# surveying

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## surveying,

method of determining accurately points and lines of direction (bearings) on the earth's surface and preparing from them maps or plans. Boundaries, areas, elevations, construction lines, and geographical or artificial features are determined by the measurement of horizontal and vertical distances and angles and by computations based on geometry and trigonometry.

### Types and Branches of Surveying

Hydrographic surveying deals with bodies of water and coast lines, is recorded on charts, and records such features as bottom contours, channels, buoys, and shoals. Land surveying includes both geodetic surveying, used for large areas and taking into account the curvature of the earth's surface (see geodesygeodesy
or geodetic surveying,
theory and practice of determining the position of points on the earth's surface and the dimensions of areas so large that the curvature of the earth must be taken into account.
), and plane surveying, which deals with areas sufficiently small that the earth's curvature is negligible and can be disregarded. Plane surveying dates from ancient times and was highly developed in Egypt. It played an important role in American history in marking boundaries for settlements; surveying was a profession of distinction—both Washington and Jefferson worked for a time as surveyors. Branches of surveying are named according to their purpose, e.g., topographic surveying, used to determine relief (see contourcontour
or contour line,
line on a topographic map connecting points of equal elevation above or below mean sea level. It is thus a kind of isopleth, or line of equal quantity.
), route surveying, mine surveying, construction surveying; or according to the method used, e.g., transit surveying, plane-table surveying, and photogrammetic surveying (securing data by photographs).

### Instruments and Techniques

In surveying, measurements may be made directly, electronically, by the use of optical instruments, by computations from known lines and angles, or by combination methods. Instruments used for direct linear measurements include the Gunter's chain (known also as the surveyor's chain), which is 66 ft (20 m) long and divided into 100 links; the engineer's chain, 100 ft (30 m) long and also consisting of 100 links; the tape, usually of steel, which has largely superseded chains; and the rod. Tapes and rods made of Invar metal (an alloy of steel and nickel) are used for very precise work because of their low coefficient of thermal expansion. In many situations electronic instruments, such as the geodimeter, which uses light waves, and the tellurometer, which uses microwaves, provide a more convenient and more accurate means of determining distance than do tapes and rods.

The height of points in relation to a datum line (usually mean sea level) is measured with a leveling instrument consisting of a telescope fitted with a spirit level and usually mounted on a tripod. It is used in conjunction with a leveling rod placed at the point to be measured and sighted through the telescope. The transit is used to measure vertical and horizontal angles and may be used also for leveling; its chief elements are a telescope that can be rotated (transited) about a horizontal and about a vertical axis, spirit levels, and graduated circles supplemented by vernier scales. Known also as a transit theodolitetheodolite
, calibrated optical instrument used to determine relative position in surveying, navigation, and meteorology. It is similar in construction to a surveyor's transit, consisting of a telescope fitted with a spirit level and mounted on a tripod so that it is free to
, or transit compass, the transit is a modification of the theodolite, an instrument that, in its original form, could not be rotated in a vertical axis. A plane table consists of a drawing board fixed on a tripod and equipped with an alidade (a rule combined with a telescope); it is used for direct plotting of data on a chart and is suitable for rapid work not requiring a high degree of precision.

The stadia method of measuring distance, a rapid system useful in surveying inaccessible terrain and in checking more precise measurements, consists in observing through a telescope equipped with two horizontal cross hairs or wires (stadia hairs) the interval delimited by the hairs on a calibrated stadia rod; the interval depends on the distance between the rod and the telescope.

Surveys based on photographs are especially useful in rugged or inaccessible country and for reconnaissance surveys for construction, mapping, or military purposes. In air photographs, errors resulting from tilt of the airplane or arising from distortion of ground relief may be corrected in part by checking against control points fixed by ground surveys and by taking overlapping photographs and matching and assembling the relatively undistorted central portions into a mosaic. These are usually examined stereoscopically.

### Bibliography

See W. H. Rayner and M. O. Schmidt, Fundamentals of Surveying (5th ed. 1969); R. F. Spier, Surveying and Mapping (1970); J. Anderson and E. Mikhail, Introduction to Surveying (1989); F. Bell, Surveying and Setting Out Procedures (1991).

## Surveying

The measurement of dimensional relationships among points, lines, and physical features on or near the Earth's surface. Basically, surveying determines horizontal distances, elevation differences, directions, and angles. These basic determinations are applied further to the computation of areas and volumes and to the establishment of locations with respect to some coordinate system.

Surveying is typically used to locate and measure property lines; to lay out buildings, bridges, channels, highways, sewers, and pipelines for construction; to locate stations for launching and tracking satellites; and to obtain topographic information for mapping and charting.

