Methods of point fixation
A control survey provides a framework of survey points, whose relative positions, in
two or three dimensions, are known to specified degrees of accuracy. The areas covered
by these points may extend over a whole country and form the basis for the national maps
of that country. Alternatively, the area may be relatively small, encompassing a
construction site for which a large-scale plan is required. Although the areas covered in
construction are usually quite small, the accuracy may be required to a very high order.
The types of engineering project envisaged are the construction of long tunnels and/or
bridges, deformation surveys for dams and reservoirs, three-dimensional tectonic
ground movement for landslide prediction, to name just a few.
Hence control networks provide a reference framework of points for:

Topographic mapping and large-scale plan production.

Dimensional control of construction work.

Deformation surveys for all manner of structures, both new and old.

The extension and densification of existing control networks.
The methods used for control surveys are:
(1) Traversing.
(2) Intersection and resection.
(3) Least squares estimation of survey networks.
(4) Satellite position fixing
Traversing
Traversing is one of the simplest and most popular methods of establishing control
networks in engineering surveying. In underground mining it is the only method of
control applicable whilst in civil engineering it lends itself ideally to control surveys
where only a few intervisible points surrounding the site are required.
Traverse networks have the following advantages:

Little reconnaissance is required compared with that needed for an interconnected
network of points.
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Surveying II Notes by Sichangi

Observations only involve three stations at a time so planning the task is simple.

Traversing may permit the control to follow the route of a highway, pipeline or
tunnel, etc., with the minimum number of stations.
Types of traverse
Link traverse
Polygonal traverse
Open (or free) traverse
Sources of error
The sources of error in traversing are:

Errors in the observation of horizontal and vertical angles (angular error).

Errors in the measurement of distance (linear error).

Errors in the accurate centering of the instrument and targets, directly over the
survey point (centering error).
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Surveying II Notes by Sichangi
Procedure of running a traverse
 To begin any traverse, a known point must be occupied. (To occupy a point
means to set up and level the transit or theodolite, directly over a monument on
the ground representing that point.)

Next, a direction must be established. This can be done by sighting with the
instrument a second known point, or any definite object, which is in a known
direction from the occupied point.

The object that the instrument is pointed to in order to establish a direction is
known as a back sight.

Possible examples would be another monument on the ground, a radio tower or
water tank on a distant hill, or anything with a known direction from the occupied
point. the entire process.

A celestial body such as Polaris or the sun could also be used to establish an initial
direction.

Once the instrument is occupying a known point, for example point number 2, and
the telescope has been pointed toward the backsight, perhaps toward point
number 1, then an angle and a distance is measured to the first unknown point.
An unknown point being measured to is called a foresight. With this data, the
position of this point (lets call it point number 100) can be determined.

The next step is to move the instrument ahead to the former foresight and
duplicate
Traverse computation
The computational steps, in the order in which they are carried out, are:

Obtain the angular misclosure W, by comparing the sum of the observed angles
(α) with the sum of error-free angles in a geometrically correct figure.

Assess the acceptability or otherwise of W.

If W is acceptable, distribute it throughout the traverse in equal amounts to each
angle.
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Surveying II Notes by Sichangi

From the corrected angles compute the whole circle bearing of the traverse lines
relative to AB.

Compute the coordinates (∆'E, ∆'N) of each traverse line.

Assess the coordinate misclosure (∆'E, ∆'N).

Balance the traverse by distributing the coordinate misclosure throughout the
traverse lines.

Compute the final coordinates (E, N) of each point in the traverse relative to A,
using the balanced values of ∆' E, ∆' N per line.
Distribution of angular error
The majority of the systematic errors associated with horizontal angles in a traverse are
eliminated by repeated double-face observation. The remaining random errors are
distributed equally around the network as follows.
In a polygon the sum of the internal angles should equal (2n−4)90◦, the sum of the external
angles should equal (2n + 4)90◦.
Where α = observed angle
n = number of angles in the traverse
The angular misclosure W is now distributed by equal amounts on each angle, thus:
Correction per angle = W/n = +10’’
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Surveying II Notes by Sichangi
However, before the angles are corrected, the angular misclosure W must be considered
to be acceptable. If W was too great, and therefore indicative of poor observations, the
whole traverse may need to be re-measured. A method of assessing the acceptability or
otherwise of W is given in the next section.
Acceptable angular misclosure
The following procedure may be adopted provided the variances of the observed angles
can be assessed, i.e.
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