# Benchmark

Geodetic benchmark
Fixed point height NN +, Kleve- Wardhausen
Fixed point on the Ötscher summit
Geodetic basic network point Berlin

In geodesy, a fixed point (sometimes also a fixed point ) is a stable measurement point that meets at least the following conditions:

• The point is permanently marketed (stabilized) in nature ,
• a clear reference point (e.g. hole , highest point) is defined according to the intended use and
• a first measurement or a repeat measurement is carried out to calculate the coordinate, height, gravity or position.

If one-dimensional coordinates of the point are given, one speaks of a height reference point (HFP) ; if two-dimensional coordinates of the point are given, from a fixed position point (LFP) .

Particularly stable points of gravity measurement are referred to as gravity fixed points (SFP) (see gravity base network ).

A holistic approach to the previously separate geometrically and physically defined components "location, 3D position, height or geopotential level and gravity" is implemented by the land surveying authorities. For the fixed points called geodetic basic network points (GGP) , at least the geodetic reference values ​​such as height, 2D coordinate, 3D position and gravity value are determined depending on the intended purpose.

## Determination of the position coordinates or the height

The determination of the position coordinates (mostly in the UTM coordinate system or in the historical Gauß-Krüger coordinate system ) must have been carried out by an exact measurement, as was customary for fixed points since the 19th century. The standard geodetic methods for this are network measurements , position determinations with GNSS , terrestrial polygonal lines and, for local additions, the determination of individual points . The coordinates, heights or gravity values ​​of extensive fixed point networks are determined by compensation calculation and allow reliable information about the accuracy achieved. Height control points are mostly determined by a net-like or line-like leveling element that is "hooked" into a wide-meshed base network of the precision leveling element.

The accuracy of modern fixed points is in the centimeter range, for special networks (monitoring, large construction sites, etc.) and for height fixed points to the millimeter. These guide values ​​apply to neighborhood accuracy , i.e. H. between several points within a range of a few kilometers to tens of kilometers.

Over greater distances, the statistically unavoidable error propagation in conventional measurement methods causes the accuracy to drop somewhat. For the classic second and first order triangulation (meshes of around 20 to 60 km) it is a few centimeters, nationwide (over hundreds of kilometers) around 5 to 10 cm. Here, however, a basic network of modern design ("state of the art") must be distinguished from the " utility network " used for cadastre and general public , which for historical reasons can be more imprecise and inconsistent. As a rule, its coordinates have been retained in order not to have to change millions of boundary points , since their local accuracy is sufficient for practice.

The coordinates and / or heights of the points are saved in a fixed point file for later use in further surveying work .

In Austria there are around 29,000 fixed points available.

## Marking or stabilization

The marking (also stabilization) of the fixed points takes place in very different ways, depending on the intended purpose, the nature of the ground, the required durability, the desired stability and legal issues. The marking of the fixed points can consist of different materials and be attached to an existing (e.g. house foundation, abutment (bridge construction) ) or a specially manufactured marking carrier (e.g. granite pillar, concrete pillar) or carry the marking with the actual reference point " ".

In the case of fixed points of the official national survey , the trigonometric points , the effort for marking is higher in order to avoid damage or removal of the point and a necessary re-measurement. The longevity of a fixed point, for example for the analysis of changes in the earth's surface (shift in position, subsidence and / or uplift), is of particular importance here.

• Several marking parts are brought into the ground, centered on top of each other, with millimeter precision and labeled as definition - e.g. B. a stone cube, above a granite plate and above a TP pillar made of granite.
• In addition to the actual point, "security points" are marketed at a distance of a few meters to tens of meters, which are also determined in terms of coordinates and combined into a group. If a point is lost, these can be used as a replacement or to restore the lost point.

## documentation

Almost every fixed point marketed in the ground is overgrown or covered by soil or sediment after a while . In order to find the precisely and cost-intensive fixed points even after a long period of non-use, documentation is made about them:

• Point description or point topography : Sketch of the immediate vicinity of the point. It contains distinctive elements that are likely to remain unchanged in the near future, especially buildings, larger trees and roadsides. For some of these elements, tie lengths are measured in order to be able to find the point a few centimeters below the ground or sward (when building roads or through winter scattering, fixed points can get up to 20 cm deep). These point descriptions are managed (on paper or in digital form) in a fixed point index.
• Fixed point overview : An overview map is created over the fixed points of an area a few km² in which the points are marked as precisely as possible (± 0.3 mm) by small circles. Depending on the size of the area and the density of the points, the point overview has scales between 1: 5,000 and 1: 50,000.

## literature

• Heribert Kahmen : Surveying , Chapters 6, 8 and 19. Gruyter textbook, Berlin 1997
• Bernhard Heck: Calculation methods and evaluation models for land surveying , 3rd edition, Wichmann-Verlag, Karlsruhe 2003

## Individual evidence

1. Integrated geodetic spatial reference on the AdV website, accessed on May 7, 2020
2. Fixed point height on the BEV website of January 23, 2008, accessed on July 13, 2009
3. The trigonometric fixed point field in North Rhine-Westphalia accessed on May 17, 2020