ENGINEERING SURVEY
2 - TACHYMETRY
PREPARED BY : PN RAIHANA BT
ABDUL MALEK
INTRODUCTION
Tachymetry word is derived from the Greek takhus
metron meaning swift measurement.
It is a branch of surveying where horizontal distance
and vertical distance can be obtained through stadia
line by using teodolite.
The distance between marks (titik) can be obtained
without using a tape or chain.
It suitable to use in valley, river and area where many
obstructed.
Use in Civil Engineering
To measure on the ground details : nature detail (e.g.
tree, river, etc..) or human creation (e.g. building,
manhole, culvert, road etc...)
To produce topographic maps contain detailed
information and contour lines for the purpose of
planning a construction project such as roads,
buildings and others.
To obtain the reduce level (RL) between points on
the surface of the earth
Tachymetry systems
5 systems
i. Stadia System - Fixed & Variable angle
ii. Tangent System
iii.Contact Line System and Substance
iv. "Optical Wedge" or "Double Image" Systems
v. EDM System
Main purpose - to calculate the horizontal and vertical distance
between two points.
- The formula, calculation and adjustments
are
different for each system.
i. Stadia System
This method using optical means
which is measuring distance
using a telescope with cross line
and a staff rod (see figure).
Contains two additional
horizontal lines known as stadia
lines.
Its placed in the middle of main
horizontal cross line (which is
above and below)
Distance between these stadia
line is called as stadia interval.
i. Stadia System - Fixed & Variable
Angle
a) Fixed angle stadia system
Stadia lines set at a certain position on the
diaphragm.
b) Variable angle stadia system
Stadia lines may be altered in position.
The interval distance can be measured using
micrometer. Therefore it called as variable stadia.
Garisan-garisan stadia boleh diubah
kedudukannya. Jarak sela diukur menggunakan
jangkahalus.
Oleh itu, sistem ini dikenali sebagai stadia berubah.
Stadia System Fixed & Variable angle can be
apply in 2 methods:
i. Inclined staff with vertical staff
ii.Inclined staff with normal staff
normal staff vertical staff
ii. Tangent system
Need 2 observation using tachymetry tool to a staff .
The distance can be obtained by computation
iii. Contact Line System and Substance
Use theodolite with 1 reading to get precise
internal angle.
Need 2 observation to compute a distance
iv. Wedge Optic or Double Image
System
A special theodolite were design to use with a
measurement tool.
The theodolite is directly towards a special staff
A sets of measurements can be done to
compute a distance.
v. EDM System
UseEDM or total station to get a distance.
Prism use as target.
In this chapter, we only learn
about 2 system which is fixed
stadia with vertical staff and
EDM system.
Basic principle of odm
Top stadia
Middle stadia A
a
c
b
C
B
Above Stadia
Basic Structure of Optical Theodolite
Staff
Diaphragm Object Lens A
Focal Point
b
i x x s
o
a
B
c f d
Tool axis f = Focus distance
o = Focal point
i = Stadia interval
s = Staff intercept
c = The distance between object lens and tool
axis.
d = The distance between focal point to staff.
D = The horizontal distance required
Apabila teleskop berada dalam keadaan fokus, imej staf
AB ialah ab dalam satah bebenang. Pancaran dari A dan
B yang melalui titik fokal o akan menghasilkan dua
segitiga sebentuk iaitu segitiga oAB dan oab.
The term f / i is a constant in the stadia formula and
denoted by the letter K.
The term ( f + c) is known as the constant and may be
denoted by the letter C.
This reduces the stadia formula to the simple linear
equation:
K = constant multiplication
s = The staff intercept
C = constant additive
D = the distance measured
Most of the theodolite with the K and C are assigned to a
single value.
