In
shooting sports, a shot grouping, or simply group, is the collective pattern of
projectile impact
Impact may refer to:
* Impact (mechanics), a high force or shock (mechanics) over a short time period
* Impact, Texas, a town in Taylor County, Texas, US
Science and technology
* Impact crater, a meteor crater caused by an impact event
* Impac ...
s on a
target
Target may refer to:
Physical items
* Shooting target, used in marksmanship training and various shooting sports
** Bullseye (target), the goal one for which one aims in many of these sports
** Aiming point, in field artillery, f ...
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
Precision, precise or precisely may refer to:
Science, and technology, and mathematics Mathematics and computing (general)
* Accuracy and precision, measurement deviation from true value and its scatter
* Significant figures, the number of digit ...
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
Accuracy and precision are two measures of ''observational error''.
''Accuracy'' is how close a given set of measurements ( observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each oth ...
.
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
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 English spelling differences#-re, -er, ...
s or
inches. Often that measurement is converted into
angular measurements such as
milliradian
A milliradian ( SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting t ...
s ("mils" or "mrads") or
minutes of angle
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of Angular unit, angular measurement equal to of one Degree (angle), degree. Since one degree is of a turn (geometry), turn (or complete rotat ...
(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 ]shot
Shot may refer to:
Arts, entertainment, and media
* ''Shot'' (album), by The Jesus Lizard
*''Shot, Illusion, New God'', an EP by Gruntruck
*'' Shot Rev 2.0'', a video album by The Sisters of Mercy
* "Shot" (song), by The Rasmus
* ''Shot'' (2017 f ...
s 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 data
...
.[
]
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 con ...
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"), a muscular flinch of the shooter at the time of the trigger
Trigger may refer to:
Notable animals and people
;Mononym
* Trigger (horse), owned by cowboy star Roy Rogers
;Nickname
* Trigger Alpert (1916–2013), American jazz bassist
* "Trigger Mike" Coppola (1900–1966), American gangster
;Surname
* Bru ...
pull, a problem with the firearm mechanism, poor tuning
Tuning can refer to:
Common uses
* Tuning, the process of tuning a tuned amplifier or other electronic component
* Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice
** Guitar tunings
** Piano tuning, adjusti ...
of barrel harmonics
A harmonic is a wave with a frequency that is a positive integer multiple of the '' fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', ...
, or inconsistency in the ammunition (e.g. bullet/ pellet weight and aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dy ...
, 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, 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 unit
The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Internati ...
s, shooting accuracy is more easily measured in milliradian
A milliradian ( SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). Milliradians are used in adjustment of firearm sights by adjusting t ...
s ("mil" or "mrad" for short), which is an arc-based angular unit
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles a ...
corresponding to 1/1,000th of a radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
, and mathematically a direct ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
between the length of a circular arc
Circular may refer to:
* The shape of a circle
* ''Circular'' (album), a 2006 album by Spanish singer Vega
* Circular letter (disambiguation)
** Flyer (pamphlet), a form of advertisement
* Circular reasoning, a type of logical fallacy
* Circular ...
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
Center or centre may refer to:
Mathematics
*Center (geometry), the middle of an object
* Center (algebra), used in various contexts
** Center (group theory)
** Center (ring theory)
* Graph center, the set of all vertices of minimum eccentrici ...
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 as ...
circle, and his lines of sight as 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 millimeter
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 English spelling differences#-re, -er, ...
s (or in centimeter
330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its deriveds scales. The Microwave are in-between 1 meter to 1 millimeter.
A centimetre (international spelling) or centimeter (American spellin ...
s and then multiplying by a conversion factor of 10) and the distance to target in meter
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
s, the numerical conversion between radians and milliradians is cancelled out, and the angular measurement can be very easily calculated as a simple division
Division or divider may refer to:
Mathematics
*Division (mathematics), the inverse of multiplication
*Division algorithm, a method for computing the result of mathematical division
Military
*Division (military), a formation typically consisting ...
:
:
And conversely, the group size of 1 milliradian at 100 meters (the default metric sighting-in distance) can be determined just as easily:
:
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 statistics ...
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
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 n ...
, though this is mathematically inconvenient due to the need to convert between central angle
A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc le ...
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
Irrationality is cognition, thinking, talking, or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. T ...
mathematical constant :
:
In the above formula, "1000" is the conversion factor between meters and millimeters; "10800" is how many arcminutes are within a 180-degree semicircle
In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180° (equivalently, radians, or a half-turn). It has only one line o ...
, 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:
:
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
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 n ...
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 n ...
s (symbol ′, also called "minutes of angle", or "MOA" for short), which is an angular unit
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles a ...
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 mathematics
...
. 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 inches) 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 yard
The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactly ...
s), 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 ...
:
:
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:
:
:
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 coincidental
A coincidence is a remarkable concurrence of events or circumstances that have no apparent causal connection with one another. The perception of remarkable coincidences may lead to supernatural, occult, or paranormal claims, or it may lead to ...
ly 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 big-game hunting
Big-game hunting is the hunting of large game animals for meat, commercially valuable by-products (such as horns/antlers, furs, tusks, bones, body fat/ oil, or special organs and contents), trophy/taxidermy, or simply just for recreation ...
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"). Handguns 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
Match grade frequently refers to quality firearm parts and ammunition that are suitable for a competitive match. Sometimes it also refers to other devices and parts that are made with high precision in mind.
Description
In firearms, the term is ...
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 arrows 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
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of ...
, 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