Week 04
Prof. Dr. Ergin TARI
Assist. Prof. Dr. Himmet KARAMAN
JDF211E COURSE - ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Information for Users
The following slides are compiled from;




The references given for the course,
The course notes of the lecturers from all around the
world,
Notes and slides published in the world wide web without
restrictions.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Information for Students

These presentations are compiled from the previous
versions of the Surveying II course slides which were
created by Prof. Dr. Muhammed Sahin and Prof. Dr.
Ergin Tarı between the years of 1998 and 2008.

The update process of these presentations will
continue, and will never end.

The responsibilities of the students for the exams will be
from the presentations, applications and practices
covered during the course.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Equipotential Surface
Equipotential surface or level surface is the surface with constant
potential. The height at each point on it is equal.
Plumb line
Topographic
surface
g
Equipotential surfaces
The lines that intersect all equipotential surfaces normally are not
exactly straight but slightly curved. These are called lines of force or
plumb line.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Level Surface & Plumb Line
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Potential Difference
Let O be a point at sea-level (geoid). Let A be another point,
connected to O by a leveling line. Then the potential difference
between A and O can be determined. The integral
 gdn  Wo  WA  C
A
o
which is the difference between the potential at the geoid (Wo)
and the potential at point A, (WA) has been introduced as the
geopotential numbers of A. The geopotential number C can be
measured by the gravity observations.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Dynamic & Orthometric Height
Orthometric height is the height above the geoid. If A and B are
two points at sea-level, while a and b are vertically above them on
the surface of a high level lake. Aa will not generally equal Bb. The
inequality is admittedly small, but other trouble results, notably
significant circuit misclosures in otherwise errorless levelling.
Dynamic heights give identical height to all points on the same
level surface. The height of any point is the number of the level
surface on which it lies.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Dynamic & Orthometric Height
The dynamic height,
H dyn 
Wo  WA

45o
o
differs from the geopotential number only in the scale or the unit.
o
45
The  o is normal gravity for an arbitrary standard latitude,
usually 45o.
The orthometric height is defined as
H
ort
Wo  WA

g
where g is the mean value of the gravity along the plumb line
between the geoid and the ground.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Orthometric Height (H)
Earth surface
Level surface
W = const.
Geoid
W = Wo
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Normal Height
The normal height is defined as
H
normal

Wo  WA

where  is the mean normal gravity along the plumb line.
Geoid is a surface coinciding with mean sea-level in the oceans,
and lying under the land. If the solid earth was perfectly a
spheroid the geoid would be a perfect spheroid, but irregularities
in the shape and density cause the geoid to depart from the
spheroidal form by amounts of 100 meters.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
11
Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
12
Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Definitions of Basic Terms

Vertical line is a line that follows the direction of gravity as indicated
by a plumb line.

Level surface is a curved surface that at every point is perpendicular
to the plumb line.

Level line is a line in a level surface, therefore a curved line.

Horizontal plane is a plane perpendicular to the direction of gravity. In
plane surveying, a plane perpendicular to the plumb line.

Horizontal line is a line in a horizontal plane. In plane surveying, a
line perpendicular to the vertical.

Datum is a level surface to which elevations are referred (for
instance mean sea-level).
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Definitions of Basic Terms (2)

Mean Sea Level (MSL) is the average height of the sea‟s surface for
all stages of the tide over a 19 year period.

Elevation is the vertical distance from a datum (usually mean sealevel) to a point or object.

Bench Mark (BM) is a relatively permanent object, natural or artificial,
having a marked point whose elevations above or below an adopted
datum is known or assumed (metal disks set in concrete, large rocks,
non movable parts of fire hydrants, and curbs.

Leveling is the process of finding elevations of points or their
difference in elevation.

