Surveying

I

Introduction

Surveying, mathematical science used to determine and delineate the form, extent, and position of features on or beneath the surface of the earth for control purposes—that is, for aligning land and construction boundaries, and for providing checks of construction dimensions. Land boundaries are set or measured for proper descriptions; the topography of landforms and natural or artificial objects are depicted on maps (see Map); and major construction and civil engineering works such as dams, bridges, railroads, and highways are controlled by surveying methods. The measurements of a survey are linear or angular, and principles of geometry and trigonometry are usually applied.

II

Surveying Instruments

Horizontal linear measurements are made with calibrated rules or tapes and sometimes by electronically timing the travel of light or radio waves between points. Vertical linear measurements are made with a graduated vertical rod to find differences of elevation and heights above sea level. The so-called engineer's level, a tripod-mounted telescope equipped with a spirit bubble and a cross wire, is used to sight the graduations on the rod. The horizontal or vertical angles are measured by a transit or theodolite, a tripod-mounted telescope with cross wires, the graduated circles of which indicate angles in degrees, minutes, and seconds.

Electronic distance-measuring devices are being perfected and can give extremely accurate results, up to 1 in 6 million or better. Under development also are electronic angle-measuring devices of great precision. Theodolites and transits using glass circles permit greater magnification and can thus be smaller than in the past; these instruments are also more accurate, being capable of measurements to hundredths of a second of arc. An automatic type of engineer's level, employing a pendulum prism or reflecting light from a liquid surface, is also used in place of the spirit-level bubble for differential leveling.

III

Plane Surveying

Plane surveys treat any small segment of land or water as a horizontal plane. Such surveys are customarily projected and calculated on a horizontal rectangular grid, oriented north-south and east-west, although the grid can be oriented in an arbitrary, rather than true, north-south direction. From a given starting point, or station, of known or assigned coordinates, the horizontal distance is measured to another point, then to another convenient point, and then to succeeding points, to close on the original point or on any point of known coordinates. A succession of such lines or courses forms a traverse. The horizontal angles between successive courses are measured with a transit or theodolite at each hub, or station. From a known or arbitrarily assigned starting direction, the directions, or bearings, of successive traverse lines can thus be calculated. Plane geometry and plane trigonometry relationships are used to determine the coordinates of traverse stations. The north or south distance of a traverse course is its length multiplied by the cosine of the bearing; the east or west distance of a traverse course is its length multiplied by the sine of the bearing. Coordinates enable the plotting of the hubs to any scale on a grid that can serve as a plot or as control for further details drawn on a map or chart.

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Triangulation can be used instead of a traverse, measuring only one baseline, but measuring all the angles in a chain of triangles, to calculated coordinates of successive hubs. The choice of traverse or triangulation is dictated by the type of terrain to be surveyed.

IV

Geodetic Surveying

For large areas, surveys must take into account the basic shape of the earth, the geoid, and are therefore called geodetic surveys. These surveys are based on a spheroidal shape approximating the geoidal or geographic (nearly spherical) shape of the earth at sea level. They are based on a true north-south meridian as defined by the earth's rotational axis and on spherical geometry. In the U.S., plane-coordinate systems exist for most states, with conversion between plane coordinates and geodetic coordinates made convenient by tabulated relationships. Typically, a highway-route survey extending for many kilometers would require geodetic adjustment to avoid accumulation of error resulting from the convergence of meridians.