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 are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one arcminute is 1/21600 of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth circumference is very near 21600 nmi. A minute of arc is π/10800 of a radian.
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or half-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects, so parallax can be used to determine distances.
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. The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing.
A spotting scope is a compact high-power telescope optimized for detailed observation of distant objects. They are used as portable optical enhancement devices for various outdoor activities such as birdwatching, skygazing and other naturalist activities, for hunting and target shooting to verify a marksman's shot placements, for tactical ranging and surveillance, and for any other application that requires higher magnification than ordinary binoculars.
In trigonometry, the gradian, also known as the gon, grad, or grade, is a unit of measurement of an angle, defined as one hundredth of the right angle; in other words, there are 100 gradians in 90 degrees. It is equivalent to 1/400 of a turn, 9/10 of a degree, or π/200 of a radian. Measuring angles in gradians is said to employ the centesimal system of angular measurement, initiated as part of metrication and decimalisation efforts.
A reticle, or reticule also known as a graticule, is a pattern of fine lines or markings built into the eyepiece of an optical device such as a telescopic sight, spotting scope, theodolite, optical microscope or the screen of an oscilloscope, to provide measurement references during visual inspections. Today, engraved lines or embedded fibers may be replaced by a digital image superimposed on a screen or eyepiece. Both terms may be used to describe any set of patterns used for aiding visual measurements and calibrations, but in modern use reticle is most commonly used for weapon sights, while graticule is more widely used for non-weapon measuring instruments such as oscilloscope display, astronomic telescopes, microscopes and slides, surveying instruments and other similar devices.
A telescopic sight, commonly called a scope informally, is an optical sighting device based on a refracting telescope. It is equipped with some form of a referencing pattern – known as a reticle – mounted in a focally appropriate position in its optical system to provide an accurate point of aim. Telescopic sights are used with all types of systems that require magnification in addition to reliable visual aiming, as opposed to non-magnifying iron sights, reflector (reflex) sights, holographic sights or laser sights, and are most commonly found on long-barrel firearms, particularly rifles, usually via a scope mount. The optical components may be combined with optoelectronics to add night vision or smart device features.
A milliradian 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 the angle of the sight compared to the barrel. Milliradians are also used for comparing shot groupings, or to compare the difficulty of hitting different sized shooting targets at different distances. When using a scope with both mrad adjustment and a reticle with mrad markings, the shooter can use the reticle as a ruler to count the number of mrads a shot was off-target, which directly translates to the sight adjustment needed to hit the target with a follow up shot. Optics with mrad markings in the reticle can also be used to make a range estimation of a known size target, or vice versa, to determine a target size if the distance is known, a practice called "milling".
Tacheometry is a system of rapid surveying, by which the horizontal and vertical positions of points on the earth's surface relative to one another are determined without using a chain or tape, or a separate levelling instrument. Instead of the pole formerly employed to mark a point, a staff similar to a level staff is used. This is marked with heights from the base or foot, and is graduated according to the form of tacheometer in use.
A filar micrometer is a specialized eyepiece used in astronomical telescopes for astrometry measurements, in microscopes for specimen measurements, and in alignment and surveying telescopes for measuring angles and distances on nearby objects. The word filar derives from Latin filum 'a thread'. It refers to the fine threads or wires used in the device.
Stadia marks, also called stadia lines or stadia hairs, are crosshairs on the reticle of a theodolite or other surveying instrument that allow stadiametric rangefinding.
Reflecting instruments are those that use mirrors to enhance their ability to make measurements. In particular, the use of mirrors permits one to observe two objects simultaneously while measuring the angular distance between the objects. While reflecting instruments are used in many professions, they are primarily associated with celestial navigation as the need to solve navigation problems, in particular the problem of the longitude, was the primary motivation in their development.
A stereoscopic rangefinder or stereoscopic telemeter is an optical device that measures distance from the observer to a target, using the observer's capability of binocular vision. It looks similar to a coincidence rangefinder, which uses different principles and has only one eyepiece. German instruments tended to use the stereoscopic principle while British ones used coincidence.
The PSO-1 is a 4×24 telescopic sight manufactured in Russia by the Novosibirsk instrument-making factory and issued with the Russian military Dragunov sniper rifle. It was introduced on 3 July 1963 together with the Dragunov sniper rifle.
A red dot sight is a common classification for a type of non-magnifying reflector sight for firearms, and other devices that require aiming, that gives the user a point of aim in the form of an illuminated red dot. A standard design uses a red light-emitting diode (LED) at the focus of collimating optics which generates a dot-style illuminated reticle that stays in alignment with the weapon the sight is attached to, regardless of eye position.
In trigonometry, a skinny triangle is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians. The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions or tables can be entirely dispensed with.
In forestry, a tree crown measurement is one of the tree measurements taken at the crown of a tree, which consists of the mass of foliage and branches growing outward from the trunk of the tree. The average crown spread is the average horizontal width of the crown, taken from dripline to dripline as one moves around the crown. The dripline is the outer boundary to the area located directly under the outer circumference of the tree branches. When the tree canopy gets wet, any excess water is shed to the ground along this dripline. Some listings will also list the maximum crown spread which represents the greatest width from dripline to dripline across the crown. Other crown measurements that are commonly taken include limb length, crown volume, and foliage density. Canopy mapping surveys the position and size of all of the limbs down to a certain size in the crown of the tree and is commonly used when measuring the overall wood volume of a tree.
In shooting sports, 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 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 is a measure of accuracy.