Vertical control is a series of bench marks or other points of known
elevation established throughout a project (first-order, second-order,
third-order leveling nets).
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Terms at a Glance
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Terms at a Glance (2)
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Terms at a Glance (3)

Vertical Angle: Angle between line AB and horizontal line

Horizontal Line: Line perpendicular to the vertical

Elevation: Vertical distance (height difference) between datum and point
A
B
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Introduction to Leveling

Areas of Application:
•
design of highways, railroads, canals, etc.
•
layout construction projects according to specific design
•
calculate earthwork volumes
•
investigate drainage characteristics
•
map earth‟s topography
•
monitor earth subsidence
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Methods

Difference in elevation may be measured by the
following methods;
1.
Direct or Spirit Leveling, by measuring vertical
distances directly. Direct leveling is the most
precise method of determining elevations and the
one commonly used.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Methods (2)
2.
Indirect or trigonometric leveling, by measuring
vertical angles and horizontal or slope distances.
3.
Stadia Leveling, in which vertical distances are
determined by tacheometry using the engineer‟s
transit and level rod; plane table and alidade and
level rod; or self reducing tacheometer and level
rod.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Methods (3)
4.
Barometric Leveling, by measuring the differences
in atmospheric pressure at various stations by
means of a barometer.
5.
Gravimetric Leveling, by measuring
the
differences in gravity at various stations by means
of a gravimeter for geodetic purposes.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Methods (4)
Inertial positioning system, in which an inertial
platform has three mutually perpendicular axes,
one of which is “up”, so that the system yields
elevation as one of the outputs.
6.

Vertical accuracies from 15 to 50 cm in distances of 60
and 100 km, respectively, have been reported.

The equipment cost is extremely high and applications
are restricted to very large projects where terrain,
weather, time, and access impose special constraints
on traditional methods.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Methods (5)
7.
GPS survey elevations are referenced to the
ellipsoid but can be corrected to the datum if a
sufficient number of points with datum elevations
are located in the region surveyed. Standard
deviations in elevations differences of 0.053 to
0.094 m are possible under these conditions.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Methods (6)

Profile leveling is the operation-usually by direct
leveling-of determining elevations of points at short
measured intervals along a definitely located line,
such as the centerline for a highway or a sewer.

Direct leveling is also employed for determining
elevations for cross sections, grades, and contours.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Differential Leveling
Differential
leveling is the operation of determining
differences in elevation of points some distance apart
or of establishing bench marks. Usually, differential
leveling is accomplished by direct leveling.
Precise
leveling is a precise form of differential
leveling.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Differential Leveling (2)

To measure the difference in height (H) between
two points A and B, vertical rods are set up at each
of these two points and a level somewhere between
them. The height difference between A and B is the
difference between the rod (staff) readings.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Calculation Procedure (From ? - To ?)
? HAB = l2 - l1 ?
l1
l2
A
B
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Rod (Staff) Readings
Backsight (BS) is the first reading when the level has been set up.
Foresight (FS) is the last staff reading.
Intersight (IS) is the other staff readings between the BS and FS.
Change point (CP) or turning point (TP) is the point (2) at which
the last staff reading has been performed.
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Three-wire Leveling
Cross-hair readings: Leveling instruments have three horizontal
cross hairs, the top and the bottom hairs being shorter than, and
equally spaced from, the center hair.
Rod
Rod
Upper hair
Center hair
Lower hair
Center = (Upper + Lower) / 2
Sight distance = 100 (Upper – Lower)
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling Field Procedure
Setting up Level:
 balance BS and FS
 Make sure rod will be visible when instrument leveled at
new position
Rod Person:
 hold rod vertical (plumb) – use staff bubble (level)
 move rod back and forth (minimum reading noted)
 select TP‟s that are stable
Differential Leveling Procedure:
 start with BS on starting BM
 take FS and BS on all intermediate points (TP‟s)
 close with FS on ending BM
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
A
First setup
Second setup
B
Third setup
MEAN SEA LEVEL (GEOID)
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Differential (Spirit) Leveling
Level Rods
Fore sight
BS
1.862
Back sight
FS
0.648
Level Instrument
BM01
Elevation unknown
∆h = BS - FS
Horizontal Line
Bench Mark
Elevation 950.495m
Elevation BM01
Vertical Datum
Elevation 0.000m
= Elevation BM + ∆h
= Elevation BM + (BS – FS)
= 950.495 + 1.862 – 0.648
= 951.709
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Leveling with Two Rods
A
STATION
BM Weil
B.S. (+)
3.58
TP 1
1.06
1
H.I.
F.S. (-) ELEVATION
125.64
129.22
4.75
124.47
5.33
120.20
6.52
118.59
0.31
124.14
4.64
125.40
4.44
25.99
125.68
125.53
TP 2
4.91
125.11
BM Hill
2
5.86
124.45
TP 3
5.90
130.04
TP 4
TP1
4.72
130.12
3
BM Weil
Sum
TP2
26.03
4
TP3
B
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Field Observations Leveling
STATION
BM Weil
B.S. (+)
3.58
H.I.
F.S. (-) ELEVATION
125.64
129.22
TP 1
1.06
4.75
124.47
5.33
120.20
6.52
118.59
0.31
124.14
4.64
125.40
4.44
25.99
125.68
125.53
TP 2
4.91
125.11
BM Hill
5.86
124.45
TP 3
5.90
130.04
TP 4
4.72
130.12
BM Weil
Sum
26.03
Loop Misclosure = SB.S. – SF.S.  0.04
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Adjustment of Misclosure


