GEOMATIC - Tacheometry Survey

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With Wisdom, We Explore

TACHEOMETRIC SURVEY

Mohd Effendi Daud (Dr. Sc)B.Surv (UTM, Malaysia) Msc (UTM, Malaysia), Dr. Sc (Nagoya Univ., Japan)

(Geomatic Division)Faculty of Civil & Environmental Engineering,

Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor, MALAYSIA.Phone : +6074537363; +60197853740; Fax : +6074537060

E-mail : [email protected] Web: http://www.fkass.uthm.edu.my/

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INTRODUCTION

• This method of survey consists of using either a level, theodolite, “total station”, or specially constructed tacheometer to make cross hair intercept reading on a leveling staff. As the angle subtended by the crosshairs is known, the distance can be calculated.

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DEFINITION

o Tacheometry is an optical solution to themeasurement of distance and elevation(vertical distance).

o The word is derived from the Greek Tacns,meaning ‘swift’, and metrot, meaning ‘ameasure’.

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METHODS OF TACHEOMETRY

• Present day methods of tacheometry can be classified in one of the following three groups.

• The last two groups will not be cover in these lectures.– Stadia System,– Electronic Tacheometry,– Subtense Bar System, and– Optical Wedge System.

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STADIA SYSTEM

• In stadia method, a theodolite is set up at one station and staff is held at another station. The staff intercept (S) which is the difference between the upper stadia and the lower stadia hair is measured.

• The vertical angle () is also measured.

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STADIA SYSTEM

• The horizontal distance (D) between the Center of Instrument and staff stations is computed using staff intercept (S) and the vertical angle ()

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• There are two types of stadia method– Fixed Hair Method

• In fixed hair method, the vertical spacing between upper and lower stadia hairs, called stadia interval I, is fixed, while the staff intercept (S) varies depending upon horizontal distance between the instrument station and the staff station.

– Movable Hair Method

STADIA SYSTEM

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• The fixed hair method is the most commonly employed method for tacheometric measurements. Figure 1.0 shows the types of diaphragms used in a fixed hair stadia tacheometer (theodolite).

STADIA SYSTEM

Fig. 1.0: Types of diaphragms

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• In stadia method, the staff is held vertical, the line of sight may be horizontal or inclined either in upward direction or downward direction.

• There can be three cases as given below:– Line of sight horizontal,– Line of sight inclined upward, and– Line of sight inclined downward.

STADIA SYSTEM

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Line of Sight Horizontal– Let us assume that the line of sight is horizontal. Figure 2.0

shows the outline of telescope with its axis horizontal. The staff is held vertically.

STADIA SYSTEM

A, B & X : positions of lower, upper, and middle hair the staff.a, b & x : positions of lower, upper, and middle hairsab : i (stadia interval)c : distance from object lens to the center of the instrumentAB : S (staff intercept)D : distance between the instrument & staff

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STADIA SYSTEM

• Line of Sight Horizontal ab

AB

V

U

ox

OX

From the diagram, triangles AOB, aOb are similar

From the lens equation:

fVU

111

Multiply both sides by Uf:

ffV

UU

From the equation 1.0 and 2.0:

ffab

ABU ff

i

SU fS

i

fU

The horizontal distance:

)( cfSi

fD

cUD

If multiplicative constant, C=f/i, and additive constant, K =f + c,The tacheometric distance formula may be stated as:

KCSD

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Line of Sight Inclined Upward– Distance and Elevation Formula

• The theory discussed so far, in The Stadia System, all applies to the situation where the staff is held vertically and the line of sight of the telescope is horizontal.

• It is very seldom, however, that this situation occurs in practice

STADIA SYSTEM

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• Generally a theodolite is sighted to a level staff held vertically (by use of a bubble), which gives rise to the situation below.

STADIA SYSTEM

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STADIA SYSTEM

,1 KCsD cos1 ss

coscos

cos2 kCs

DS

• Let the actual distance between upper and lower stadia be S and the required projection of it at right angles to IQ be s1

sin2

2sin

sinsincos

sin

kSc

kCs

DV

2sin50

cos100 2

sV

ss

but

Now

Also

In practice,

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STADIA SYSTEM

CLVHIH

The difference in height betweenThe two points is given by:

And the Relative Level (R.L) ofThe points is given by

CLVHIRLRL A

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ELECTRONIC TACHEOMETRIC

• Used a Total Station, able to read distance by reflecting off a prism.

• The stadia procedure is used less and less often these days, more commonly geomatic engineers or civil engineers use a Total Station

• This instrumentation has facilitated the development of this method of detail and contour surveying into a very slick operation.

• It is now possible to produce plans of large areas that previously would have taken weeks, in a matter of days.

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ELECTRONIC TACHEOMETRIC

HTVHIRLRL

DS

A cos

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DETAILING & BOOKING

• Tacheometric surveys are generally conducted for contouring, and plotting the details of the area on undulating ground.

• There are two main steps in tacheometric surveys:– Running a traversing around the area to be surveyed,– Locating details and elevations of the features in the area

with reference to the traverse stations

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DETAILING & BOOKING

Figure above shows a part of the traverse with three stations A, B and C andSome features in the area. The following observation procedure is adoptedFor detailing.

