Week 9 Tacheometry Survey2
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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/
mailto:[email protected]://www.fkass.uthm.edu.my/http://www.fkass.uthm.edu.my/mailto:[email protected] -
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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 ona 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 the
measurement of distance and elevation
(vertical distance).
o The word is derived from the Greek Tacns,
meaning swift, and metrot, meaning a
measure.
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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 theselectures.
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 thevertical 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 downwarddirection.
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 hairs
ab: i (stadia interval)c: distance from object lens to the center
of the instrument
AB: S (staff intercept)
D: distance between the instrument &
staff
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STADIA SYSTEM
Line of Sight Horizontalab
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
cos
2 kCs
DS
Let the actual distance between upper and lower
stadia be Sand 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 between
The two points is given by:
And the Relative Level (R.L) of
The points is given by
CLVHIRLRL A
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ELECTRONIC
TACHEOMETRIC
Used a Total Station, able to read distance byreflecting off a prism.
The stadia procedure is used less and less often
these days, more commonly geomatic engineers orcivil engineers use a Total Station
This instrumentation has facilitated the developmentof this method of detail and contour surveying into avery slick operation.
It is now possible to produce plans of large areasthat previously would have taken weeks, in a matterof 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 and
Some features in the area. The following observation procedure is adopted
For 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 mheight, and the RL of
Station 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 the
Reduced 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 intacheometric 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 1:1,0001:250
PLOTTING OF
TACHEOMETRIC DATA
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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.
PLOTTING OF
TACHEOMETRIC DATA
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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.
PLOTTING OF
TACHEOMETRIC DATA
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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.
PLOTTING OF
TACHEOMETRIC DATA
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Map
Layout
PLOTTING OF
TACHEOMETRIC DATA
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CONTOURING AND CROSS-
SECTIONSMohd 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 allpoints of the same elevation above or below adatum.
Contours of different elevation cannot cross eachother except in the case of overhanging cliff or acave.
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 carriedout along the center line of a proposed alignmentse.g. highways, railways, pipelines or canals.
The profile is usually plotted with the vertical scalemuch larger than the horizontal scale.
The term cross-sectioning refers to a relatively shortprofile view of the ground, which is drawn
perpendicular to the route center line of a highwaysor 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