ANGULAR MEASUREMENT · distances. A more modern and sophisticated equipment is the electronic theodolite, and another more sophisticated instrument is the theodolite known as the

ANGULAR MEASUREMENT

doc. Ing. Hana Staňková, Ph.D

VŠB - Technical University of Ostrava

SUMMARY

1. Introduction2. Theodolite3. Construction of theodolite4. Method of measuring angles5. Sources of error6. Instrument error7. References

VŠB - Technical University of Ostrava Engineering Geodesy

1. INTRODUCTION

The purpose of all the topographic work is the observation in the field of a series of points that allows later in the cabinet the obtaining of its coordinates for:• Make a graphic representation of a zone.• Know its geometry.• Know your altimetry.• Calculate a surface, length, slope, ...

This science studies the methods and procedures to make measurements on relatively small terrains and capture them in graphic form and scale in a plane, with all the necessary characteristics to project architecture and civil engineering works.


2. THEODOLITE

A theodolite through the use of other auxiliary tools, can also measure distances and slopes.

The theodolite is portable and manual; it is used in topography and engineering, especially in triangulations. With the help of a look and through tachymetry, measure distances. A more modern and sophisticated equipment is the electronic theodolite, and another more sophisticated instrument is the theodolite known as the total station.

Basically, the current theodolite is a telescope mounted on a tripod and with two graduated circles, one vertical and one horizontal, with which the angles are measured with the help of lenses.


Definition

Universal mechanical-optical measuring instrument used to measure vertical and, above all, horizontal angles with high precision.

3. CONSTRUCTION OF THEODOLITE



A) Visual tube

B) Alidade

C) Leveling base


Components of a theodolite


The tribrach is the support of the instrument, which in turn is made up of: the base plate, the bolts, the spherical level and the aliform button.

It is the part of the tribrach that is distal to the instrument, the base of the plate has its center a threaded hole that allows to fix the instrument on the base of the tripod. It is attached to the fishing screws by means of an elastic plate.


Leveling Base and Motherboard


The ally is the upper and rotating element of the instrument, is formed by the optical plummet, the macro screw of the azimuth movement, the ally level, vertical circle, vertical movement macrometric screw, vertical movement micrometric screw, vertical automatic index, screw minute hand, reflector mirror and carrying handle.


Alidade


It is the part of the telescope by means of which the visuals are launched from the station towards the observed points. It consists of the eyepiece of the telescope, the eye lenses, the focus ring, the lens and lens mount, the reticle, the optical viewfinder with centering tip and the reading microscope.


Visual Tube



Main Axis

Main or vertical axis:

It coincides with the vertical to the center of the plane of the support platform and allows the general movement or rotation of the instrument.

Horizontal or secondary axis:

Perpendicular to the previous one and on which the observation device.

Observation or collimation axis:

Defined by the visual or direction chosen by the operator. This axis must coincide with the optical axis of the telescope. The main axis must be perpendicular to the horizontal and this to the visual axis.



Id Element Id Element Id Element

1 Locking screw and fixation of vertical movement. 7 Telescope or collimator 13 Mirror to see the longitudinal

tubular level

2 Fine adjustment screws, vertical circle. 8 Reader viewfinder focus

horizontal and vertical limbs. 14 Vertical circle protected.

3 Locking screw and locking the horizontal movement. 9 Viewer reader horizontal and

vertical limbs. 15 Support for flashlight, night lighting.

4 Setting screw horizontal circle. 10 Ocular of the telescope 16 Circular level.

5 Transverse tubular level. 11 Focus eyepiece 17 Locking lever horizontal circle.

6 Mirror reflector to illuminate horizontal and vertical limbs. 12 Focus of the reticule 18 Horizontal circle protected.

19 Base leveling screws.

4. METHOD OF MEASURING ANGLES



There are several methods based on angular measurements.


1. Triangulation method

It consists in determining the coordinates of a series of points distributed in triangles starting from two known, which define the base, and measuring all the angles of the triangles:




1. Triangulation method

If A and B are two points of known coordinates (base), to calculate those of C it is enough to measure the angles α, β and γ. These angles are determined by parking at A, B and C and taking the horizontal readings at the other vertices.




2. Intersection method

The intersections are methods in which to determine the position of a point only the measurement of angles is required. If the observations are made from points of known coordinates, they are called direct intersections, and if they are made from the point whose coordinates are to be determined, they are called inverses.If, in addition to measuring horizontal angles, verticals are measured, the Z coordinate can be calculated.





Direct intersection

The method consists of starting from a side AB of known length and azimuth.It is stationed in A and B by measuring α and β as accurately as possible.

This determines the point V that is intended to lift.





Direct intersection

In the simple intersection, the points of known coordinates are designated as D and I according to whether they lie to the right or left of the point V that is to be calculated.The DVI triangle is defined because the base (DI) and two angles are known.





Inverse intersection

At the inverse intersection, the angular observations are made from the point P whose coordinates are to be determined. In the simple intersection, the horizontal readings are taken at three points of known coordinates, which are the minimums that are needed to solve the geometry. In the multiple intersection measurements are made to more than three points, and it is a more advisable method to make checks.





