An optical theodolite, manufactured in the Soviet Union in 1958 and used for topographic surveying.

Diagram of an Optical Theodolite.

View of the data readout of a Geotec FX-1 theodolite, showing azimuth (left) and elevation (right).

A theodolite is an instrument for measuring both horizontal and vertical angles, as used in triangulation networks. It is a key tool in surveying and engineering work, but theodolites have been adapted for other specialized purposes in fields like meteorology and rocket launch technology. A modern theodolite consists of a telescope mounted movably within two perpendicular axes, the horizontal or trunnion axis, and the vertical axis. When the telescope is pointed at a desired object, the angle of each of these axes can be measured with great precision, typically on the scale of arcseconds. Image File history File links SovietTheodolite. ... Image File history File links SovietTheodolite. ... Illustration of an Optical Theodolite. ... Illustration of an Optical Theodolite. ... This article is about angles in geometry. ... Triangulation can be used to find the distance from the shore to the ship. ... Surveyor at work with a leveling instrument. ... Engineering is the discipline and profession of applying scientific knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and processes that realize a desired objective and meet specified criteria. ... // Meteorology (from Greek: μετέωρον, meteoron, high in the sky; and λόγος, logos, knowledge) is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. ... Rockets (including missiles) can be launched from the following: for a launch into an orbital spaceflight and beyond: a launch pad, including a floating platform (see San Marco platform, Sea Launch) for the launch into a suborbital flight also: a missile silo a mobile launcher vehicle a submarine air launch... The trunnions are the protrusions from the side of the barrel that rest on the carriage A trunnion is a cylindrical protrusion used as a mounting point. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 ≈ 7. ...

The transit refers to a specialized type of theodolite that was developed in the early 19th century. It featured a telescope that could "flop over" ("transit the scope") to allow easy back-sighting and doubling of angles for error reduction. Some transit instruments were capable of reading angles directly to thirty arc-seconds. In the middle of the 20th century, transits came to be known as a simple form of theodolite with less precision, lacking features such as scale magnification and mechanical meters. The importance of transits is waning since compact, accurate electronic theodolites have become widespread tools, but transits still find use as a lightweight tool for construction sites. Some transits do not measure vertical angles. Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999 in the...

The builder's level is often mistaken for a transit, but is actually a type of inclinometer. It measures neither horizontal nor vertical angles. It simply combines a spirit level and telescope to allow the user to visually establish a line of sight along a level plane. Dumpy level in use on a construction site Leveler for use by hand A dumpy level, builders auto level, leveling instrument or automatic level is an instrument used in surveying and building to transfer, measure, or set horizontal levels. ... Compass with inclinometer An inclinometer or clinometer is an instrument for measuring angles of slope (or tilt), elevation or inclination of an object with respect to gravity. ... A spirit level A spirit level or bubble level is an instrument designed to indicate whether a surface is level or plumb. ... This article does not cite any references or sources. ...

Concept of operation

The axes and circles of a theodolite.

Both axes of a theodolite are equipped with graduated circles that can be read out through magnifying lenses. The vertical circle (the one associated with the horizontal axis) should read 90° or 100 grad when the sight axis is horizontal (or 270°, 300 grad, when the instrument is in its second position, "turned over" or "plunged"). If not, we call half of the difference with 300 grad index error. Image File history File links Theodolite_vermeer. ... Image File history File links Theodolite_vermeer. ... Circle illustration This article is about the shape and mathematical concept of circle. ... This article describes the unit of angle. ... The grad is a measurement of plane angles of value 1/400 of a full circle, thus dividing a right angle in 100. ...

The horizontal and vertical axes of a theodolite must be mutually perpendicular. The condition where they deviate from perpendicularity (and the amount by which) is referred to as horizontal axis error. The optical axis of the telescope, called sight axis and defined by the optical center of the objective and the center of the crosshairs in its focal plane, must similarly be perpendicular to the horizontal axis. If not, we call the deviation from perpendicularity collimation error. A drawing of different reticles used in telescopic sights. ...

