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96-568: The Struve Geodetic Arc is a chain of survey triangulations stretching from Hammerfest in Norway to the Black Sea , through ten countries and over 2,820 kilometres (1,750 mi), which yielded the first accurate measurement of a meridian arc . The chain was established and used by the German-born Russian scientist Friedrich Georg Wilhelm von Struve in the years 1816 to 1855 to establish

192-644: A geocentric coordinate frame. One such frame is WGS84 , as well as frames by the International Earth Rotation and Reference Systems Service ( IERS ). GNSS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. To monitor the Earth's rotation irregularities and plate tectonic motions and for planet-wide geodetic surveys, methods of very-long-baseline interferometry (VLBI) measuring distances to quasars , lunar laser ranging (LLR) measuring distances to prisms on

288-495: A plane table in 1551, but it is thought that the instrument was in use earlier as his description is of a developed instrument. Gunter's chain was introduced in 1620 by English mathematician Edmund Gunter . It enabled plots of land to be accurately surveyed and plotted for legal and commercial purposes. Leonard Digges described a theodolite that measured horizontal angles in his book A geometric practice named Pantometria (1571). Joshua Habermel ( Erasmus Habermehl ) created

384-406: A "reference frame" for the same. The ISO term for a datum transformation again is a "coordinate transformation". General geopositioning , or simply positioning, is the determination of the location of points on Earth, by myriad techniques. Geodetic positioning employs geodetic methods to determine a set of precise geodetic coordinates of a point on land, at sea, or in space. It may be done within

480-444: A GPS on large scale surveys make them popular for major infrastructure or data gathering projects. One-person robotic-guided total stations allow surveyors to measure without extra workers to aim the telescope or record data. A fast but expensive way to measure large areas is with a helicopter, using a GPS to record the location of the helicopter and a laser scanner to measure the ground. To increase precision, surveyors place beacons on

576-566: A coordinate system ( point positioning or absolute positioning ) or relative to another point ( relative positioning ). One computes the position of a point in space from measurements linking terrestrial or extraterrestrial points of known location ("known points") with terrestrial ones of unknown location ("unknown points"). The computation may involve transformations between or among astronomical and terrestrial coordinate systems. Known points used in point positioning can be GNSS continuously operating reference stations or triangulation points of

672-420: A country, usually documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements. In geometrical geodesy, there are two main problems: The solutions to both problems in plane geometry reduce to simple trigonometry and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in

768-477: A fixed base station and a second roving antenna. The position of the roving antenna can be tracked. The theodolite , total station and RTK GPS survey remain the primary methods in use. Remote sensing and satellite imagery continue to improve and become cheaper, allowing more commonplace use. Prominent new technologies include three-dimensional (3D) scanning and lidar -based topographical surveys. UAV technology along with photogrammetric image processing

864-423: A great step forward in the instrument's accuracy. William Gascoigne invented an instrument that used a telescope with an installed crosshair as a target device, in 1640. James Watt developed an optical meter for the measuring of distance in 1771; it measured the parallactic angle from which the distance to a point could be deduced. Dutch mathematician Willebrord Snellius (a.k.a. Snel van Royen) introduced

960-450: A height above sea level. As the surveying profession grew it created Cartesian coordinate systems to simplify the mathematics for surveys over small parts of the Earth. The simplest coordinate systems assume that the Earth is flat and measure from an arbitrary point, known as a 'datum' (singular form of data). The coordinate system allows easy calculation of the distances and direction between objects over small areas. Large areas distort due to

1056-418: A higher-order network. Traditionally, geodesists built a hierarchy of networks to allow point positioning within a country. The highest in this hierarchy were triangulation networks, densified into the networks of traverses ( polygons ) into which local mapping and surveying measurements, usually collected using a measuring tape, a corner prism , and the red-and-white poles, are tied. Commonly used nowadays

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1152-433: A known size. It was sometimes used before to the invention of EDM where rough ground made chain measurement impractical. Historically, horizontal angles were measured by using a compass to provide a magnetic bearing or azimuth. Later, more precise scribed discs improved angular resolution. Mounting telescopes with reticles atop the disc allowed more precise sighting (see theodolite ). Levels and calibrated circles allowed

