Vertical deflection

The deflection of the vertical is the angle between the plumb line and the ellipsoidal at a certain point. You can in European high mountains reach about 0.01 ° (30-50 " ), in the lowlands less, and corresponds to the local slope of the geoid to the ellipsoid of land surveying.

Even if the vertical deflection is zero, the plumb line (realized eg by a freely suspended plumb bob ) not center of the earth, but because of the flattening of the earth (centrifugal force of Earth's rotation ) up to 0.2 ° over.

Sometimes they speak also in the construction of vertical deflection when a building or a wall out of plumb device.

Definition of the deflection of the vertical

According to the International Federation of Géomètres dictionary the vertical deflection of the angle between the plumb line is a dot and the allocated to this point through a projection normal to an ellipsoid of revolution.

One speaks of a astrogeodetic vertical deflection when determining the plumb line with the methods of geodetic astronomy took place and occurs in the transformation between the local coordinate systems. In contrast, the gravimetric deflection of the vertical is based on determining the perpendicular direction by gravity measurements and obtained via the solution of the geodetic boundary value problem.

Vertical deflections depend on the ellipsoidal coordinates and thus the parameters of the reference or Referenzellipsoides and of its bearing towards the earth. If it is at the reference ellipsoid to a geocentric ( in Erdschwerpunkt ) mounted and at the same average Erdellipsoid, one speaks of absolute deviations of the vertical, otherwise relative deflections of the vertical.

Size of the deflections of the vertical

What amounts can reach the vertical deflection depends on several factors:

While in the high mountains of Europe the average deflections of the vertical at 0.5 '= 30 " remain ( the maximum values ​​can about 60 " reach ), almost double the amounts are possible in the Andes and Himalayas.

Given the accuracy of modern measurements, the deflection of the vertical affects in almost every project or survey network as soon as the sightings ( line of sight ) differ by more than a few degrees from the horizontal. The effects must therefore usually be mathematically reduced, which is the subject of Astro Higher Geodesy and Geodesy ( Geodesy ).

In the hill country achieve these effects on the measurements a few arc seconds or a few centimeters per kilometer, in the mountains up to ten times of it. That, for example, still fit together the previous tunnels relatively accurate, is located on the approximate symmetry of most mountain ranges.


Extensive measurements of the deflections of the vertical were first carried out in 1800 by theoretical studies by Carl Friedrich Gauss in the course of Hannovera niches land surveying, in the area of the resin, where Gauss and his assistants expected the greatest effects. In the 1970s, here established the Technical University of Hanover under Wolfgang chance of scoring a modern astro- geodetic network test Westharz.

But for 20 years before there was such considerations and appropriate astrogeodätische measurements by the Scottish explorer James Hutton and Nevil Maskelyne. To determine the density of the rock Shehellien Mountains, they selected measuring points on both sides and compared their (then laboriously ) measured distance with the difference in their astronomically measured widths. The angle difference was found to be 11.6 " and the rock density to 2.6 to 2.8 g / cm ³.

In the early 19th century showed the Indian Land Surveying under George Everest that the deflections of the vertical are particularly high in the Himalayas. Nevertheless, the observations showed markedly lower values ​​than calculated from the mountain masses. The researchers Airy and Pratt explained this about 1855 by a mass compensation in the lower crust, which led to two theories of isostasy.

While one could measure the north-south component attempts of the deflection of the vertical (or the astronomical latitude) already more than 200 years, the East-West component requires a precise astronomical length determination and therefore a precise time system. Such is only since the invention of wireless technology and the subsequent establishment of world time available, which is distributed today by the time signal transmitters. In a larger scale to determine the vertical deflection was therefore possible only in the 20th century.

Around 1930 were astro- geodetic measurements to a standard method of geodesy and the main basis for the required Astro geodetic network adjustment, since the accuracy of the survey networks no longer met the growing needs. From the 1950s to the accelerating until then elaborate Lotrichtungsmessungen by semi-automatic angle and time registration succeeded. Between 1970 and 2000, the research reached on the subjects of deflection of the vertical, geoid and geodetic gravimetry a climax, and this for the same four current requirements:

Through various major projects in Central Europe (mainly Germany, Austria, Switzerland, and Slovenia and Slovakia), in Southern Europe ( Croatia, Greece, Turkey) and South America (especially Argentina) was the geoid of 20-50 cm accuracy in the German language on 2 -5 cm, elsewhere improved to 5-10 cm. In Germany, the deflections of the vertical stands out certain " Astrogeoid " in competition with the " gravimetric geoid ", while mountainous countries such as Austria, Switzerland, Slovakia and Greece prefer the Astrogeoid. In these countries, since about 1990 have a large network of thousands Lotabweichungs and hundreds Laplacepunkten available ( point distances between 7-10 and 50 km), around the world there are tens of thousands of survey points where on earth the exact perpendicular direction was measured.

  • Geodesy
  • Geophysics
  • Astrometry
  • Geodesy
  • Gravimetry
  • Astro Geodesy