Typically, the value K = 100 and C = 0. So stadia formula
would be:
D = 100S
EXERCISE 1
From the table below, calculate the actual
distance for each point. K = 100, C = 0
Middle Below Stadia
Point Top stadia
stadia stadia Different, s
A 1.983 1.583 1.183
B 2.205 1.405 0.605
C 2.187 1.287 0.387
D 2.445 1.945 1.445
E 1.387 1.187 0.987
Stadia Different, s = top stadia below stadia
Stadia
Top Middle Below
Point Different, Distance
stadia stadia stadia
s
A 1.983 1.583 1.183 0.800
B 2.205 1.405 0.605 1.600
C 2.187 1.287 0.387 1.800
D 2.445 1.945 1.445 1.000
E 1.387 1.187 0.987 0.400
How about distance? formula: D = Ks + C
Point Calculation Distance
A 0.800x100 80.000
B 1.600x100 160.000
C 1.800x100 180.000
D 1.000x100 100.000
E 0.400x100 40.000
Fixed Stadia with Vertical Staff
Fixed stadia vertical staff suitable for details survey.
This method used by surveyor for tachymetry work
manually.
Equipment : Teodolite & staff
Fixed Stadia with Vertical Staff
Staff
A
A
D s
C
B
h
B
v
X
Theodolite
H
Based on figure:
s = staff reading from A to B
If staff is held inclined (condong) and
perpendicular (bersudut tepat) with line
view, stadia reading should was A' B'.
To get slope distance;
D = Ks + C
= K(AB) + C
But, AB = ABCos or Cos
D = KABCos + C
D = Ks.Cos + C
Horizontal distance and vertical distance;
H = DCos
= Ks.Cos2 + C.Cos
V = Dsin
= Ks.Cos .Sin + C.Sin
= (Ks.Sin 2 ) + C.Sin
D = Ks.Cos
H = Ks.Cos 2 D = Slope Distance
V = (Ks.Sin 2 ) H = Horizontal Distance
V = Vertical Distance
Question 1:
Based on the figure, calculate the above
information. If the bearing from the station 1
to point A is 10 30 '40 and the bearing
from
the station 1 to point B is 70 50' 40",
calculate:
i. Reduce level at the station 1, point A
and point B
ii. The horizontal distance from A to B.
Given height station (Hi) given as 1.214m &
R.L. TBM is 40.00m.
Height Stadia Stadia Stadia Vertical Notes
Station Above Center Below Angle
1 1.011 0.777 0.542 3 10 T.B.M
1.214 m 1.742 1.532 1.321 2 45 A
3.210 3.103 2.955 -4 10 B
The answer
When staff at TBM
STBM =Top stadia below stadia
= 1.011- 0.542 When staff at station A
= 0.469 m SA = Top stadia below stadia
= 1.742 - 1.321 When staff at station B
= 0.421 m SB = Top stadia below stadia
= 3.210 - 2.955
VTBM = K s Sin 2
= 0.255m
= 100 (0.469) Sin 2 (3 10)
= 2.586 m
VA = K s Sin 2
= 100 (0.421 ) Sin 2(+2 45)
= 2.018 m
VB = K s Sin 2
= 100 (0.255 ) Sin 2(-4 10)
= -1.848 m
H = Ks.Cos
The answer V = Ks.Sin
2
Height Vertical Above Middle Below Horizontal Vertical
Notes
Station Angle Stadia stadia stadia Distance Distance
1.214 m 3 10 1.011 0.777 0.542 46.8 + 2.587 T.B.M
2 45 1.742 1.532 1.321 42.0 + 2.018 A
-4 10 3.210 3.103 2.955 25.4 - 1.848 B
+/-
Symbol.
R.L. 1 = RLTBM- HiV+ h
= 40.00 1.214 2.587 + 0.777
= 36.976m
R.L. A = RL1 + Hi + V- h
= 36.977 + 1.214 + 2.018 - 1.532
= 38.677m
R.L. B = RL 1 + Hi- V- h
= 36.977 + 1.214 - 1.848 - 3.103
= 33.240m
R.L. = reduce level
Hi = height instrument
V=vertical distance
h=middle stadia
Horizontal 1 to A (HA)
HA =Ks.Cos
= 100(1.742 - 1.321)(Cos+2 45)
= 42.003 m
Horizontal 1 to B (HA)
HB = Ks.Cos
= 100(3.210 - 2.955)(Cos-4 10)
= 25.365 m
Angle A1B = 60 20 00 Station A
Distance (1 A) = 42.003 m
Distance (1 B) = 25.365 m
60 20 00
Therefore AB distance; 1
Station B
AB2 = (1A)2 + (1B)2 2(1A)(1B)Kos(A1B)
= (42.003)2 + (25.365)2 2(42.003)(25.365 )Cos 60 20
00
AB = 36.783m
TACHYMETRY INSTRUMENT
fixed stadia with vertical staff
Invar staff Tripod Bubble
Teodolite
Picket
Measurement Method using Electronic
Equipment
Purpose - To get the height of reduced level for a
point.