1248-416: A large extent, Earth's shape is the result of rotation , which causes its equatorial bulge , and the competition of geological processes such as the collision of plates , as well as of volcanism , resisted by Earth's gravitational field. This applies to the solid surface, the liquid surface ( dynamic sea surface topography ), and Earth's atmosphere . For this reason, the study of Earth's gravitational field

1344-434: A loop pattern or link between two prior reference marks so the surveyor can check their measurements. Many surveys do not calculate positions on the surface of the Earth, but instead, measure the relative positions of objects. However, often the surveyed items need to be compared to outside data, such as boundary lines or previous survey's objects. The oldest way of describing a position is via latitude and longitude, and often

1440-618: A multi frequency phase shift of light waves to find a distance. These instruments eliminated the need for days or weeks of chain measurement by measuring between points kilometers apart in one go. Advances in electronics allowed miniaturization of EDM. In the 1970s the first instruments combining angle and distance measurement appeared, becoming known as total stations . Manufacturers added more equipment by degrees, bringing improvements in accuracy and speed of measurement. Major advances include tilt compensators, data recorders and on-board calculation programs. The first satellite positioning system

1536-509: A physical (real-world) realization of a coordinate system used for describing point locations. This realization follows from choosing (therefore conventional) coordinate values for one or more datum points. In the case of height data, it suffices to choose one datum point — the reference benchmark, typically a tide gauge at the shore. Thus we have vertical datums, such as the NAVD 88 (North American Vertical Datum 1988), NAP ( Normaal Amsterdams Peil ),

1632-410: A plan or map, and the points at the ends of the offset lines could be joined to show the feature. Traversing is a common method of surveying smaller areas. The surveyors start from an old reference mark or known position and place a network of reference marks covering the survey area. They then measure bearings and distances between the reference marks, and to the target features. Most traverses form

1728-406: A point inside a triangle using the angles cast between the vertices at the unknown point. These could be measured more accurately than bearings of the vertices, which depended on a compass. His work established the idea of surveying a primary network of control points, and locating subsidiary points inside the primary network later. Between 1733 and 1740, Jacques Cassini and his son César undertook

1824-472: A profession. They established the basic measurements under which the Roman Empire was divided, such as a tax register of conquered lands (300 AD). Roman surveyors were known as Gromatici . In medieval Europe, beating the bounds maintained the boundaries of a village or parish. This was the practice of gathering a group of residents and walking around the parish or village to establish a communal memory of

1920-482: A projection is UTM ( Universal Transverse Mercator ). Within the map plane, we have rectangular coordinates x and y . In this case, the north direction used for reference is the map north, not the local north. The difference between the two is called meridian convergence . It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be α and s respectively, then we have The reverse transformation

2016-428: A reflector or prism to return the light pulses used for distance measurements. They are fully robotic, and can even e-mail point data to a remote computer and connect to satellite positioning systems , such as Global Positioning System . Real Time Kinematic GPS systems have significantly increased the speed of surveying, and they are now horizontally accurate to within 1 cm ± 1 ppm in real-time, while vertically it

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2112-481: A series expansion — see, for example, Vincenty's formulae . As defined in geodesy (and also astronomy ), some basic observational concepts like angles and coordinates include (most commonly from the viewpoint of a local observer): The reference surface (level) used to determine height differences and height reference systems is known as mean sea level . The traditional spirit level directly produces such (for practical purposes most useful) heights above sea level ;

2208-543: A single global, geocentric reference frame that serves as the "zero-order" (global) reference to which national measurements are attached. Real-time kinematic positioning (RTK GPS) is employed frequently in survey mapping. In that measurement technique, unknown points can get quickly tied into nearby terrestrial known points. One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control. There can be thousands of those geodetically determined points in

2304-473: A star is determined, the bearing can be transferred to a reference point on Earth. The point can then be used as a base for further observations. Survey-accurate astronomic positions were difficult to observe and calculate and so tended to be a base off which many other measurements were made. Since the advent of the GPS system, astronomic observations are rare as GPS allows adequate positions to be determined over most of