Horizontal distances are usually assumed to be parallel to a common plane. Each measurement has both length and direction. Length is expressed in feet or in meters. Direction is expressed as a bearing of the azimuthal angle relationship to a reference meridian, which is the north-south direction. It can be the true meridian, a grid meridian, or some other assumed meridian. The degree-minute-second system of angular expression is standard in the United States.

Reference, or control, is a concept that applies to the positions of lines as well as to their directions. In its simplest form, the position control is an identifiable or understood point of origin for the lines of a survey. Conveniently, most coordinate systems have the origin placed west and south of the area to be surveyed so that all coordinates are positive and in the northeast quadrant.

Vertical measurement adds the third dimension to an object's position. This dimension is expressed as the distance above some reference surface, usually mean sea level, called a datum. Mean sea level is determined by averaging high and low tides during a lunar month.

#### Horizontal control

The main framework, or control, of a survey is laid out by traverse, triangulation, or trilateration. Some success has been achieved in locating control points from Doppler measurements of passing satellites, from aerial phototriangulation, from satellites photographed against a star background, and from inertial guidance systems. In traverse, adopted for most ordinary surveying, a line or series of lines is established by directly measuring lengths and angles. In triangulation, used mainly for large areas, angles are again directly measured, but distances are computed trigonometrically. This necessitates triangular patterns of lines connecting intervisible points and starting from a baseline of known length. New baselines are measured at intervals. Trigonometric methods are also used in trilateration, but lengths, rather than angles, are measured. The development of electronic distance measurement (EDM) instruments brought trilateration into significant use.

#### Distance measurement

Traverse distances are usually measured with a surveyor's tape or by EDM, but also may sometimes be measured by stadia, subtense, or trig-traverse.

Whether on sloping or level ground, it is horizontal distances that must be measured. In taping, horizontal components of hillside distances are measured by raising the downhill end of the tape to the level of the uphill end. On steep ground this technique is used with shorter sections of the tape. The raised end is positioned over the ground point with the aid of a plumb bob. Where slope distances are taped along the ground, the slope angle can be measured with the clinometer. The desired horizontal distance can then be computed.

In EDM the time a signal requires to travel from an emitter to a receiver or reflector and back to the sender is converted to a distance readout. The great advantage of electronic distance measuring is its unprecedented precision, speed, and convenience. Further, if mounted directly onto a theodolite, and especially if incorporated into it and electronically coupled to it, the EDM instrument with an internal computer can in seconds measure distance (even slope distance) and direction, then compute the coordinates of the sighted point with all the accuracy required for high-order surveying.

In the stadia technique, a graduated stadia rod is held upright on a point and sighted through a transit telescope set up over another point. The distance between the two points is determined from the length of rod intercepted between two horizontal wires in the telescope.

In the subtense technique the transit angle subtended by a horizontal bar of fixed length enables computation of the transit-to-bar distance (Fig. 1). In trig-traverse the subtense bar is replaced by a measured baseline extending at a right angle from the survey line whose distance is desired. The distance calculated in either subtense or trig-traverse is automatically the horizontal distance and needs no correction.

#### Angular measurement

The most common instrument for measuring angles is the transit or theodolite. It is essentially a telescope that can be rotated a measurable amount about a vertical axis and a horizontal axis. Carefully graduated metal or glass circles concentric with each axis are used to measure the angles. The transit is centered over a point with the aid of either a plumb bob suspended by a string from the vertical axis or (on some theodolites) an optical plummet, which enables the operator to sight along the instrument's vertical axis to the ground through a right-angle prism.

#### Elevation differences

Elevations may be measured trigonometrically in conjunction with reduction of slope measurements to horizontal distances, but the resulting elevation differences are of low precision.

Most third-order and all second- and first-order measurements are made by differential leveling, wherein a horizontal line of sight of known elevation is sighted on a graduated rod held vertically on the point being checked (Fig. 2). The transit telescope, leveled, may establish the sight line, but more often a specialized leveling instrument is used. For approximate results a hand level may be used.

Other methods of measuring elevation include trigonometric leveling which involves calculating height from measurements of horizontal, distance and vertical angle; barometric leveling, a method of determining approximate elevation difference with aid of a barometer; and airborne profiling, in which a radar altimeter on an aircraft is used to obtain ground elevations.

#### Astronomical observations

To determine meridian direction and geographic latitude, observations are made by a theodolite or transit on Polaris, the Sun, or other stars. Direction of the meridian (geographic north-south line) is needed for direction control purposes; latitude is needed where maps and other sources are insufficient. The simplest meridian determination is made by sighting Polaris at its elongation, as the star is rounding the easterly or westerly extremity of its apparent orbit. An angular correction is applied to the direction of sighting, which is referenced to a line on the ground. The correction value is found in an ephemeris.

## surveying

That branch of engineering concerned with a determination of the earth’s surface features in relation to each other, as the relative position of points, a determination of areas, etc., and their recording on a map.
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