units first defined in the British Weights and Measures Act 1824 and continued to be developed th ...
, shooting accuracy is more easily measured in minutes of arc or
arcminute A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
s (symbol ′, also called "minutes of angle", or "MOA" for short), which is an angular unit equal to 1/60th of a
degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathemati ...
. A full 360-degree circle surrounding a shooter therefore always has 360 × 60 = 21,600 arcminutes, and a semi-circle always has 10,800 arcminutes. By measuring the grouping size as a short arc (measured in
inch Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelft ...
es) on a circle whose
radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
corresponds to the distance to target (measured in yards), the angular measurement can be calculated using simple
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
: :\text = \frac \times 10800 = \frac \times \frac \approx \frac In the above formula, "36" is the
conversion factor Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Overview The process ...
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 = \frac = \frac \approx 1.04719755 \approx \text 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, roughly the size of a dollar coin. This coincidentally can be
rounded Round or rounds may refer to: Mathematics and science * The contour of a closed curve or surface with no sharp corners, such as an ellipse, circle, rounded rectangle, cant, or sphere * Rounding, the shortening of a number to reduce the num ...
down to just 1 inch, and the
round-off error A roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are d ...
of assuming 1 MOA equals "1 inch at 100 yards" is about 4.5%, which is considered acceptable in most shooting applications.


Benchmarks

A big-game hunting rifle is considered accurate if its shots fall within 1.5 MOA (≈ 0.5mil), while a rifle intended for small animals is expected to have an accuracy of 1 MOA or less (under 0.3mil, also known as "sub-MOA").
Handgun A handgun is a short- barrelled gun, typically a firearm, that is designed to be usable with only one hand. It is distinguished from a long gun (i.e. rifle, shotgun or machine gun, etc.), which needs to be held by both hands and also brac ...
s are typically less accurate; at a shooting distance of 25yd, a grouping is considered acceptable for
self-defense Self-defense (self-defence primarily in Commonwealth English) is a countermeasure that involves defending the health and well-being of oneself from harm. The use of the right of self-defense as a legal justification for the use of force ...
if the shots fall within a circle of 4 to 5 inches, which is 15 to 19 MOA (equivalent to a grouping of 100-150mm at 25 meters, which is 4-6 mils), representing the shot pattern needed to hit the vital organs of a human target. Expensive and well-machined 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 30mm at 25 meters, which is 1.2 mil).


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
arrow An arrow is a fin-stabilized projectile launched by a bow. A typical arrow usually consists of a long, stiff, straight shaft with a weighty (and usually sharp and pointed) arrowhead attached to the front end, multiple fin-like stabilizers ...
s are grouping on target but off center, this shows consistent basic form, with better results achievable after slight adjustments. 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.


Example groupings

File:Nra-b3-targ-kimber-raptor.jpg, Handgun and paper target showing grouping of ten shots File:Offhandgroup25.jpg, A grouping made with a five-shot revolver File:Paper Target.jpg, Eight-shot grouping File:Glock31 220510.jpg, Multiple shots from a semi-automatic handgun File:Archery practice.jpeg, Arrow grouping with fairly consistent results but slightly off center


References

{{DEFAULTSORT:Firearm shot grouping Firearm terminology Grouping