Measurement of
Vertical
Distances
GE 100: General Surveying I
Lecture No. 3
Caraga State University
College of Engineering and Information Technology
Leveling
 It is the process of directly or
indirectly measuring vertical
distances to determine the
elevation of points or their
difference in elevation.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Definition of Terms
1.
2.
3.
Level Surface – it is a curved surface which is
at any point perpendicular to the direction of
gravity or the plumb line.
Level Line – it is a curved line in a level
surface all points of which are normal to the
direction of gravity and equidistant from the
center of the earth.
Horizontal Surface – it is a plane that is
tangent to a level surface at a particular point.
It also perpendicular to the plumb line at the
same point.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Definition of Terms
4.
5.
6.
Horizontal Line – a straight line in a
horizontal plane which is tangent to a level
line at one point. It is perpendicular to the
direction of gravity at the point of tangency.
Vertical Line – is a line parallel to the
direction of gravity.
Mean Sea Level – is an imaginary surface of
the sea which is midway between high and
low tides.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Definition of Terms
7.
8.
9.
Datum – is any convenient level surface
coincident or parallel with mean sea level to
which elevations of a particular area are
referred.
Elevation – is the vertical distance above or
below mean sea level or any other selected
datum.
Difference in Elevation – is the vertical distance
between the two level surfaces in which the
points lie.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Relationship Between Level
Surfaces
Diff. in Elev.
Between A & B
Earth’ s Surface
Elevation
of B (+)
B
Elevation
of A (+)
Le ve
l Li ne
Thru
B
Le ve l L
ine Thr
u A
A
LEV EL
Le ve l Li ne Th
ru C
Line
C
To Earth’ s
Center
Ve rtic
al
Li ne
Diff. in Elev.
Between A & C
SEA
Vertical
Line
Ve rtica l
ME AN
Elevation
of C (-)
Diff. in Elev.
Between B & C
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Leveling Methods
1.
Direct or Spirit Leveling –
method of determining the
elevation
of
points
some
distance apart by a series of set
ups of a leveling instrument
along a selected route. It is also
referred to spirit leveling since
the device used is a spirit level.
Forms of Direct Leveling
a. Differential Leveling
b. Double – Rodded Leveling
c. Three – Wire Leveling
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Leveling Methods
2.
3.
Reciprocal Leveling – is the process of accurately determining
the difference in elevation between two inter visible points
located at a considerable distance apart and between which
points leveling could not be performed in the usual manner.
Profile Leveling – is used to determine difference in elevation
between points at designated short measured intervals along
an established line to provide data from which a vertical
section of the ground surface can be plotted.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Leveling Methods
4.
5.
Lecture No. 3
Trigonometric Leveling – is
employed in determining by
trigonometric computations the
difference in elevation between
two points from measurements of
its horizontal and slope distance
and the vertical angle between the
points.
Stadia Leveling – combines
features of direct leveling with
those of trigonometric leveling. It is
in fact a form of trigonometric
leveling.
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Leveling Methods
6.
7.
8.
Barometric Leveling – it involves the
determination of differences in elevation
between points by measuring the variation in
atmospheric pressure at each point by means
of barometer.
Cross-Section Leveling – in highways or
railroad construction it is often necessary to
obtain a representation of the ground surface
on either side of the centerline.
Borrow-Pit Leveling – is a method of
determining the relative elevations of points in
borrow-pit excavations for the purpose of
calculating volumes of earthwork.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Types of Levels
DUMPY LEVEL
TILTING LEVEL
WYE LEVEL
GEODETIC LEVEL
BUILDER’S LEVEL
TRANSIT AS A LEVEL
AUTOMATIC LEVEL
LASER LEVEL
HAND LEVEL
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
DUMPY LEVEL
WYE LEVEL
BUILDER’S LEVEL
AUTOMATIC LEVEL
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
LASER LEVEL
TILTING AND
GEODETIC LEVEL
LASER SYSTEM
MOUNTED ON
BUILDER’S LEVEL
HAND LEVEL
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Leveling Rods
It is a graduated rod
which is used for
measuring the vertical
distance between the
line of sight through a
leveling
instrument
and the point whose
elevation
is
either
required or known.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Two Classification of Leveling Rod
1. Self-Reading Rod – it is the
most commonly used type of
leveling rod. It can be read
directly by the instrumentman
through the telescope by
noting
the
apparent
intersection of the horizontal
hair on the rod.