2400-495: A theodolite with a compass and tripod in 1576. Johnathon Sission was the first to incorporate a telescope on a theodolite in 1725. In the 18th century, modern techniques and instruments for surveying began to be used. Jesse Ramsden introduced the first precision theodolite in 1787. It was an instrument for measuring angles in the horizontal and vertical planes. He created his great theodolite using an accurate dividing engine of his own design. Ramsden's theodolite represented

2496-593: A time component. Before EDM (Electronic Distance Measurement) laser devices, distances were measured using a variety of means. In pre-colonial America Natives would use the "bow shot" as a distance reference ("as far as an arrow can slung out of a bow", or "flights of a Cherokee long bow"). Europeans used chains with links of a known length such as a Gunter's chain , or measuring tapes made of steel or invar . To measure horizontal distances, these chains or tapes were pulled taut to reduce sagging and slack. The distance had to be adjusted for heat expansion. Attempts to hold

2592-677: A variety of mechanisms: Geodynamics is the discipline that studies deformations and motions of Earth's crust and its solidity as a whole. Often the study of Earth's irregular rotation is included in the above definition. Geodynamical studies require terrestrial reference frames realized by the stations belonging to the Global Geodetic Observing System (GGOS ). Techniques for studying geodynamic phenomena on global scales include: [REDACTED] Geodesy at Wikibooks [REDACTED] Media related to Geodesy at Wikimedia Commons Surveying Surveying or land surveying

2688-454: Is approximately the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination – measuring the direction of the plumbline by astronomical means – works reasonably well when one also uses an ellipsoidal model of the figure of the Earth. One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One nautical mile

2784-466: Is GPS, except for specialized measurements (e.g., in underground or high-precision engineering). The higher-order networks are measured with static GPS , using differential measurement to determine vectors between terrestrial points. These vectors then get adjusted in a traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the IERS is the basis for defining

2880-474: Is a staple of contemporary land surveying. Typically, much if not all of the drafting and some of the designing for plans and plats of the surveyed property is done by the surveyor, and nearly everyone working in the area of drafting today (2021) utilizes CAD software and hardware both on PC, and more and more in newer generation data collectors in the field as well. Other computer platforms and tools commonly used today by surveyors are offered online by

2976-399: Is a term used when referring to moving the level to take an elevation shot from a different location. To "turn" the level, one must first take a reading and record the elevation of the point the rod is located on. While the rod is being kept in exactly the same location, the level is moved to a new location where the rod is still visible. A reading is taken from the new location of the level and

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3072-400: Is also appearing. The main surveying instruments in use around the world are the theodolite , measuring tape , total station , 3D scanners , GPS / GNSS , level and rod . Most instruments screw onto a tripod when in use. Tape measures are often used for measurement of smaller distances. 3D scanners and various forms of aerial imagery are also used. The theodolite is an instrument for

3168-412: Is an alternate method of determining the position of objects, and was often used to measure imprecise features such as riverbanks. The surveyor would mark and measure two known positions on the ground roughly parallel to the feature, and mark out a baseline between them. At regular intervals, a distance was measured at right angles from the first line to the feature. The measurements could then be plotted on

3264-505: Is because divergent conditions further away from the base reduce accuracy. Surveying instruments have characteristics that make them suitable for certain uses. Theodolites and levels are often used by constructors rather than surveyors in first world countries. The constructor can perform simple survey tasks using a relatively cheap instrument. Total stations are workhorses for many professional surveyors because they are versatile and reliable in all conditions. The productivity improvements from

3360-518: Is called physical geodesy . The geoid essentially is the figure of Earth abstracted from its topographical features. It is an idealized equilibrium surface of seawater , the mean sea level surface in the absence of currents and air pressure variations, and continued under the continental masses. Unlike a reference ellipsoid , the geoid is irregular and too complicated to serve as the computational surface for solving geometrical problems like point positioning. The geometrical separation between

3456-585: Is currently about half of that to within 2 cm ± 2 ppm. GPS surveying differs from other GPS uses in the equipment and methods used. Static GPS uses two receivers placed in position for a considerable length of time. The long span of time lets the receiver compare measurements as the satellites orbit. The changes as the satellites orbit also provide the measurement network with well conditioned geometry. This produces an accurate baseline that can be over 20 km long. RTK surveying uses one static antenna and one roving antenna. The static antenna tracks changes in