Horizontal axis error, collimation error and index error are regularly determined by calibration, and removed by mechanical adjustment at the factory in case they grow overly large. Their existence is taken into account in the choice of measurement procedure in order to eliminate their effect on the measurement results. calibration refers to the process of determining the relation between the output (or response) of a measuring instrument and the value of the input quantity or attribute, a measurement standard. ...

A theodolite is mounted on the tripod head by means of a forced centering plate or tribrach, containing four thumbscrews (or in some modern theodolites three thumbscrews) for rapid levelling. Before use, a theodolite must be placed precisely and vertically over the point to be measured — centering — and its vertical axis aligned with local gravity — leveling. The former is done using a plumb bob or optical plummet, the latter using a spirit level. Fast and accurate procedures for doing both have been developed. Look up tripod in Wiktionary, the free dictionary. ... In surveying science, a tribrach means an instrument attachment plate containing three thumbscrews (see theodolite). ... It has been suggested that this article or section be merged with plumb line. ... A spirit level A spirit level or bubble level is an instrument designed to indicate whether a surface is level or plumb. ...

History

In old texts, one might find the term diopter used as a synonym for theodolite.^[1] This usage would derive from an older instrument called a dioptra. A dioptra is a instrument dating back to ancient Greece, at least 300 B.C.E. It is said to have been long used by Greek astronomers, such as Hipparchus(sometimes credited with inventing it). ...

Prior to the theodolite, instruments such as the geometric square and various graduated circles (see circumferentor) and semi-circles (see graphometer) were used to obtain either vertical or horizontal angle measurements. It was only a matter of time before someone put two measuring devices into a single instrument that could measure both angles simultaneously. Gregorius Reisch showed such an instrument in the appendix of his book, Margarita Philosophica, which he published in Strasburg in 1512.^[2] It was described in the appendix by Martin Waldseemüller, a Rhineland topographer and cartographer, who made the device in the same year.^[3] Waldseemüller called his instrument the polimetrum.^[4] Drawing of a circumferentor from the Cyclopaedia A circumferentor, or surveyors compass, is an instrument used in surveying to measure horizontal angles, now superseded by the theodolite. ... Strasburg is the name of several places: Strasburg, Colorado (USA) divided between Adams County, Colorado and Arapahoe County, Colorado Strasburg, Illinois (USA) Strasburg, Michigan (USA) Strasburg, Missouri (USA) Strasburg, North Dakota (USA) Strasburg, Ohio (USA) Strasburg, Pennsylvania (USA) Strasburg, Virginia (USA) Strasbourg, Saskatchewan (Can) Strasburg, Mecklenburg-Western Pomerania (Germany) the... Martin Waldseemüller (19th century painting). ... The Rhineland (Rheinland in German) is the general name for the land on both sides of the river Rhine in the west of Germany. ... Topography, a term in geography, has come to refer to the lay of the land, or the physiogeographic characteristics of land in terms of elevation, slope, and orientation. ... Cartography is the study of map making and cartographers are map makers. ...

The first occurrence of the name theodolite, or 'theodelitus', is found in the surveying textbook A geometric practice named Pantometria (1571) by Leonard Digges. This was published posthumously by his son, Thomas Digges. Digges senior invented the name, but its origin is unclear.^[2] Events January 11 - Austrian nobility is granted Freedom of religion. ... Leonard Digges (1520 - 1559), father of Thomas Digges was a well-known mathematician and surveyor, credited to the invention of the theodolite and a great populariser of science through his publications in English. ...

There is some confusion about the instrument to which the name originally applied. Some identify the early theodolite as an azimuth instrument only, while others specify it as an altazimuth instrument. In Digges' book, the name theodolite described an instrument for measuring horizontal angles only. He also described an instrument that measured both altitude and azimuth, which he called a topographicall instrument [sic].^[5] Thus the name originally applies only to the azimuth instrument and only later became associated with the altazimuth instrument. The 1728 Cyclopaedia compares graphometer to "half-theodolite".^[6] Even as late as the 19^th century, the instrument for measuring horizontal angles only was called a simple theodolite and the altazimuth instrument, the plain theodolite.^[7] Azimuth is the horizontal component of a direction (compass direction), measured around the horizon, from the north toward the east (i. ... An Altazimuth or alt-azimuth mount is a simple mount used for moving a telescope or camera along two perpendicular axes of motion. ... 1913 advertisement for Encyclopædia Britannica. ...