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Procedure – Set up the instrument at a station (say station B), centre

and level it accurately.– Measure the height of instrument (HI) from the top of the

peg at the station to the centre of the trunion of the instrument.

– Orientate the instrument correctly with respect to a reference line (traverse line, BA) whose bearing from the station is already known by traversing.

DETAILING & BOOKING

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Procedure … cont.,– Take the pole reading held vertical on the nearest

available temporary benchmark (TBM) to determine the reduced level of the instrument station.

– Located the detail points around the traverse station (B) as given below:

• Observe the horizontal angle between the reference line and the line from the instrument station towards the point of interest.

• Observe the vertical angle and the pole readings.Repeat the steps above for all the points of interest.

DETAILING & BOOKING

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WORK EXAMPLE 1

• Determine the difference in elevation and the horizontal distance between the points A and B from the following observations.

The instrument was set up at O at 1.500 m height, and the RL ofStation O was 12.635 m.

Calculate the following:(i) Horizontal distances OA and OB(ii) RLs of station A and B(iii) Difference in elevation between A and B

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• The following observations obtained from tacheometry survey.

WORK EXAMPLE 2

The RL of P is 58.775 m. Determine the distances PQ and QR and theReduced levels of Q and R.

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ACCURACY AND TYPES OF ERRORS

• Besides all the errors discussed in the topic on total station, there are four (4) specific sources of errors needed to be mentioned in tacheometric observations– Staff readings– Tilt of the pole or staff– Vertical angle, and– Horizontal angle

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PLOTTING OF TACHEOMETRIC DATA

• The process of tying the topographic details to the control stations fixed by traversing is called detailing.

• A map is the final product of a tacheometric survey.

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Type of Maps• Maps produced or normally used by engineers may

fall into one of the following three categories:– Topographic maps 1:50,000 to 125,000 which shows

natural and cultural features of an area.– Plans 1:10,000 or larger, which shows boundaries and

main features like roads, bridges and main buildings.– Detail survey plans (construction plans) at 1:1,000 – 1:250


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Plotting Methods• Can be carried out manually, or by employing

computer aided design (CAD) systems.• The procedure consists fundamentally of plotting

individual points, regardless of which method is used.– Lines are drawn from point to point to show the features.– Points can be plotted in different ways using distances and

directions, and lines can be scaled and plotted directly.


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Plotting Methods• There are two main methods of plotting details as

discussed below:– Plotting by Coordinates– Plotting by Angle/bearing and Distances.


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Map Layout• The surveyed area should be plotted to fit neatly in

the centre of a map sheet at the largest possible scale.– North Direction

• Every map must display a north line for orientation purpose.– Topographic Symbols (Legends)

• Standard symbols should be used to portray topographic features.– Title of Map

• Place title of the map where it is balanced on the sheet.


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Map Layout


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CONTOURING AND CROSS-SECTIONS

Mohd Effendi Daud (Dr. Sc)B.Surv (UTM, Malaysia) Msc (UTM, Malaysia), Dr. Sc (Nagoya Univ., Japan)

(Geomatic Division)Faculty of Civil & Environmental Engineering,

Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor, MALAYSIA.Phone : +6074537363; +60197853740; Fax : +6074537060

E-mail : [email protected] Web: http://www.fkass.uthm.edu.my/

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CONTOURING

• For planning and development of an engineering project, the engineer requires the topographic of the natural ground.

• An understanding of contours is therefore essential in the interpretation of surface topography.

• Some basic understanding of contours is as follow:

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CONTOURING

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– A contour is an imaginary line connecting all points of the same elevation above or below a datum.

– Contours of different elevation cannot cross each other except in the case of overhanging cliff or a cave.

– The height between successive contours is called the contour interval

• Its value depends on the variation in height of the area being contoured.

• The contour interval is kept constant for a plan or map

CONTOURING

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– The plan spacing between contour line indicates the steepness of slopes.

• Closely spaced lines indicated a steep slope• Widely spaced lines indicate a gentle slope.

CONTOURING

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CONTOURING

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Production of contours• There are TWO types of contouring method:

– Direct Methods, and– Indirect Method:

• from random spot heights• from a grid of spot heights

CONTOURING

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CONTOUR INTERPOLATION & PLOTTING

• There are THREE methods of interpolating contours:– Mathematical calculation,– Graphical method, and– Estimation method.

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PROFILE AND CROSS-SECTIONS

• Profiles (longitudinal sections) is generally carried out along the center line of a proposed alignments e.g. highways, railways, pipelines or canals.

• The profile is usually plotted with the vertical scale much larger than the horizontal scale.

• The term cross-sectioning refers to a relatively short profile view of the ground, which is drawn perpendicular to the route center line of a highways or other linear type projects.

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• Cross-section drawing are particularly important for estimating the earthwork volumes needed to construct a roadway, canal, railroad, etc.

• They show the existing ground elevations, the proposed cut or fill side slopes, and the grade elevation for the road base.

• For one route profile, there are many cross-sections; a km-long route, for example, will have more than 100 cross-sections every 50 m.

PROFILE AND CROSS-SECTIONS

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Pheewww! End of Part V

GEOMATIC - Tacheometry Survey

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