3552-416: Is described by (apparent) sidereal time , which accounts for variations in Earth's axial rotation ( length-of-day variations). A more accurate description also accounts for polar motion as a phenomenon closely monitored by geodesists. In geodetic applications like surveying and mapping , two general types of coordinate systems in the plane are in use: One can intuitively use rectangular coordinates in

3648-399: Is given by: In geodesy, point or terrain heights are " above sea level " as an irregular, physically defined surface. Height systems in use are: Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m s ) and not metric. The reference surface is

3744-570: Is located in ten countries, the second most of any UNESCO World Heritage after the Ancient and Primeval Beech Forests of the Carpathians and Other Regions of Europe . The measurements of the 30° Meridian Arc in 1816–1852 as well the description of the geodesic, topographical, and map making works in the Balkans from the nineteenth century until the beginning of the twentieth century by Russian Czarist Army

3840-578: Is off by 200 ppm in the current definitions). This situation means that one kilometre roughly equals (1/40,000) * 360 * 60 meridional minutes of arc, or 0.54 nautical miles. (This is not exactly so as the two units had been defined on different bases, so the international nautical mile is 1,852 m exactly, which corresponds to rounding the quotient from 1,000/0.54 m to four digits). Various techniques are used in geodesy to study temporally changing surfaces, bodies of mass, physical fields, and dynamical systems. Points on Earth's surface change their location due to

3936-457: Is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator same as with the nautical mile. A metre was originally defined as the 10-millionth part of the length from the equator to the North Pole along the meridian through Paris (the target was not quite reached in actual implementation, as it

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4032-421: Is purely geometrical. The mechanical ellipticity of Earth (dynamical flattening, symbol J 2 ) can be determined to high precision by observation of satellite orbit perturbations . Its relationship with geometrical flattening is indirect and depends on the internal density distribution or, in simplest terms, the degree of central concentration of mass. The 1980 Geodetic Reference System ( GRS 80 ), adopted at

4128-406: 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 designated positions of structural components for construction or

4224-432: Is with an altimeter  using air pressure to find the height. When more precise measurements are needed, means like precise levels (also known as differential leveling) are used. When precise leveling, a series of measurements between two points are taken using an instrument and a measuring rod. Differences in height between the measurements are added and subtracted in a series to get the net difference in elevation between

4320-695: The Great Pyramid of Giza , built c.  2700 BC , affirm the Egyptians' command of surveying. The groma instrument may have originated in Mesopotamia (early 1st millennium BC). The prehistoric monument at Stonehenge ( c.  2500 BC ) was set out by prehistoric surveyors using peg and rope geometry. The mathematician Liu Hui described ways of measuring distant objects in his work Haidao Suanjing or The Sea Island Mathematical Manual , published in 263 AD. The Romans recognized land surveying as

4416-499: The Principal Triangulation of Britain . The first Ramsden theodolite was built for this survey. The survey was finally completed in 1853. The Great Trigonometric Survey of India began in 1801. The Indian survey had an enormous scientific impact. It was responsible for one of the first accurate measurements of a section of an arc of longitude, and for measurements of the geodesic anomaly. It named and mapped Mount Everest and

4512-601: The Torrens system in South Australia in 1858. Torrens intended to simplify land transactions and provide reliable titles via a centralized register of land. The Torrens system was adopted in several other nations of the English-speaking world. Surveying became increasingly important with the arrival of railroads in the 1800s. Surveying was necessary so that railroads could plan technologically and financially viable routes. At

4608-785: The U.S. Federal Government and other governments' survey agencies, such as the National Geodetic Survey and the CORS network, to get automated corrections and conversions for collected GPS data, and the data coordinate systems themselves. Surveyors determine the position of objects by measuring angles and distances. The factors that can affect the accuracy of their observations are also measured. They then use this data to create vectors, bearings, coordinates, elevations, areas, volumes, plans and maps. Measurements are often split into horizontal and vertical components to simplify calculation. GPS and astronomic measurements also need measurement of