The first instrument more like a true theodolite was likely the one built by Joshua Habermel (de:Erasmus Habermehl) in Germany in 1576, complete with compass and tripod.^[3]

The earliest altazimuth instruments consisted of a base graduated with a full circle at the limb and a vertical angle measuring device, most often a semi-circle. An alidade on the base was used to sight an object for horizontal angle measurement and a second alidade was mounted on the vertical semi-circle. Later instruments had a single alidade on the vertical semi-circle and the entire semi-circle was mounted so as to be used to indicate horizontal angles directly. Eventually, the simple, open-sight alidade was replaced with a sighting telescope. This was first done by Jonathan Sisson in 1725.^[7] A simple alidade for use with a ceiling projector The Alhidade or alidade is the part of a theodolite that rotates around the vertical axis, and that bears the horizontal axis around which the telescope (or visor, in early telescope-less instruments) turns up or down. ... This article does not cite any references or sources. ...

The theodolite became a modern, accurate instrument in 1787 with the introduction of Jesse Ramsden's famous great theodolite, which he created using a very accurate dividing engine of his own design.^[7] As technology progressed, in the 1840s, the vertical partial circle was replaced with a full circle and both vertical and horizontal circles were finely graduated. This was the transit theodolite. This, with continuing refinements, evolved into the modern theodolite used by surveyors today. Jesse Ramsden (October 6, 1735 - November 5, 1800) was an English astronomical instrument maker. ...

Using theodolites in surveying

U.S. National Geodetic Survey technicians observing with a 0.2 arcsecond resolution Wild T-3 theodolite mounted on an observing stand. Photo was taken during an Arctic field party (circa 1950).

Triangulation, as invented by Gemma Frisius around 1533, consists of making such direction plots of the surrounding landscape from two separate standpoints. After that, the two graphing papers are superimposed, providing a scale model of the landscape, or rather the targets in it. The true scale can be obtained by just measuring one distance both in the real terrain and in the graphical representation. The National Geodetic Survey is the successor agency in the United States to the U.S. Coast and Geodetic Survey. ... A second of arc or arcsecond is a unit of angular measurement which comprises one-sixtieth of an arcminute, or 1/3600 of a degree of arc or 1/1296000 ≈ 7. ... Triangulation can be used to find the distance from the shore to the ship. ... Gemma Frisius, seventeenth-century woodcut by E. de Boulonois For the crater, see Gemma Frisius (crater) Gemma Frisius (or Reiner Gemma, December 9, 1508 - May 25, 1555) was a mathematician, cartographer and instrument maker. ... Events January 25 - King Henry VIII of England marries Anne Boleyn, his second Queen consort. ...

Modern triangulation as, e.g., practiced by Snellius, is the same procedure executed by numerical means. Photogrammetric block adjustment of stereo pairs of aerial photographs is a modern, three-dimensional variant. Willebrord Snel Willebrord Snel (1580–October 30, 1626), also known as Snel van Royen or Snellius, was a Dutch astronomer and mathematician, most famous for the law of refraction now known as Snells law. ...

In the late 1780s Jesse Ramsden, a Yorkshireman from Halifax, England who had developed the dividing engine for dividing angular scales accurately to within a second of arc, was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation. Nothing much really happened in the 1780s only that Mary-Anne Tobin was hung in public for wearing a flase beard and voting. ... Jesse Ramsden (October 6, 1735 - November 5, 1800) was an English astronomical instrument maker. ... For other uses, see Halifax. ... Part of an Ordnance Survey map at 1 inch to the mile scale from 1945 Ordnance Survey (OS) is an executive agency of the United Kingdom government. ... The Ramsden theodolite was used in the first Ordnance Survey of Southern Britain. ...

In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-mm precision. Nowadays GPS antennas used for geodetic positioning use a similar mounting system. The height of the reference point of the theodolite -- or the target -- above the ground bench mark must be measured precisely. Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ...

