Lesson 10 - Leveling

FUNDAMENTALS
OF SURVEYING
CE010
E.G. Escondo
COURSE TOPICS (MIDTERMS)
I. Balancing the traverse
II. Area Computation
III. Curvature and Refraction; Elevation Determination
IV. Leveling
V. The Stadia Theory; Measurement by Stadia for Horizontal Distance
VI. Measurement by Stadia for Inclined Distance; Sources of Error in
Stadia Work
VII.Stadia Interval Factor
LEVELING
WHAT IS LEVELING?
• The process of finding the elevation at a specified location relative to another known
elevation
• Leveling is the determination of the elevation of a point or difference between points
referenced to some datum
• The general term applied to any of the various processes by which elevations of points
or differences in elevation are determined
WHAT IS LEVELING?
Leveling is the general term applied to any of the various processes by which elevation
are determined. It is a vital operation in producing necessary data for mapping,
engineering design, and construction. Leveling results are used to:
(1) design highways, railroads, canals, sewers, water supply systems, and other
facilities having grade line that best conform to existing topography
(2) lay out construction projects according to planned elevations
(3) calculate volumes of earthwork and other materials
(4) investigate drainage characteristics of an area
(5) develop maps showing general ground configurations
(6) study earth subsidence and crustal motion
SOURCES OF ERROR IN LEVELING
The accuracy of leveling work may be affected by numerous factors.
Accuracy is primarily influenced by the type of instrument used. It will also depend on the
skills of the members of a level party and the degree of refinement with which the whole
operation is performed.
The principal sources of error in leveling work may emanate from either instrumental,
personal, or natural errors.
1. Instrumental Errors. These errors are attributed to imperfections in the instruments
either from faults in their manufacture or from improper adjustment. (e.g. defective
tripod, leveling rod not of standard length, or when the instrument used is out of
adjustment)
a.) Instrument Out of Adjustment

b.) Rod Not Standard Length
c.) Defective Tripod
Image Source: https://www.nytimes.com/wirecutter/reviews/the-best-tape-measure/

2. Personal Errors. These are usually caused by erroneous manipulations and
careless handling of instruments when making observations.
a.) Bubble Not Centered

b.) Parallax
c.) Faulty Rod Readings
d.) Rod Not Held Plumb
e.) Incorrect Setting of Target
f.) Unequal Backsight and Foresight Distances
3. Natural Errors. These are errors which are due to natural sources that include the
effects of the earth’s curvature, atmospheric refraction, variations in temperature,
wind, and etc.
a.) Curvature of the Earth

b.) Atmospheric Refraction
c.) Temperature Variations
d.) Wind
e.) Settlement of the Instrument
f.) Faulty Turning Points
COMMON MISTAKES IN LEVELING
1. Misreading The Rod.
2. Incorrect Recording
3. Erroneous Computations
4. Rod Not Fully Extended
5. Moving Turning Points
LEVELING METHODS
1. Differential Leveling
2. Profile Leveling
DIFFERENTIAL LEVELING
DIFFERENTIAL LEVELING
Differential leveling is the process of determining the difference in elevation between two or
more points some distance apart.
It requires a series of set ups of the instrument along a general route and, for each set up, a
rod reading back to the point of known elevation and forward to a point of unknown
elevation are taken.
The basic equipment used in differential leveling include a graduated leveling rod and a
leveling instrument such as a dumpy level, automatic level, or an engineer’s transit.
These leveling instruments are used to establish a horizontal line of sight and to measure
the vertical distance between the line of sight and the point on which the rod is held.
DEFINITION OF TERMS AND
PROCEDURE
DEFINITION OF TERMS
1. Bench Mark (BM). A bench mark is a fixed point of reference whose elevation is either
known or assumed. They may be permanent or temporary. Permanent bench marks
(PBM) are those which are established at intervals throughout the country by the
Philippine Coast and Geodetic Surveys (PCGS) or the Bureau of Lands. Accurate records
should be kept for each bench mark since they may be frequently referred to later by other
surveyors. They should be thoroughly described in the field notes.
DEFINITION OF TERMS
2. Backsight (BS). A backsight is a reading taken on a rod held on a point of known or