4704-637: The exact size and shape of the earth . At that time, the chain passed merely through three countries: Norway , Sweden and the Russian Empire . The Arc's first point is located in Tartu Observatory in Estonia , where Struve conducted much of his research. Measurement of the triangulation chain comprises 258 main triangles and 265 geodetic vertices. The northernmost point is located near Hammerfest in Norway and

4800-446: The geoid , an equigeopotential surface approximating the mean sea level as described above. For normal heights, the reference surface is the so-called quasi-geoid , which has a few-metre separation from the geoid due to the density assumption in its continuation under the continental masses. One can relate these heights through the geoid undulation concept to ellipsoidal heights (also known as geodetic heights ), representing

4896-527: The geoids within their areas of validity, minimizing the deflections of the vertical over these areas. It is only because GPS satellites orbit about the geocenter that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system. Geocentric coordinate systems used in geodesy can be divided naturally into two classes: The coordinate transformation between these two systems to good approximation

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4992-702: The tachymeter determines, electronically or electro-optically , the distance to a target and is highly automated or even robotic in operations. Widely used for the same purpose is the method of free station position. Commonly for local detail surveys, tachymeters are employed, although the old-fashioned rectangular technique using an angle prism and steel tape is still an inexpensive alternative. As mentioned, also there are quick and relatively accurate real-time kinematic (RTK) GPS techniques. Data collected are tagged and recorded digitally for entry into Geographic Information System (GIS) databases. Geodetic GNSS (most commonly GPS ) receivers directly produce 3D coordinates in

5088-461: The topographic surface of Earth — is also realizable. The locations of points in 3D space most conveniently are described by three cartesian or rectangular coordinates, X , Y , and Z . Since the advent of satellite positioning, such coordinate systems are typically geocentric , with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis. Before the era of satellite geodesy ,

5184-485: The GRS 80 reference ellipsoid. The geoid is a "realizable" surface, meaning it can be consistently located on Earth by suitable simple measurements from physical objects like a tide gauge . The geoid can, therefore, be considered a physical ("real") surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, so it is an abstract surface. The third primary surface of geodetic interest —

5280-611: The Kronstadt datum, the Trieste datum, and numerous others. In both mathematics and geodesy, a coordinate system is a "coordinate system" per ISO terminology, whereas the International Earth Rotation and Reference Systems Service (IERS) uses the term "reference system" for the same. When coordinates are realized by choosing datum points and fixing a geodetic datum, ISO speaks of a "coordinate reference system", whereas IERS uses

5376-580: The Moon, and satellite laser ranging (SLR) measuring distances to prisms on artificial satellites , are employed. Gravity is measured using gravimeters , of which there are two kinds. First are absolute gravimeter s, based on measuring the acceleration of free fall (e.g., of a reflecting prism in a vacuum tube ). They are used to establish vertical geospatial control or in the field. Second, relative gravimeter s are spring-based and more common. They are used in gravity surveys over large areas — to establish

5472-671: The XVII General Assembly of the International Union of Geodesy and Geophysics ( IUGG ), posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. GRS 80 essentially constitutes the basis for geodetic positioning by the Global Positioning System (GPS) and is thus also in widespread use outside the geodetic community. Numerous systems used for mapping and charting are becoming obsolete as countries increasingly move to global, geocentric reference systems utilizing

5568-438: The basis for dividing the western territories into sections to allow the sale of land. The PLSS divided states into township grids which were further divided into sections and fractions of sections. Napoleon Bonaparte founded continental Europe 's first cadastre in 1808. This gathered data on the number of parcels of land, their value, land usage, and names. This system soon spread around Europe. Robert Torrens introduced

5664-457: The bearing from every vertex in a figure, a surveyor can measure around the figure. The final observation will be between the two points first observed, except with a 180° difference. This is called a close . If the first and last bearings are different, this shows the error in the survey, called the angular misclose . The surveyor can use this information to prove that the work meets the expected standards. The simplest method for measuring height

5760-462: The beginning of the century, surveyors had improved the older chains and ropes, but they still faced the problem of accurate measurement of long distances. Trevor Lloyd Wadley developed the Tellurometer during the 1950s. It measures long distances using two microwave transmitter/receivers. During the late 1950s Geodimeter introduced electronic distance measurement (EDM) equipment. EDM units use