Measurement method - same as vertical stadia
method
The different between using fixed stadia vertical
staff is staff was replaced with reflector equipment
which is prism.
Staff prism
TACHYMETRY INSTRUMENT EDM
SYSTEM
prism
EDM
Tripod
EDM SYSTEM
Prism
V h
H.I H
STN B
EDM equipment
(STN A)
Hi = Instrument Height
V = Vertical distance (+ve for angles of the elevation,
-ve
for angles depression)
h = Height pole
Determination of Different in Height
If using theodolite, h = middle stadia
Different in Height (AB) = Hi V h
Hi = Instrument Height
V = Vertical distance (+ve for angles of the
elevation, -ve for angles depression)
h = Height pole
Reduce Level Determination
If R.L. for STN A is known, the R.L. stations of other
pole/prism stations can be determine by using the following
formula:
R.L. Pole= R.L. STN A + H.I V h
Example 2:
A fieldwork was carried out using a Total Station at STN 5 where the R.L.
height and H.i is 16.235m and 1.452m. Vertical angle () = +3 20 30 and
height pole = 1.250m. Vertical distance is 35.214m. Calculate R.L. for pole
station.
Using this formula :
R.L. Pole = R.L. STN 5 + Hi V h
The answer..
Pole R.L.= R.L. STN 5 + Hi V h
= 16.235+1.452+(35.214 sin32030) 1.250
= 16.235 + 1.452 + 2.056 1.250
= 18.493m
Question 3
A fieldwork was carried out using the EDM at STN A
which the R.L. height and H.i is 16.000m and 1.500m.
Vertical angle () = +2 20 30 and pole height(pole) =
1.500m. Slope distance is 36.204m.Give R.L. for pole
station.
Answer.
R.L pole = R.L STN A+H.IV h
=16.000+1.500+( 36.204 sin22030)1.500
= 16.000 + 1.500 + 1.479 1.500
= 17.479m
STUDENT MUST KNOW HOW TO USE
THIS FORMULA.
Different stadia, s = Above stadia below stadia
Different height, dH = Hi V-h
Vertical distance, V = Ks.Sin2
Horizontal distance, H= Ks. Cos2
Reduce level staf A, R.L. staff A = R.L. station +Hi V-h
Trigonometry formula, a2= (b)2 + (c)2 2(b)(c).Cos
Question 4
Table A show a tachymetry observation (vertical
staff) using fix stadia method. If reduce level P is
given as 100.027m, compute reduce level for Q and
horizontal distance for PQ. Use K constant as 100,
and C constant as 0.Height instrument is 1.250m
Equipment Staff Bearing Vertical Upper Middle Below
station angle stadia stadia stadia
reading reading reading
R P 140 25 +12 10 2.003 1.803 1.603
R Q 255 20 -7 30 1.661 1.461 1.261
Question 5
Below data were obtain from a tachymetry survey
work using vertical staff method.
If reduce level for station 1 = 150.00 m and
teodolite height = 1.525 m, K and C constant =
100 and 0.
Station Staff Bearing Vertical Upper Middle Below
statio angle stadia stadia stadia
n reading reading reading
1 A 120 30 00 12 34 00 2.100 1.700 1.300
1 B 250 10 00 -8 31 00 2.210 1.988 1.765
Question 6
If reduce level for station 1 = 150.00 m and theodolite
height =
1.525 m, K and C constant = 100 and 0.
Compute:
Vertical distance from station 1 to station A and station 1
to station B
Reduce level for station A and station B
Slope or gradient form station A to station B