Lecture No. 3
GE 100
Elementary Surveying
2. Target Rod – it is
the type of rod has
a sliding target
which is set and
read by a rodman
at
the
position
selected by the
instrumentman.
Measurement of
Vertical Distances
Other Types of Rod
Philadelphia Rods
1. Rods Named
After Cities or
States
2. Rod Ribbons
3. Precise Rod
4. Geodetic Rod
5. Tape Rod
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Rod Level
• It is a device used
for fast and correct
plumbing
of
a
leveling rod.
• It is L-shape in
design and consists
of a small circular
spirit level fastened
the rod or to small
bracket held against
the side of the rod.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Targets
• It is a small device
attached to the rod
when
extremely
long sights make
direct reading of
the rod difficult or
impossible.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Other Forms of Targets
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Telescope
• It is a metal tube
containing a system
of lenses which are
used to fix the
direction of the line
of sight and is
magnifying
the
apparent size of the
objects in its field of
view.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Parts of Telescope
Objective Lens
Eyepiece
Cross Hairs
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Cross Hair Ring or Reticule
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Types of Telescope
1. Internal Focusing Telescope
•
It has an additional auxiliary lens which moves
back and forth between the objective and the
cross hairs as the focusing screw it turned.
2. External Focusing Telescope
•
It has an objective lens mounted on a sleeve
which moves back and forth in the telescope
barrel as an object is brought into focus.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Eyepiece
Reticule
Auxiliary
Lens
Objective Lens
dust cap
Internal Focusing Telescope
Eyepiece
Reticule
Draw Tube
Objective Lens
External Focusing Telescope
Lecture 3
Lecture No. 3
GE 100
Elementary Surveying
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Measurement of
Vertical Distances
Magnification of the Telescope
• It is the ratio of the apparent size of an
object viewed through a telescope to its
size as seen by the unaided eye from the
same distance.
• It may also be taken as the amount by
which an object is increased in apparent
size.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Level Vial
• It is sealed graduated glass tube containing some
amount of liquid and a small air bubble.
• It is used to determine the direction of gravity.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Coincidence Bubble
• Type of bubble used on
most modern precise
instruments such as the
tilting and automatic
level.
• It employs an optical
device which splits the
bubble
longitudinally,
then turns one end
around to make it appear
adjacent to the other
end.
Appearance of Bubbles Before Centering
And Direction Taken in Turning the
Leveling Screws
Appearance of bubbles
when Centered
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Tripods
• It serves as a base to prevent movement of the instrument after it is
set up.
• It consists of three wooden or aluminum legs which are securely
fastened the tripod head by means of a hinged joint.
Fixed-Leg Tripod
Lecture No. 3
Extension Tripod
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Setting up the Level
• The leveling instrument may be set up at any suitable or
desired location.
• Solid ground should be selected when setting up the
instrument.
• Tripod legs are spread so that the foot plate will be
approximately horizontal and they should be pushed
firmly into the ground to make it stand stable.
• The preferable and convenient of set up is one which will
enable the instrumentman to sight through the telescope
without having to stretch or stoop.
• The legs of the tripod when setting up on hillsides or
along a slope, one leg should extend uphill and two legs
downhill.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Leveling the Instrument
1.
Instruments with Four Leveling Screws
Direction of Bubble Movement
Motion of
Left Thumb
Direction
of Bubble
Movement
Motion of
Left Thumb
Lecture No. 3
Motion of
Right Thumb
GE 100
Elementary Surveying
Motion of
Right Thumb
Measurement of
Vertical Distances
Leveling the Instrument
2.
Instruments with Three Leveling Screws
Direction of Bubble Movement
Motion of
Left Thumb
Direction
Of Bubble
Movement
Motion of
Left Thumb
Lecture No. 3
Motion of
Right Thumb
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Holding the Leveling Rod
• The leveling rod is held on a point by a
rodman when a sight is to be taken on it.