5856-516: The boundaries. Young boys were included to ensure the memory lasted as long as possible. In England, William the Conqueror commissioned the Domesday Book in 1086. It recorded the names of all the land owners, the area of land they owned, the quality of the land, and specific information of the area's content and inhabitants. It did not include maps showing exact locations. Abel Foullon described

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5952-414: The coordinate systems associated with a geodetic datum attempted to be geocentric , but with the origin differing from the geocenter by hundreds of meters due to regional deviations in the direction of the plumbline (vertical). These regional geodetic datums, such as ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to

6048-405: The development of the human environment since the beginning of recorded history . It is used in the planning and execution of most forms of construction . It is also used in transportation, communications, mapping, and the definition of legal boundaries for land ownership. It is an important tool for research in many other scientific disciplines. The International Federation of Surveyors defines

6144-562: The early days of surveying, this was the primary method of determining accurate positions of objects for topographic maps of large areas. A surveyor first needs to know the horizontal distance between two of the objects, known as the baseline . Then the heights, distances and angular position of other objects can be derived, as long as they are visible from one of the original objects. High-accuracy transits or theodolites were used, and angle measurements were repeated for increased accuracy. See also Triangulation in three dimensions . Offsetting

6240-914: The equatorial radius was 6,378,136.8 metres (20,925,646 ft). An earlier survey, in 1740, had given flattening at one part in 178 and an equatorial radius of 6,396,800 metres (20,986,900 ft). Northernmost point: Hammerfest (Fuglenes): 70° 40' 11.23″ N Southernmost point: Ismail (Staro-Nekrassowka): 45° 20' 02.94″ N Difference in Geodetic Latitude: 25° 20' 08.29″ Distance in kilometres: 2,821.853 ± 0.012 Download coordinates as: Geodesy Geodynamical phenomena, including crustal motion, tides , and polar motion , can be studied by designing global and national control networks , applying space geodesy and terrestrial geodetic techniques, and relying on datums and coordinate systems . Geodetic job titles include geodesist and geodetic surveyor . Geodesy began in pre-scientific antiquity , so

6336-471: The figure of the geoid over these areas. The most accurate relative gravimeters are called superconducting gravimeter s, which are sensitive to one-thousandth of one-billionth of Earth-surface gravity. Twenty-some superconducting gravimeters are used worldwide in studying Earth's tides , rotation , interior, oceanic and atmospheric loading, as well as in verifying the Newtonian constant of gravitation . In

6432-466: The first prototype satellites of the Global Positioning System (GPS) in 1978. GPS used a larger constellation of satellites and improved signal transmission, thus improving accuracy. Early GPS observations required several hours of observations by a static receiver to reach survey accuracy requirements. Later improvements to both satellites and receivers allowed for Real Time Kinematic (RTK) surveying. RTK surveys provide high-accuracy measurements by using

6528-467: The first triangulation of France. They included a re-surveying of the meridian arc , leading to the publication in 1745 of the first map of France constructed on rigorous principles. By this time triangulation methods were well established for local map-making. It was only towards the end of the 18th century that detailed triangulation network surveys mapped whole countries. In 1784, a team from General William Roy 's Ordnance Survey of Great Britain began

6624-509: The function of surveying as follows: A surveyor is a professional person with the academic qualifications and technical expertise to conduct one, or more, of the following activities; Surveying has occurred since humans built the first large structures. In ancient Egypt , a rope stretcher would use simple geometry to re-establish boundaries after the annual floods of the Nile River . The almost perfect squareness and north–south orientation of

6720-401: The future, gravity and altitude might become measurable using the special-relativistic concept of time dilation as gauged by optical clocks . Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles , not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. This direction

6816-412: The geoid and a reference ellipsoid is called geoidal undulation , and it varies globally between ±110 m based on the GRS 80 ellipsoid. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f . The quantity f = ⁠ a − b / a ⁠ , where b is the semi-minor axis (polar radius),

6912-399: The global scale, or engineering geodesy ( Ingenieurgeodäsie ) that includes surveying — measuring parts or regions of Earth. For the longest time, geodesy was the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field; however, geodetic science and operations are applied to other astronomical bodies in our Solar System also. To