Inverse intersection

• Simple reverse intersection solution:

Starting data: coordinates of A, B and C. Observations: from P the horizontal readings are taken at A, B and C.




2. Intersection method Inverse intersection

The analytical solution consists of calculating the reduced distance and the azimuth from A, B or C. To do this, the triangles ABP or BCP must be solved. From these two triangles we know an angle and a side, and we will look for a third data:

• Triangle ABP

• Triangle BCP




2. Intersection method Inverse intersection

To calculate the angles in A and C, two equations will be searched where those unknowns appear:

• 1st equation:It is established by matching the BP side of the ABP and BCP triangles.

(known value k)

• 2nd equation:It is established by knowing the value of

the sum of the angles of the polygon ABCP.

This will have the value of A, and replacing it in the 2nd equation, that of C.

5. SOURCES OF ERROR


5. SOURCES OF ERROR

ERROR: Difference between the true value to be found and the one found.


Any observation can be affected by two types of errors, one of them in a safe way, the accidental ones; the others may or may not exist depending on the state of the instrument, the systematic.

1. Systematic errorsThey are those that are repeated equally throughout the set of measurements. These are associated with imperfections or decalibration of the instruments

2. Accidental errorsThis type of errors are associated with those responsible for making the measurements, however they have the condition that they do not commit negligence but for causes that they can not eliminate from them. This is why these types of errors are called fortuitous.

5. SOURCES OF ERROR ERROR: Difference between the true value to be found and the one found.


3. Reading errors

4. Casual errors

5. Human errors

6. Atmosphericerrors

They are the errors of observation produced by imperfections in the measuring instruments or by deficiency in the experimental method.

They are the errors of observation produced by uncontrolled or unknown causes, being the observer himself the most determining cause.

Are caused by the same condition of human imperfection, these errors can be presented by distraction of people who perform any type of work.

Nature acts on all the elements that surround it and on those that are interacting with it, for that reason equipment and tools are also affected by factors such as temperature, atmospheric pressure, altitude, humidity, radiation, cloudiness, etc ...

5. SOURCES OF ERROR


Azimuth observations Zenith observations

Vertical error.

Direction error.------------------

Read error.

Pointing error

Total error angle

MINIMIZE ERRORS AND INCREASE ACCURACY


There are different methods to increase the accuracy of a theodolite, minimizing systematicerrors and accidents.

Besel Rule:Reading each horizontal angle to a point in two diametrically opposite areas to thelimbus. Performed the first reading with the telescope position normal(direct circle),reverse the telescope, and we aim at the same point, rotatingthe instrument on its vertical axis (circle reverse).

Repeat method:Read an azimuth angle several times repeated that accumulate to a value of readingin the horizontal circle of n times the value of the angle.

Iteration method:Measure an angle several times, independent of each other, with application of theRule of Bessel for each repetition. The average of all measures will be the mostprobable angle value.

6. INSTRUMENT ERROR


6. INSTRUMENT ERROR

Are the errors that arise due to improper use, careless handling or wear of equipment, patterns or devices that we use to make or check measurements or magnitudes, whether angular or linear distances.

As regards topography equipment, they should be kept clean, if possible stored in a dry place, transported properly in their original boxes or cases without receiving strong shocks or vibrations, should be cleaned with products that are not abrasive or that deteriorate the physical properties of the materials, the equipment should not be carried on the external parts of a vehicle or truck, should not be thrown to the ground or use their transport boxes as a seat, ladder or base to place things, when takes into account all these observations it is advisable to reduce the time between each maintenance to give the equipment an appropriate adjustment and verification, it must be taken into account that the durability and correct operation of any machine depends on the maintenance and care of the operator.


6. INSTRUMENT ERROR

The most common instrumental errors are:


1. The alidade levels are out of adjustment.2. The collimation line is not perpendicular to the height axis3. The height axis is not perpendicular to the azimuthal axis.4. The guideline of the telescope level is not parallel to the collimation

line5. Eccentricity of the vernieres. (Vernier is a small scale used to obtain

fractional parts of the smaller divisions of the main scale without recourse to interpolation).

7. REFERENCES

http://ocw.upm.es/expresion-grafica-en-la-ingenieria/dibujo-de-construccion/contenidos/MetodosTopograficos/dc3_metodos_topograficos.pdf

http://www.academia.edu/16092284/ERRORES_EN_MEDICIONES_TOPOGR%C3%81FICAS

https://prezi.com/xi04rxdxmsbm/caracteristicas-basicas-de-construccion-de-los-teodolitos/

https://es.scribd.com/document/254279183/Construccion-de-Un-Teodolito


http://ocw.upm.es/expresion-grafica-en-la-ingenieria/dibujo-de-construccion/contenidos/MetodosTopograficos/dc3_metodos_topograficos.pdf

http://www.academia.edu/16092284/ERRORES_EN_MEDICIONES_TOPOGR%C3%81FICAS

https://prezi.com/xi04rxdxmsbm/caracteristicas-basicas-de-construccion-de-los-teodolitos/

https://es.scribd.com/document/254279183/Construccion-de-Un-Teodolito

VŠB - Technical University of Ostrava

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ANGULAR MEASUREMENT · distances. A more modern and sophisticated equipment is the electronic theodolite, and another more sophisticated instrument is the theodolite known as the