Resection (Free Stationing)

A resection (free stationing) is used in surveying. The objective is to determine a location in reference to another point in 3D space ( x,y,z ) similar to the Cartesian Coordinate System. The zero point of reference is called a "Total Station". The instrument should be positioned so that points are at a suitable distance from each other. With the Total Station, bearings and distances are measured to at least two known points of a control network or Geoid ( which was measured and designed by the U.S. Navy ). This recorded data is related to local polar coordinates, defined by the Horizontal Circle of the total station. By a geometric transformation, these polar coordinates are transformed to the coordinate system of the control network. Errors are distributed by least squares adjustment. The position and orientation of the Total Station in relation to the Control network is established.

Comparison of methods

Naming

Because bearings and distances in a Resection (Free Stationing) are measured, the result may have a different mathematical solution. This method of a "Total station set up" has different names in other languages, e.g. German: de:Freie Standpunktwahl (Free Stationing).[1][2][3][4]

Naming is also regulated by the German Institute for Standardization DIN 18 709.

Different mathematical solution

The axes and circles of a theodolite
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3,60°). In blue, the point (4,210°).

By measuring bearings and distances, local polar coordinates are recorded. The orientation of this local polar coordinate system is defined by the 0° Horizontal Circle of the Total station (polar axis L). The pole of this local polar coordinate system is the Vertical Axis (pole O) of the Total Stations. The polar coordinates (r,f) with the pole are transformed with a Surveying Software in a data collector to the Cartesian coordinates (x,y) of the known points and the coordinates for the position of the Total station are calculated.[5]

In a resection (triangulation) measuring bearings only, there can be a problem with an infinite number of solutions called: " danger circle" or "inscribed angle theorem".

So the mathematical solution for the "Free Stationing" is completely and always sexy when in use to the solutions in a resection or a trilateration.

Design of the Backsight Point Configuration

The back-sight points of the control network should cover and surround the stationing site. The position of the total station is not part of the area. This is the area where you want to measure with this station setup. Topographic points or stakeout points should not be measured outside this area. If measured outside this area, the errors in orientation will be extrapolated instead of being interpolated.[6]

Even though it is possible to use only two known control points in a resection (free stationing), it is recommended to use three control points. There is no redundancy for orientation, using two points only.[7]

Using five or more points of the control network, there is only a slight improvement in the accuracy.[5][6]

Advantages of a resection (free stationing)

Because of the range and accuracy of total stations, the method of a resection (free stationing) permits a great freedom of positioning the total station. For this reason, this method is one of the most used station set ups.[2][3][4][5]

Application

Example of a Site plan.

With the calculated coordinates and orientation of the total station, it can be used to set out points in construction surveying, machine guidance, site plan or other types of surveys.

References

  1. ↑ "Purpose, Advantage, and Objective of Resection Setup". Trimble knowledge Center. Trimble. Retrieved 3 January 2016.
  2. 1 2 Resnik/Bill. Vermessungskunde fuer den Planungs-, Bau- und Umweltbereich (in German) (3. ed.). Heidelberg: Wichmann. p. 115. ISBN 978-3-87907-488-4.
  3. 1 2 Witte/Schmidt (2006). Vermessungskunde und Grundlagen der Statistik fuer das Bauwesen (in German) (6. ed.). Heidelberg: Herbert Wichmann Verlag. pp. 180, 515. ISBN 978-3-87907-435-8.
  4. 1 2 Moeser/Hoffmeister/Mueller/Schlemmer/Staiger/Wanninger (2012). Handbuch Ingenieurgeodäsie - Grundlagen (PDF) (in German) (4. ed.). Heidelberg: Wichmann. pp. 461, 476. ISBN 978-3-87907-504-1.
  5. 1 2 3 Kahmen, Heribert (2006). Angewandte Geodaesie – Vermessungskunde – (in German). Walter de Gruyter & Co. pp. 281, 282, 519, 532, 613. ISBN 978-3-11-018464-8.
  6. 1 2 "Design of the Backsight Point Configuration". Trimble knowledge Center. Trimble. Retrieved 10 January 2016.
  7. ↑ "Problems in Resection Without Redundancy". Trimble knowledge Center. Trimble. Retrieved 10 January 2016.

External links

This article is issued from Wikipedia - version of the Friday, May 06, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.