• The rod be held plumb when the reading
is made.
• The instrumentman checks the rod by
observing through the telescope and
noting if its is held parallel to the vertical
cross hair.
• The rod is lightly supported between the
fingers of both hands and is allowed to
balance on its own weight.
• The fingers must not cover the face of
the rod.
• The graduations of the rod are always
clearly visible and not obstructed.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Taking a Rod Reading
POSITION THE ROD
FOCUS ON THE ROD
READ THE ROD
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Determining Difference in
Elevation
Rod
Horizontal
Line of Sight
Horizontal
Line of Sight
A
B
A
B
Difference in
Elevation between
A and B
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Length of Sight
• It is always best to take sights at moderate
lengths to attain speed and accuracy in leveling
work.
• A very short or extremely long sights should be
avoided.
• The most suitable sight lengths will depend upon
the required degree of precision, the surface of
the terrain, the type of instrument used, and upon
the distance at which the rod remains readable to
the instrumentman.
• It should not exceed 90 m where elevations to the
nearest 0.001 m are desired.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Waving the Rod
• Is used to determine whether the rod is plumb
when a reading is taken on it.
• It is accomplished by slowly waving or tilting
the top of the rod through the arc, first toward
the instrument and then away from it.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Carrying the Instruments
• The levels should always be kept in a box when it is not used.
• It should remain in its carrying case when transported to the
work site or when ot has to be moved to another distant set
up or over rough terrain.
• The level does not detached from the tripod when transferring
to another nearby station provided that it is securely fastened
to the tripod and is carried properly.
• In open spaces, the level may be carried on the shoulder in
preferably a near-vertical position.
• The spindle is clamped slightly so that the telescope does not
rotates when carried.
• In densely forested areas, the level should be cradled
between the arms and held close to one’s chest left or right
chest.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Arm and Hand Signals
Move Right or Left
Plumb the Rod
Give a Sight
Establish a Turning Point
All Right
This is a Turning Point
This a Point
Wave the Rod
Move Back
Face the Rod
Pick Up Instruments
Reverse the Rod
Raise or ( Lower ) Target
Move Forward
Come In
Use the Long Rod
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Sources of Error in Leveling
1. Instrumental Errors
– these errors are attributed to imperfections
in the instruments either from faults in their
manufacture or from improper adjustment.
Examples:
•
•
•
Instruments out of Adjustmennt
Rod not Standard Length
Defective Tripod
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Sources of Error in Leveling
2. Personal Errors
-
occur largely due to the limitations of the senses of touch,
sight or hearing of individuals, skills, training, and teamwork
of the members of a leveling party.
Examples:
•
•
•
•
•
•
Bubble not Centered
Parallax
Faulty Rod Readings
Rod not Held Plumb
Incorrect Setting of Target
Unequal Backsight and Foresight
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Sources of Error in Leveling
3. Natural Errors
–
errors due to natural sources and could not be
totally removed but their effects can be reduced by
applying corrections and using good judgment.
Examples:
•
•
•
•
•
•
Curvature of the Earth
Atmospheric Refraction
Temperature Variations
Wind
Settlement of the Instrument
Faulty Turning Points
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Common Mistakes in
Leveling
The following are some of the most
commonly made mistakes in leveling
work:
1. Misreading the Rod
2. Incorrect Recording
3. Erroneous Computations
4. Rod not Fully Extended
5. Moving Turning Points
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Adjustment of the
Dumpy Level
The following are the three field adjustments often required
for a dumpy level:
1. Adjustment of the Cross Hair
– the reticule or the cross hair ring is adjusted to see
to it the horizontal cross hair lies in a plane
perpendicular to the vertical axis of the instrument
2. Adjustment of the Level Vial
– is to make the axis of the level vial perpendicular to
the vertical axis of the instrument.
3. Adjustment of the Line of Sight
– the line of sight is adjusted to make it parallel to the
axis of the level vial.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
TWO-PEG TEST
Two Peg Test
d
d’
c
b
b’
L1
a
L2
B
TDE
A
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
where:
a = rod reading on A with instrument set up near A.
b = rod reading on B with instrument set up near A.
c = rod reading on B with instrument set up near B.
d = rod reading on A with instrument set up near B.
