surveying Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geom ...

, free stationing (also known as resection) is a method of determining a location of one unknown point in relation to known points. There is a zero point of reference called a

total station A total station or total station theodolite 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 vertic ...

. The instrument can be freely positioned so that all survey points are at a suitable sight from the instrument. When setting up the total station on a known point, it is often not possible to see all survey points of interest. When performing a resection (free stationing) with the total station, bearings and distances are measured to at least two known points of a control network. With use of a handheld computer, recorded data can be related to local

polar coordinates In mathematics, the polar coordinate system specifies a given point (mathematics), point in a plane (mathematics), plane by using a distance and an angle as its two coordinate system, coordinates. These are *the point's distance from a reference ...

, defined by the horizontal circle of the total station. By a

geometric transformation In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning, such as preserving distances, angles, or ratios (scale). More specifically, it is a function wh ...

, these polar coordinates are transformed to the coordinate system of the control network. Error can be distributed by least squares adjustment. Upon completion of observations and calculations, a coordinate is produced, and the position and orientation of the total station in relation to where the control network is established.

Comparison of methods

* Angular resection and

triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle m ...

: only bearings are measured to the known points. *

Trilateration Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth ( geopositioning). When more than three distances are involved, it may be called multilateration, f ...

: only distances are measured to the known points. * Free stationing and triangulateration: both bearings and distances are measured to the known points.

Naming

Because bearings and distances are measured in a full resection (free stationing), the result may have a different mathematical solution. This method has different names in other languages, e.g. in German: '' Freie Standpunktwahl'' (free stationing). Naming is also regulated by the

German Institute for Standardization German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

DIN 18 709.

Different mathematical solution

By measuring bearings and distances, local

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 In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular o ...

(pole O) of the total stations. The polar coordinates (r,f) with the pole are transformed using surveying software on a data collector to the

Cartesian coordinates In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular o ...

(x,y) of the known points. The coordinates for the position of the total station are then calculated. In a resection (triangulation) measuring bearings only, there can be a problem with an infinite number of solutions known as a " danger circle", or "

inscribed angle theorem In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an ...

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. 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. When performing a resection (free-stationing) on more than 4 points, diminishing returns are achieved in the returned results.

Advantages

The surveyor may freely set a station point: * Where there is best visibility to all points that must be staked out or recorded * Where there are no obstructions or traffic * Where there is the highest safety for the operator and the instrument 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.

Application

With the calculated coordinates and orientation of the total station, it can be used to set out points in

construction surveying Construction surveying or building surveying (otherwise known as "staking", "stake-out", "lay-out", or "setting-out") is to provide dimensional control for all stages of construction work, including the stake out of reference points and markers t ...

, machine guidance, site plan or other types of surveys.

References

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External links

Topcon Magnet Field 1.0 Help

Leica SmartWorx Viva Field Software Datasheet

CarlsonSurvCE Reference Manual

12d Field – Helmert Resection

Trimble: Advantages and Disadvantages of the Stationing Programs

Trimble: Neighborhood Adjustment
Surveying Surveying instruments Geodesy Civil engineering