The American transit gained popularity during the 19th century with American railroad engineers pushing west. The transit replaced the railroad compass, sextant and octant and was distinguished by having a telescope shorter than the base arms, allowing the telescope to be vertically rotated past straight down. The transit had the ability to 'flop' over on its vertical circle and easily show the exact 180 degree sight to the user. This facilitated the viewing of long straight lines, such as when surveying the American Wild West. Previously the user rotated the telescope on its horizontal circle to 180 and had to carefully check his angle when turning 180 degree turns. A sextant is a measuring instrument generally used to measure the angle of elevation of a celestial object above the horizon. ... Octant Octant is a measuring instrument similar to a sextant. ...

Modern theodolites

Modern theodolite Nikon DTM-520

In today's theodolites, the reading out of the horizontal and vertical circles is usually done electronically. The readout is done by a rotary encoder, which can be absolute, e.g. using Gray codes, or incremental, using equidistant light and dark radial bands. In the latter case the circles spin rapidly, reducing angle measurement to electronic measurement of time differences. Additionally, lately CCD sensors have been added to the focal plane of the telescope allowing both auto-targeting and the automated measurement of residual target offset. All this is implemented in embedded software. Image File history File linksMetadata Download high-resolution version (676x1246, 123 KB) [edit] Summary en: Modern theodolite Nikon DTM-520 pl: Nowoczesny teodolit Nikon DTM-520 Author : Krzysztof Blachnicki [edit] Licensing Cateogry:Theodolites File links The following pages on the English Wikipedia link to this file (pages on other projects... Image File history File linksMetadata Download high-resolution version (676x1246, 123 KB) [edit] Summary en: Modern theodolite Nikon DTM-520 pl: Nowoczesny teodolit Nikon DTM-520 Author : Krzysztof Blachnicki [edit] Licensing Cateogry:Theodolites File links The following pages on the English Wikipedia link to this file (pages on other projects... For other uses, see Nikon (disambiguation). ... A rotary encoder, also called a shaft encoder, is an electro-mechanical device used to convert the angular position of a shaft or axle to an analog or digital code, making it a sort of transducer. ... The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit. ... A specially developed CCD used for ultraviolet imaging in a wire bonded package. ... The focal plane of a lens is a plane that is perpendicular to the axis of the lens and passes through its focus. ... This article does not cite any references or sources. ...

Also, many modern theodolites are equipped with integrated electro-optical distance measuring devices, generally infrared based, allowing the measurement in one go of complete three-dimensional vectors -- albeit in instrument-defined polar co-ordinates -- which can then be transformed to a pre-existing co-ordinate system in the area by means of a sufficient number of control points. This technique is called a resection solution or free station position surveying and is widely used in mapping surveying. The instruments, "intelligent" theodolites called self-registering tachometers or "total stations", perform the necessary operations, saving data into internal registering units, or into external data storage devices. Typically, ruggedized laptops or PDAs are used as data collectors for this purpose. For other uses, see Infrared (disambiguation). ... This article is about vectors that have a particular relation to the spatial coordinates. ... In the mathematical subfield of numerical analysis a spline is a special curve defined piecewise by polynomials. ... Resection has multiple meanings: Resectioning involves enlarging the cross-section of a river channel by deepening or widening the river to increase its hydraulic efficiency. ... A total station is an optical instrument used in modern surveying. ... Laptop with touchpad. ... User with Treo (PDA with smartphone functionality) Personal digital assistants (PDAs) are handheld computers, but have become much more versatile over the years. ...

Gyrotheodolites

The gyrotheodolite is used when the north-south reference bearing of the meridian is required in the absence of astronomical star sights. This mainly occurs in the underground mining industry and in tunnel engineering. For example, where a conduit must pass under a river, a vertical shaft on each side of the river might be connected by a horizontal tunnel. A gyrotheodolite can be operated at the surface and then again at the foot of the shafts to identify the directions needed to tunnel between the base of the two shafts. Unlike an artificial horizon or inertial navigation system, a gyrotheodolite cannot be relocated while it is operating. It must be restarted again at each site.

