Plumb direction

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If one neglects gravity anomalies (e.g. due to mountains) and different flattening, the geoid would be like an ellipsoid of revolution (thick curve). Its shape results from the interplay of gravity / gravitation and centrifugal force. The perpendicular direction is also a resultant of these two forces and would then be like a normal correspondingly perpendicular to this ellipsoid of revolution.
Due to gravity anomalies in the earth and different flattening in the northern and southern hemisphere, there is a vertical deviation : Difference between the true vertical direction and a theoretical earth ellipsoid .
Mountains curve the perpendicular direction by up to 0.01 °. The plumb lines penetrate the geoid and all other level surfaces at exactly 90 °
Inclinometer with plumb bob

The perpendicular direction is the local direction of the gravitational acceleration , so it points " downwards ".

This direction, also called the perpendicular , is perpendicular to the level surfaces of the earth's gravity field in the direction of the resultant from the earth's gravitation and the centrifugal force due to the earth's rotation . Because of the latter, the vertical direction deviates by up to 0.2 ° from the direction in which the center of the earth is located. To determine the local plumb a simple means, the plumb bob .

A straight line in the perpendicular direction at the location , also called vertical or perpendicular , shows the zenith upwards and the nadir downwards as the two points of intersection with the celestial sphere . A straight line or plane at right angles to this is called a horizontal , also horizontal or horizontal . A horizontal plane at the position of the observer is the mathematical horizon (see also tangential plane ).

Physical definition

From a physical point of view, the vertical direction in the gravitational field of the rotating earth is a consequence of gravity and - to a lesser extent - centrifugal force . Therefore it usually does not point to the center of the earth . The rotation (and the resulting centrifugal force and flattening ) causes a deflection that is up to 0.2 ° on Earth and almost 10 ° on Saturn. This amount which is geocentric latitude (with ( psi )) is smaller than the geographical ( , ( beta ) or ( phi )).

More precisely, the perpendicular direction is not a straight line, but a space curve . As a plumb line, it penetrates all level surfaces of the gravitational field orthogonally . The plumb line curvature can be determined by complex measurements (see gravimetry or gradiometry ) or by calculation by modeling the masses of the terrain (topography) and the geological subsurface. The curvature is about 1 ″ in the lowlands , but more than 10 ″ in the high mountains , which is about 0.5 cm (lowlands) to over 5 cm (high mountains) per kilometer.

Astronomical and geographical coordinates

Precise values ​​for astronomical latitude and longitude can be determined from the vertical direction or the position of the zenith in the starry sky . The difference to the geographical latitude and longitude is the so-called vertical deviation , which is caused by the irregularities of the earth's gravity field. They form an important coordinate system for the geosciences - especially geodesy .

On the other hand, the horizon and plumb line form a topocentric horizontal coordinate system , which is of the greatest importance for everyday life and is also called the natural coordinate system .

Measurement and accuracies

The perpendicular direction is measured :


“Plumb line” is derived from the plumb line, “vertical” from plumb line, “horizontal” presumably from “scales” as a synonym for a water surface in equilibrium - see also spirit level as the original measuring device for this purpose. “Horizontal” refers to the level of the horizon and also has to do with distance vision . In medicine, vertical refers to the line that runs from the top of the head to the sole. "Vertical" comes from the Latin ( vertex " vertex (point)"; the same meaning is based on the "zenith").


  • Franz Ackerl : Geodesy and Photogrammetry (= technical manuals for construction practitioners . Vol. 8, ZDB -ID 409611-3 ). 2 volumes. Fromme, Vienna 1950–1956.
  • Gottfried Gerstbach : Significance of a geographic information system for earth measurements. In: Gottfried Gerstbach (Ed.): Geoscientific, geotechnical data in land information systems. Needs and opportunities in Austria. Contributions to the GeoLIS conference, 3. – 4. April 1986, Vienna University of Technology (= Geoscientific Communications. Issue 27, ZDB -ID 409611-3 ). Technical University of Vienna - Study of Surveying, Vienna 1986, pp. 9–15.
  • Karl Ledersteger : Astronomical and Physical Geodesy (Earth Measurement) (= Handbook of Surveying. Vol. 5). 10th, completely revised and restructured edition. Metzler, Stuttgart 1969.
  • Wolfgang Torge : Geodesy. 3rd, completely revised and extended edition. de Gruyter, Berlin et al. 2001, ISBN 3-11-017072-8 .

Web links

Commons : Plumb line  - collection of images, videos and audio files
Wiktionary: Plumb line  - explanations of meanings, word origins, synonyms, translations