Triangulation Figures And Layouts

UNIVERSITY OF LAGOS AKOKA, YABA

FIGURES/LAYOUTS USED IN TRIANGULATION NAME: OLUWO ABISOYE I.T. MATRIC NO: 070405027 LEVEL: 300 COURSE: SVY 302 (GEODETIC SURVEYING) LECTURER: EPUH (DR.)

June, 2009

TRIANGULATION FIGURES AND LAYOUTS The basic figures used in triangulation are listed as follows: -

Triangle

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Braced or geodetic quadrilateral

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Polygon with a central station

Triangle Polygon with central station

Braced Equilateral

The triangles in triangulation system can be arranged in a number of ways. Some of the commonly used arrangements, also called layouts are as follows; 1) Single chain of triangles 2) Double chain of triangles 3) Braced quadrilaterals 4) Centred triangles and polygons 5) A combination of the above systems

1) Single Chain Triangles When the control points are required to establish in a narrow strip of terrain such as a valley between ridges, a layout consisting of single chain of triangles is generally used below. This system is rapid and economical due to its simplicity of sighting four other stations, and does not involve observations of long diagonals.

On he other hand, simple triangles of a triangulation system provide only one route through which distances can be computed, and hence, this system does not provide any check on the accuracy of observations. Check base lines and astronomical observations for azimuths have to be provided at frequent intervals to avoid excessive accumulation of errors in this layout.

Single Chain of triangles

2) Double Chain of Triangles A layout of double chain of triangles is shown below. This arrangement is used for covering the larger width of a belt. This system also has disadvantages of single chain of triangles system.

Double chain of triangles

3) Braced Quadrilaterals A triangulation system consisting of figures containing four corner stations and observed diagonals shown below in a diagram known as a layout of braced quadrilaterals. In fact, braced quadrilaterals consist of overlapping triangles. This system is treated to be the strongest and the best arrangement of triangles, and it provides a means of computing the lengths of the sides using different combinations of sides and angles. Most of the triangulation systems use this method.

Braced quadrilaterals

4)

Centred Triangles and Polygons

A triangulation system which consists of figures containing interior stations in triangle and polygon as shown below is known as centred triangles and polygons.

Centred triangles and polygons

This layout in a triangulation system is generally used when vast area in all directions is required to be covered. The centred figures generally are quadrilaterals, pentagons, or hexagons with central stations. Though this system provides check on the accuracy of the work, generally it is not as strong as the braced quadrilateral arrangement. Moreover, the progress of work is quite slow due to the fact that more settings of the instrument are required. Other permissible figures include; a)

Simple Quadrilateral:

The simple quadrilateral is the best figure, and it should be employed wherever possible. It combines maximum strength and progress with a minimum of essential geometrical conditions when approximately equilateral or square and therefore the square quadrilateral is the perfect figure. It has a strength factor.

b)

Four-sided central point-figure with one diagonal: When one diagonal of the quadrilateral is obscured, a central point, which is visible from the four corners, can be inserted. This figure requires the solution of two side equations and five angle equations, and hence adds to the labour of adjusting. Its strength factor is 0.56.

c)

Four-sided central-point figure without diagonal : At times, neither diagonal can be made visible and the figure becomes a simple four sided central-point quadrilateral with a strength factor of 0.64. The central point in this case should be carefully located to maintain the strength of the R1 chain of triangles. An excellent location is near on side line and about midway along it. If too near the side line, however, refraction errors may be also the same for the closely adjacent lines, and furthermore,

the R2 value will be so large as to be of little value as a check on lengths computed through the R1 triangles.

d)

Three-sided central-point figure: This is a simple and usually strong figure. It is often used to compensate for a great variation in length of the side lines of adjacent quadrilaterals, and to quickly change the direction of the scheme. Its strength factor is 0.6 and the equations required for its adjustment are the same of a regular quadrilateral.

e) Five sided figure with four diagonals : This figure may be considered as a four centre point figure with one diagonal, in which the central point falls outside the figure. It is used to afford a check when either a diagonal or a side line is obstructed. It has the same strength factor, 0.56, as the above four sided centre point figure with one diagonal, (B), and requires the same adjustment equations and precautions against making any if the angles too small. This figure can often be used by the observing party when a sideline of a quadrilateral is found to be obstructed.

f)

Five sided figure with three diagonals: The figure is similar to four sided centre point figure, (C), except that the centre point falls outside the figure. The strength factor is 0.64.

g)

Five sided figure central point figure with two diagonals: This figure is an overlap of an overlap of a central point quadrilateral and is the most complicated figure employed. It has been used to carry the scheme over difficult or convex areas. This figure can generally be made strong. Its strength factor is 0.55,

h) Five and six sided central point figures without diagonals : Any polygon with a central point, having separate chains of triangle on either side of the central point, wiil give a double determination of length,

since it is permissible to carry the two lengths through the same triangle provided different combination of distance objects are employed. However, the five and six sided central point polygons are the only ones that should receive considerations, and they are inferior to the simpler quadrilaterals. The factors of strength are 0.67 for five sides and 0.68 for six.