The computed difference in elevation for the two set ups
are:
DEa = ( a-b ) and DEb = ( d-c )
Note: If the two differences in elevation are equal, the line
of sight is in adjustment.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
TDEa = a – (b-e) and TDEb = (d-e) - c
TDEa  TDEb
2
a (b e) (d e)c

2
a b e d ec

2
(a b) (d c)

2
TDE 
If DEa is not equal to Deb, the correct rod reading at A with
the instrument still set up near B is :
( a b)  ( d c )
d '  c  TDE  c 
2
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
ALTERNATE PROCEDURE FOR TWOALTERNATE PROCEDURE FOR
PEG TEST
TWO-PEG TEST
en
L2
c’
d’
c
I
d
L1
a
P
ef
b
TDE
A
M
(Db-Da)
Da
B
Db
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
where:
a = rod reading on A with instrument set up at M.
b = rod reading on B with instrument set up at M.
c = rod reading on A with instrument set up at P.
d = rod reading on B with instrument set up at P.
c’ = correct rod reading on A for a horizontal line of sight.
d’ = correct rod reading on B for a horizontal line of sight.
Da = horizontal distance between points A and P.
Db = horizontal distance between points B and P.
en = error in the reading on the near rod ( held at A )
ef = error in the reading on the far rod ( held at B )
I = inclination of the line of sight in the net distance.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
The true difference in elevation between the two pegs:
TDE = DEm = a – b
DEp = c – d
The inclination of the line of sight from the horizontal is:
I = DEm – DEp = ( a – b ) – ( c – d )
The error in the reading on the far rod at B can be
determined by proportion as follows:
ef
Db
Db

or e f 
(I )
I
Db  Da
Db  Da
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
The correct rod reading d’ at the far rod ( held at B ) for a horizontal
line of sight. Thus,
d’ = d – ef
Similarly, the error in the reading on the near rod at A is:
en
Da
Da

or en 
(I )
I
Db  Da
Db  Da
The correct rod reading c’ at the near (held at A) for a horizontal
line of sight. Thus,
c’ = c – en
To check the computation, we have:
( a – b ) = ( c’ – d’ )
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
EXAMPLE PROBLEM
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Example # 1:
1.
•
•
•
•
In the two-peg test of a dumpy level, the following observation
were taken:
Rod Reading
Instrument Set up
Near A
Instrument Set
up Near B
on point A
1. 505 m.
0. 938 m.
on point B
2. 054 m.
1. 449 m.
Determine if the line of sight is in adjustment.
If the line of sight is not in adjustment, determine the correct rod
reading on A with the instrument still set near B.
Determine the error in the line of sight for the net distance AB.
Explain how the line of sight of the instrument should be adjusted.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
TWO-PEG TEST
Illustration:
L1
b
a
L2
d
c
B
A
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
Example # 2:
In the two-peg test of a dumpy level, the following observations are taken:
a.
b.
c.
d.
e.
Rod Reading
Instrument Set up
near M
Instrument Set up
near P
on point A
0. 296
1. 563
on point B
0. 910
2. 140
Point M is equidistant from both A and B, while P is 2.50 m. away from A
along the extension of line AB and 79.27 m. from B.
determine the true difference in elevation between points A and B.
Check if the line of sight is in adjustment.
If the instrument needs to be adjusted, determine the “false” difference in
elevation, inclination of the line of sight, and the error in the reading on the
far rod.
With the level still set up at P, determine the rod reading on B to which the
line of sight should be adjusted
Perform the customary check.
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances
ALTERNATE PROCEDURE FOR TWOPEG TEST
Illustration:
L2
c=1.563 m.
L1
a=0.296 m.
P
d=2.140 m.
b=0.910 m.
A
La=2.5 m.
M
(Lb-La) = 76.77 m.
B
Lb = 79.27
Lecture No. 3
GE 100
Elementary Surveying
Measurement of
Vertical Distances