General

A gyrotheodolite comprises a normal theodolite with an attachment that contains a gyroscope mounted so as to sense rotation of the Earth and from that the alignment of the meridian. The meridian is the plane that contains both the axis of the Earth’s rotation and the observer. The intersection of the meridian plane with the horizontal contains the true north-south geographic reference bearing required. The gyrotheodolite is usually refered to as being able to determine or find true north.

Construction

When not in operation the gyroscope assembly is anchored within the instrument. The electrically powered gyroscope is started while restrained and then released for operation. During operation the gyroscope is supported within the instrument assembly typically on a thin vertical tape that constrains the gyroscope spinner axis to remain horizontal. The alignment of the spin axis is however permitted to rotate in azimuth by only the small amount required during operation. An initial approximate estimate of the meridian is needed. This might be determined with a magnetic compass, from an existing survey network or by the use of the gyrotheodolite in an extended tracking mode.

How it works

When the spinner is released from restraint with its axis of rotation aligned close to the meridian, the gyroscopic reaction of spin and Earth’s rotation results in precession of the spin axis in the direction of alignment with the plane of the meridian. This is because the daily rotation of the Earth is in effect continuously tilting the east-west axis of the station. The spinner axis then accelerates towards and overshoots the meridian, it then slows to a halt at an extreme point before similarly swinging back towards the initial point of release. This oscillation in azimuth of the spinner axis about the meridian repeats with a period of a few minutes. In practice the amplitude of oscillation will only gradually reduce as energy is lost due to the minimal damping present. Gyrotheodolites employ an undamped oscillating system because a determination can be obtained in less than about 20 minutes, while the asymptotic settling of a damped gyrocompass would take many times that before any reasonable determination of meridian could possibly be made.

Operation

The attachment containing the gyroscope is mounted so as to rotate with the theodolite. A separate optical system within the attachment permits the operator to rotate the theodolite and thereby bring a zero mark on the attachment into conicidence with the gyroscope spin axis. By tracking the spin axis as it oscillates about the meridian, a record of the azimuth of a series of the extreme stationary points of that oscillation may be determined by reading the theodolite azimuth circle. A mid point can later be computed from these records that represents a refined estimate of the meridian. Careful setup and repeated observations can give an estimate that is within about 10 arc seconds of the true meridian. This estimate of the meridian contains errors due to the zero torque of the suspension not being aligned precisely with the true meridian and to measurement errors of the slightly damped extremes of oscillation. These errors can be moderated by refining the initial estimate of the meridian to within a few arc minutes and correctly aligning the zero torque of the suspension.

Limitations

A gyrotheodolite will function at the equator and in both the northern and southern hemispheres. The meridian is undefined at the geographic poles. A gyrotheodolite can not be used at the poles where the Earth’s axis is precisely perpendicular to the horizontal axis of the spinner, indeed it is not normally used within about 15 degrees of the pole because the east-west component of the Earth’s rotation is insufficient to obtain reliable results. When available, astronomical star sights are able to give the meridian bearing to better than one hundred times the accuracy of the gyrotheodolite. Where this extra precision is not required, the gyrotheodolite is able to produce a result quickly without the need for night observations.

References

1. ^ The Compact Edition of the Oxford English Dictionary, Oxford University Press, 1971 - see entry for diopter
2. ^ ^{a b} Daumas, Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989 ISBN 978-0713407273
3. ^ ^{a b} Geomatica Online Colombo, Luigi, Selvini, Attilio, Sintesi di una storia degli strumenti per la misura topografica
4. ^ Mills, John FitzMaurice, Encyclopedia of Antique Scientific Instruments, Aurum Press, London, 1983, ISBN 0-906053-40-4
5. ^ Turner, Gerard L'E., Elizabethan Instrument Makers: The Origins of the London Trade in Precision Instrument Making, Oxford University Press, 2000, ISBN 978-0198565666
6. ^ Cyclopaedia, vol. 2 p. 50 for "Semi-Circle"
7. ^ ^{a b c} Turner, Gerard L'E. Nineteenth Century Scientific Instruments, Sotheby Publications, 1983, ISBN 0-85667-170-3

1913 advertisement for Encyclopædia Britannica. ...

See also

Wikimedia Commons has media related to:

Theodolite

• Tacheometry
• clinometer
• Surveying
• Rankine's method
• Dumpy level