MINUTE OF ARC

A 'minute of arc', 'arcminute', or 'MOA' is a unit of angular measurement, equal to one sixtieth (1/60) of one degree. ^[1] Since one degree is defined as one three hundred sixtieth (1/360) of a circle, 1 MOA is 1/21600 of the amount of arc in a closed circle, or (π/10800) radians. It is used in those fields which require a unit for the expression of small angles, such as astronomy. The SI symbol for marking the arcminute is the prime (′) (U+2032), though a single quote (') (U+0027) is commonly used where only ASCII characters are permitted. One arcminute is written 1′ (or 1'''''). It is also abbreviated as 'arcmin' or 'amin' or, less commonly, the prime with a circumflex over it ($hat\{\text{'}\}$).
The subdivision of the minute of arc is the 'second of arc', or 'arcsecond'. There are 60 arcseconds in an arcminute. Therefore, the arcsecond is 1/1296000 of a circle, or (π/648000) radians, which is approximately 1/206265 radian. The symbol for the arcsecond is the double prime (″) (U+2033). To express even smaller angles, standard SI prefixes can be employed; in particular, the 'milliarcsecond', abbreviated 'mas', is sometimes used in astronomy.

Contents

Uses

Firearms

Cartography

Astronomy

Human vision

References

Uses

Firearms

This unit is commonly found in the firearms industry and literature, particularly that concerning the accuracy of rifles. People in that industry tend to refer to it as ''minute of angle'' rather than ''minute of arc''. It is popular because 1 MOA subtends approximately one inch at 100 yards, a traditional distance on target ranges. A shooter can easily readjust his rifle scope by measuring the distance in inches the bullet hole is from the desired impact point, and adjusting the scope that many MOA in the same direction. Most target scopes designed for long distances are adjustable in quarter (¼) or eighth (⅛) MOA "clicks". One eighth MOA is equal to approximately an eighth of an inch at 100 yards or one inch at 800 yards.
Calculating the physical equivalent group size equal to one minute of arc can be done using the equation: equivalent group size = tan(MOA ∕ 60)
★ distance. In the example previously given and substituting 3600 inches for 100 yards, tan(1 MOA ∕ 60)∙ 3600 inches = 1.04719756 inches.
Sometimes, a firearm's accuracy will be measured in MOA. This simply means that under ideal conditions, the gun is capable of repeatedly producing a group of shots whose center points (center-to-center) fit into a circle, the diameter of which can be subtended by that amount of arc. (E.g.: a "1 MOA rifle" should be capable, under ideal conditions, of shooting a 1-inch group at 100 yards, a "2 MOA rifle" a 2-inch group at 100 yards, etc.) Some manufacturers such as Weatherby and Cooper offer actual guarantees of real-world MOA performance.
Rifle manufacturers and gun magazines often refer to this capability as "Sub-MOA", meaning it shoots under 1 MOA. This is typically a single group of 3 to 5 shots at 100 yards, or the average of several groups. If larger samples are taken, IE more shots per group, then group size typically increases. ^[2]

Cartography

Minutes of angle (and its subunit, seconds of angle or SOA—equal to a sixtieth of a MOA) are also used in cartography and navigation. At sea level, one minute of angle (around a great circle such as the equator or a meridian) equals about 1.15 miles or 1.86 km, approximately one nautical mile (approximately, because the Earth is slightly oblate).
Traditionally positions are given using degrees, minutes, and seconds of angles in two measurements: one for latitude, the angle north or south of the equator; and one for longitude, the angle east or west of the Prime Meridian. Using this method, any position on or above the face of the Earth can be precisely given. However, because of the somewhat clumsy base-60 nature of MOA and SOA, many people now prefer to give positions using degrees only, expressed in decimal form to an equal amount of precision. Degrees, given to three decimal places (1/1000 of a degree), give almost as much precision as degrees-minutes-seconds (1/3600 of a degree).

Astronomy

Similarly to cartography above, astronomy also uses the arcminute and arcsecond. Degrees (and therefore arcminutes) are used to measure declination, or angular distance north or south of the celestial equator. The arcsecond is also often used to describe parallax, due to very small parallax angles, and tiny angular diameters (e.g. Venus varies between 10″ and 60″). The parallax, proper motion and angular diameter of a star may also be written in milli-arcseconds (mas), or thousandths of an arcsecond.

Human vision

In humans, the ability to resolve a spatial pattern separated by a visual angle of one minute of arc is considered normal visual acuity.^[3]

References

1. http://wordnet.princeton.edu/perl/webwn?s=minute%20of%20arc
2. http://www.bobwheeler.com/guns/GroupStat.pdf
3. ''Guns and Shooting Online'', Chuck Hawks