Adjustment per leg = Misclosure / n = 0.04 / 6 = 0.0067 per leg
Station
Correction
Adjusted Elevation
TP1
-1 (0.0067)
124.46
TP2
-2 (0.0067)
120.19
BmHill
-3 (0.0067)
118.57
TP3
-4 (0.0067)
124.11
TP4
-5 (0.0067)
125.37
BMWeil
-6 (0.0067)
125.64 (check)
Notes:





Correction is negative (closing elevation of Weil is too high)
Error is cumulative
Balancing BS and FS will eliminate curvature and refraction
No check on side shots
3-wire leveling gives check on readings
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
ELIMINATING COLLIMATION ERRORS
D(BS)
D(FS)
Horizontal Line
c(bs)
c(fs)
c(bs) and c(fs) are the collimation
Errors (Instrument not adjusted)
c(bs)=c(fs) ONLY IF D(BS)=D(FS)
ELIMINATING EFFECTS OF CURVATURE AND REFRACTION
D(BS)
D(FS)
Line of sight
e(bs)
e(fs)
e(bs) and e(fs) are the Curvature
and Refraction effects
e(bs)=e(fs) ONLY IF D(BS)=D(FS)
HENCE ALWAYS KEEP FORE SIGHTS AND BACK SIGHTS BALANCED!!!!!
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Sources of Error in Leveling
INSTRUMENTAL: COLLIMATION (Adjust Instrument and keep FS=BS)
A
1
INCORRECT ROD GRADUATIONS (Check rods)
CROSS HAIR NOT HORIZONTAL (Read rod at centre)
NATURAL:
2
CURV. & REFRACTION (Keep FS=BS)
TEMPERATURE (Avoid low sights)
TP1
WIND (Work in calm conditions)
3
SETTLEMENT OF ROD OR INSTR.
(Use turn plates and good tripod)
TP2
4
PERSONAL:
Bubble not centered
Parallax (Focus Objective & eye piece)
Faulty rod readings (Sights too long, careless
interpolation)
Rod not plumb (Swing rod or use rod level)
TP3
B
COMMON MISTAKES:
•Moving the rod between fore- and
back sights
•Careless readings
•Improper rod „footing‟
•Incorrect bookings
•Disturbing instrument between BS
and FS readings
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
i--
gA
g-A
iB
hA --
--
hA -- = gA - i-h-- B = g-- - iB
hA B = hA -- + h-- B
hA B = g - i
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN
h-- B
B
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
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Class Presentations for Surveying II (JDF211E) Course by E. TARI, H.KARAMAN