Free stationing

Last updated

In surveying, free stationing (also known as resection) is a method of determining a location of one unknown point in relation to known points. [1] There is a zero point of reference called a total station. The instrument can be freely positioned so that all survey points are at a suitable sight from the instrument. Setting up the total station on a known point, often it is not possible to see all survey points. With the total station, bearings and distances are measured to at least two known points of a control network. This with a handheld computer 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 where the control network is established.

Contents

Comparison of methods

Naming

Because bearings and distances are measured in a full resection (free stationing), the result may have a different mathematical solution. This method of a "total station set up" has different names in other languages, e.g. in German: 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 Theodolite vermeer.svg
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 (3,60deg). In blue, the point (4,210deg). Examples of Polar Coordinates.svg
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".

Back-sight points

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]

While 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

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 PLANTA proceso.JPG
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.

Related Research Articles

<span class="mw-page-title-main">Geodesy</span> Science of measuring the shape, orientation, and gravity of the Earth and other astronomical bodies

Geodesy is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems.

<span class="mw-page-title-main">Surveying</span> Science of determining the positions of points and the distances and angles between them

Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.

<span class="mw-page-title-main">Coordinate system</span> System for determining the position of a point by a tuple of scalars

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

<span class="mw-page-title-main">Triangulation</span> Method of determining a location

In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.

<span class="mw-page-title-main">Bearing (angle)</span> In navigation, horizontal angle between the direction of an object and another object

In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:

<span class="mw-page-title-main">Theodolite</span> Optical surveying instrument

A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.

<span class="mw-page-title-main">Total station</span> Electro-optical instrument used in surveying and building construction

A total station (TS) or total station theodolite (TST) is an electronic/optical instrument used for surveying and building construction. It is an electronic transit theodolite integrated with electronic distance measurement (EDM) to measure both vertical and horizontal angles and the slope distance from the instrument to a particular point, and an on-board computer to collect data and perform triangulation calculations.

<span class="mw-page-title-main">Levelling</span>

Levelling or leveling is a branch of surveying, the object of which is to establish or verify or measure the height of specified points relative to a datum. It is widely used in geodesy and cartography to measure vertical position with respect to a vertical datum, and in construction to measure height differences of construction artifacts.

<span class="mw-page-title-main">Geodetic control network</span>

A geodetic control network is a network, often of triangles, which are measured precisely by techniques of control surveying, such as terrestrial surveying or satellite geodesy.

Resection may refer to:

<span class="mw-page-title-main">Benchmarking (hobby)</span> Game

Benchmarking, also known as benchmark hunting, is a hobby activity in which participants find benchmarks. The term "bench mark" is used only to refer to survey markers that designate a certain elevation, but hobbyists often use the term benchmarks to include triangulation stations or other reference marks. They typically then log their finds online. Like geocaching, the activity has become popular since 1995, propelled by the availability of on-line data on the location of survey marks and by the rise of hobbyist-oriented websites.

Traverse is a method in the field of surveying to establish control networks. It is also used in geodesy. Traverse networks involve placing survey stations along a line or path of travel, and then using the previously surveyed points as a base for observing the next point. Traverse networks have many advantages, including:

A positioning system is a system for determining the position of an object in space. One of the most well-known and commonly used positioning systems is the Global Positioning System (GPS).

<span class="mw-page-title-main">Earth-centered, Earth-fixed coordinate system</span> 3-D coordinate system centered on the Earth

The Earth-centered, Earth-fixed coordinate system, also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth as X, Y, and Z measurements from its center of mass. Its most common use is in tracking the orbits of satellites and in satellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion.

<span class="mw-page-title-main">Survey marker</span>

Survey markers, also called survey marks, survey monuments, or geodetic marks, are objects placed to mark key survey points on the Earth's surface. They are used in geodetic and land surveying. A benchmark is a type of survey marker that indicates elevation. Horizontal position markers used for triangulation are also known as triangulation stations. Benchmarking is the hobby of "hunting" for these marks.

<span class="mw-page-title-main">Fire control tower</span>

A fire control tower is a structure located near the coastline, used to detect and locate enemy vessels offshore, direct fire upon them from coastal batteries, or adjust the aim of guns by spotting shell splashes. Fire control towers came into general use in coastal defence systems in the late 19th century, as rapid development significantly increased the range of both naval guns and coastal artillery. This made fire control more complex. These towers were used in a number of countries' coastal defence systems through 1945, much later in a few cases such as Sweden. The Atlantic Wall in German-occupied Europe during World War II included fire control towers.

The term fundamental station is used for special observatories which combine several space positioning techniques like VLBI, satellite laser ranging, GPS, Glonass, etc. They are the basis of plate tectonic analysis, allowing the monitoring of continental drift rates with millimetre accuracies. A fundamental point is the geometric origin of a geodetic network and defines the geodetic datum of a national survey.

Position resection and intersection are methods for determining an unknown geographic position by measuring angles with respect to known positions. In resection, the one point with unknown coordinates is occupied and sightings are taken to the known points; in intersection, the two points with known coordinates are occupied and sightings are taken to the unknown point.

Construction surveying or building surveying is to stake out reference points and markers that will guide the construction of new structures such as roads or buildings. These markers are usually staked out according to a suitable coordinate system selected for the project.

<span class="mw-page-title-main">Triangulation (surveying)</span> Using measures of converging rays to improve fixed points for mapping

In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline by using trigonometry, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as the third point of a triangle with one known side and two known angles.

References

  1. 1 2 "Purpose, Advantage, and Objective of Resection Setup". Trimble knowledge Center. Trimble. Retrieved 3 January 2016.
  2. 1 2 Resnik/Bill (2009). 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.