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 are also known as plane angles as they 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.
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another. The field of navigation includes four general categories: land navigation, marine navigation, aeronautic navigation, and space navigation.
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with magnetic north. Other methods may be used, including gyroscopes, magnetometers, and GPS receivers.
An azimuth is the angular measurement in a spherical coordinate system which represents the horizontal angle from a cardinal direction, most commonly north.
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.
In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:
A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
Magnetic declination is the angle between magnetic north and true north at a particular location on the Earth's surface. The angle can change over time due to polar wandering.
The basic principles of air navigation are identical to general navigation, which includes the process of planning, recording, and controlling the movement of a craft from one place to another.
In geography and geodesy, a meridian is the locus connecting points of equal longitude, which is the angle east or west of a given prime meridian. In other words, it is a line of longitude. The position of a point along the meridian is given by that longitude and its latitude, measured in angular degrees north or south of the Equator. On a Mercator projection or on a Gall-Peters projection, each meridian is perpendicular to all circles of latitude. A meridian is half of a great circle on Earth's surface. The length of a meridian on a modern ellipsoid model of Earth has been estimated as 20,003.93 km (12,429.87 mi).
A nephoscope is a 19th-century instrument for measuring the altitude, direction, and velocity of clouds, using transit-time measurement. This is different from a nephometer, which is an instrument used in measuring the amount of cloudiness.
Magnetic deviation is the error induced in a compass by local magnetic fields, which must be allowed for, along with magnetic declination, if accurate bearings are to be calculated.
In geology, strike and dip is a measurement convention used to describe the plane orientation or attitude of a planar geologic feature. A feature's strike is the azimuth of an imagined horizontal line across the plane, and its dip is the angle of inclination measured downward from horizontal. They are used together to measure and document a structure's characteristics for study or for use on a geologic map. A feature's orientation can also be represented by dip and dip direction, using the azimuth of the dip rather than the strike value. Linear features are similarly measured with trend and plunge, where "trend" is analogous to dip direction and "plunge" is the dip angle.
Diver navigation, termed "underwater navigation" by scuba divers, is a set of techniques—including observing natural features, the use of a compass, and surface observations—that divers use to navigate underwater. Free-divers do not spend enough time underwater for navigation to be important, and surface supplied divers are limited in the distance they can travel by the length of their umbilicals and are usually directed from the surface control point. On those occasions when they need to navigate they can use the same methods used by scuba divers.
A circumferentor, or surveyor's compass, is an instrument used in surveying to measure horizontal angles. It was superseded by the theodolite in the early 19th century.
A hand compass is a compact magnetic compass capable of one-hand use and fitted with a sighting device to record a precise bearing or azimuth to a given target or to determine a location. Hand or sighting compasses include instruments with simple notch-and-post alignment ("gunsights"), prismatic sights, direct or lensatic sights, and mirror/vee (reflected-image) sights. With the additional precision offered by the sighting arrangement, and depending upon construction, sighting compasses provide increased accuracy when measuring precise bearings to an objective.
Position resection and intersection are methods for determining an unknown geographic position by measuring angles with respect to known positions. In resection, the one point with unknown coordinates is occupied and sightings are taken to the known points; in intersection, the two points with known coordinates are occupied and sightings are taken to the unknown point.
The rule of marteloio is a medieval technique of navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to plot the traverse between two different navigation courses by means of resolving triangles with the help of the Toleta and basic arithmetic.
While compass surveying, the magnetic needle is sometimes disturbed from its normal position under the influence of external attractive forces. Such a disturbing influence is called as local attraction. The external forces are produced by sources of local attraction which may be current carrying wire or metal objects. The term is also used to denote amount of deviation of the needle from its normal position. It mostly causes errors in observations while surveying and thus suitable methods are employed to negate these errors.
Burt's solar compass or astronomical compass/sun compass is a surveying instrument that makes use of the Sun's direction instead of magnetism. William Austin Burt invented his solar compass in 1835. The solar compass works on the principle that the direction to the Sun at a specified time can be calculated if the position of the observer on the surface of the Earth is known, to a similar precision. The direction can be described in terms of the angle of the Sun relative to the axis of rotation of the planet.