7008-748: The ground (about 20 km (12 mi) apart). This method reaches precisions between 5–40 cm (depending on flight height). Surveyors use ancillary equipment such as tripods and instrument stands; staves and beacons used for sighting purposes; PPE ; vegetation clearing equipment; digging implements for finding survey markers buried over time; hammers for placements of markers in various surfaces and structures; and portable radios for communication over long lines of sight. Land surveyors, construction professionals, geomatics engineers and civil engineers using total station , GPS , 3D scanners, and other collector data use land surveying software to increase efficiency, accuracy, and productivity. Land Surveying Software

7104-509: The ground to large beacons that can be seen from long distances. The surveyors can set up their instruments in this position and measure to nearby objects. Sometimes a tall, distinctive feature such as a steeple or radio aerial has its position calculated as a reference point that angles can be measured against. Triangulation is a method of horizontal location favoured in the days before EDM and GPS measurement. It can determine distances, elevations and directions between distant objects. Since

7200-400: The height difference is used to find the new elevation of the level gun, which is why this method is referred to as differential levelling . This is repeated until the series of measurements is completed. The level must be horizontal to get a valid measurement. Because of this, if the horizontal crosshair of the instrument is lower than the base of the rod, the surveyor will not be able to sight

7296-430: The height of a point above the reference ellipsoid . Satellite positioning receivers typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid. Because coordinates and heights of geodetic points always get obtained within a system that itself was constructed based on real-world observations, geodesists introduced the concept of a "geodetic datum" (plural datums ):

7392-405: The inverse problem, the azimuths differ going between the two end points along the arc of the connecting great circle . The general solution is called the geodesic for the surface considered, and the differential equations for the geodesic are solvable numerically. On the ellipsoid of revolution, geodesics are expressible in terms of elliptic integrals, which are usually evaluated in terms of

7488-464: The measurement of angles. It uses two separate circles , protractors or alidades to measure angles in the horizontal and the vertical plane. A telescope mounted on trunnions is aligned vertically with the target object. The whole upper section rotates for horizontal alignment. The vertical circle measures the angle that the telescope makes against the vertical, known as the zenith angle. The horizontal circle uses an upper and lower plate. When beginning

7584-409: The measurement of vertical angles. Verniers allowed measurement to a fraction of a degree, such as with a turn-of-the-century transit . The plane table provided a graphical method of recording and measuring angles, which reduced the amount of mathematics required. In 1829 Francis Ronalds invented a reflecting instrument for recording angles graphically by modifying the octant . By observing

7680-424: The measuring instrument level would also be made. When measuring up a slope, the surveyor might have to "break" (break chain) the measurement- use an increment less than the total length of the chain. Perambulators , or measuring wheels, were used to measure longer distances but not to a high level of accuracy. Tacheometry is the science of measuring distances by measuring the angle between two ends of an object with

7776-411: The modern systematic use of triangulation . In 1615 he surveyed the distance from Alkmaar to Breda , approximately 72 miles (116 km). He underestimated this distance by 3.5%. The survey was a chain of quadrangles containing 33 triangles in all. Snell showed how planar formulae could be corrected to allow for the curvature of the Earth . He also showed how to resect , or calculate, the position of

7872-496: The more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid , as GPS only gives heights above the GRS80 reference ellipsoid. As geoid determination improves, one may expect that the use of GPS in height determination shall increase, too. The theodolite is an instrument used to measure horizontal and vertical (relative to the local vertical) angles to target points. In addition,

7968-642: The other Himalayan peaks. Surveying became a professional occupation in high demand at the turn of the 19th century with the onset of the Industrial Revolution . The profession developed more accurate instruments to aid its work. Industrial infrastructure projects used surveyors to lay out canals , roads and rail. In the US, the Land Ordinance of 1785 created the Public Land Survey System . It formed

8064-507: The plane for one's current location, in which case the x -axis will point to the local north. More formally, such coordinates can be obtained from 3D coordinates using the artifice of a map projection . It is impossible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen — called a conformal projection — preserves angles and length ratios so that small circles get mapped as small circles and small squares as squares. An example of such

8160-474: The rod and get a reading. The rod can usually be raised up to 25 feet (7.6 m) high, allowing the level to be set much higher than the base of the rod. The primary way of determining one's position on the Earth's surface when no known positions are nearby is by astronomic observations. Observations to the Sun, Moon and stars could all be made using navigational techniques. Once the instrument's position and bearing to

8256-422: The satellite positions and atmospheric conditions. The surveyor uses the roving antenna to measure the points needed for the survey. The two antennas use a radio link that allows the static antenna to send corrections to the roving antenna. The roving antenna then applies those corrections to the GPS signals it is receiving to calculate its own position. RTK surveying covers smaller distances than static methods. This

8352-422: The sky to a traveler headed South. In English , geodesy refers to the science of measuring and representing geospatial information , while geomatics encompasses practical applications of geodesy on local and regional scales, including surveying . In German , geodesy can refer to either higher geodesy ( höhere Geodäsie or Erdmessung , literally "geomensuration") — concerned with measuring Earth on

8448-587: The southernmost point near the Black Sea in Ukraine. In 2005, the chain was inscribed on the World Heritage List , because of its importance in geodesy and its testimony to international scientific cooperation. The World Heritage site includes 34 commemorative plaques or built obelisks out of the original 265 main station points which are marked by drilled holes in rock, iron crosses, cairns, others. This inscription

8544-678: The surface location of subsurface features, or other purposes required by government or civil law, such as property sales. A professional in land surveying is called a land surveyor . Surveyors work with elements of geodesy , geometry , trigonometry , regression analysis , physics , engineering, metrology , programming languages , and the law. They use equipment, such as total stations , robotic total stations, theodolites , GNSS receivers, retroreflectors , 3D scanners , lidar sensors, radios, inclinometer , handheld tablets, optical and digital levels , subsurface locators, drones, GIS , and surveying software. Surveying has been an element in

8640-423: The surface of the Earth. Few survey positions are derived from the first principles. Instead, most surveys points are measured relative to previously measured points. This forms a reference or control network where each point can be used by a surveyor to determine their own position when beginning a new survey. Survey points are usually marked on the earth's surface by objects ranging from small nails driven into

8736-406: The survey, the surveyor points the instrument in a known direction (bearing), and clamps the lower plate in place. The instrument can then rotate to measure the bearing to other objects. If no bearing is known or direct angle measurement is wanted, the instrument can be set to zero during the initial sight. It will then read the angle between the initial object, the theodolite itself, and the item that

8832-536: The telescope aligns with. The gyrotheodolite is a form of theodolite that uses a gyroscope to orient itself in the absence of reference marks. It is used in underground applications. The total station is a development of the theodolite with an electronic distance measurement device (EDM). A total station can be used for leveling when set to the horizontal plane. Since their introduction, total stations have shifted from optical-mechanical to fully electronic devices. Modern top-of-the-line total stations no longer need

8928-459: The two endpoints. With the Global Positioning System (GPS), elevation can be measured with satellite receivers. Usually, GPS is somewhat less accurate than traditional precise leveling, but may be similar over long distances. When using an optical level, the endpoint may be out of the effective range of the instrument. There may be obstructions or large changes of elevation between the endpoints. In these situations, extra setups are needed. Turning

9024-455: The very word geodesy comes from the Ancient Greek word γεωδαισία or geodaisia (literally, "division of Earth"). Early ideas about the figure of the Earth held the Earth to be flat and the heavens a physical dome spanning over it. Two early arguments for a spherical Earth were that lunar eclipses appear to an observer as circular shadows and that Polaris appears lower and lower in

9120-567: Was described in Astronomy, geodesy and map- drawing in Moldova since the middle ages till the World War I . At publication in 1858, the flattening of the earth was estimated at one part in 294.26. The earth's equatorial radius was estimated at 6,378,360.7 meters (20,926,380 ft). In 2005, the work was repeated using satellite navigation. The new flattening estimate was one part in 298.257 222 101 and

9216-497: Was the US Navy TRANSIT system . The first successful launch took place in 1960. The system's main purpose was to provide position information to Polaris missile submarines. Surveyors found they could use field receivers to determine the location of a point. Sparse satellite cover and large equipment made observations laborious and inaccurate. The main use was establishing benchmarks in remote locations. The US Air Force launched

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