assumed elevation.
3. Foresight (FS). A reading taken on a rod held on a point whose elevation is to be
determined.
4. Backsight Distance (BSD). The backsight distance is measured from the center of the
instrument to the rod on which a backsight is taken.
5. Foresight Distance (FSD). The horizontal distance from the center of the instrument to
the rod on which a foresight is taken is referred to as the foresight distance.
6. Turning Point (TP). A turning point is an intervening point between two bench marks
upon which point foresight and backsight rod readings are taken to enable a leveling
operation to continue from a new instrument position.
7. Height of Instrument (HI). The height of instrument is the elevation of the line of sight
of an instrument above or below a selected reference datum.
LEVELING NOTES
It is important that all data gathered in differential leveling work be properly
recorded in a special field notebook ruled with suitable lines. There is a standard
format used in recording leveling notes and a typical example is as shown:
EXAMPLE 1
DIFFERENTIAL LEVELING. Complete the differential level notes shown below and
perform the customary arithmetic check.
STA BS HI FS ELEV
BM1 1.256 127.133m
TP1 1.116 1.886
TP2 1.228 1.527
BM2 1.189 2.246
BM3 1.070 2.017
TP3 1.831 2.656
BM4 2.765
EXAMPLE 1
EXAMPLE 1
EXAMPLE 1
EXAMPLE 1
EXAMPLE 2
DIFFERENTIAL LEVELING. Prepare and complete the differential level notes for the
information shown in the accompanying illustration, include the customary arithmetic
check.
EXAMPLE 2
STA BS HI FS ELEV
BMa 0.68 125.45m
TP1 0.98 3.75
TP2 3.73 3.52
TP3 3.90 1.64
BMb 0.35
EXAMPLE 2
PROFILE LEVELING
PROFILE LEVELING
The process of determining differences in elevation along a fixed line at designated
short measured intervals is referred to as profile leveling.
It is executed to provide data from which a vertical section of the ground surface can be
plotted.
A profile is necessary for the design and construction of roads, railroads, canals,
culverts, bridges, sewer lines, etc.
The fieldwork involved is identical to differential leveling since it also requires the
establishment of turning points on which foresight and backsight readings are taken
before the terminal point is reached.
DEFINITION OF TERMS
1. Profile. The profile is a curved line which graphically portrays the intersection of
a vertical plane with the surface of the earth.
2. Stationing. A numerical designation given in terms of horizontal distance any
point along a profile line is away from the starting point.
3. Intermediate Foresights. These sights, which are also known as ground rod
readings, are taken along the centerline of the proposed project to provide an
accurate representation of the ground surface.
4. Full Stations. Are points which are established along the profile level route at
uniformly measured distances.
5. Plus Stations. Any other intermediate point established along a profile level
route which is not designated as a full station is called a plus station.
6. Vertical Exaggeration. Is a process of drawing the vertical scale for a profile
much larger than the horizontal scale in order to accentuate the differences in
elevation.
7. Profile Paper. A special heavy grade graphing paper used for plotting profiles.
PROCEDURE OF PROFILE LEVELING
1. Before profile levels are run, the line joining the initial and terminal points must
first be established.
2. A transit and tape survey is undertaken starting at the beginning of the line which
is designated as station 0+00.
3. The length of the level route is measured and stakes are set at each full station
to define the path to be followed.
4. The instrument is set up at a convenient location and a backsight is taken on a

reference bench mark near the initial point to determine the height of the
instrument.
5. A series of intermediate foresights are next taken along the center line to
determine elevations of ground points.
6. By the time it is no longer possible to continue with the foresight readings on

intermediate points from the instrument position, a turning point is established.
PROFILE LEVEL NOTES
PROFILE LEVEL NOTES
EXAMPLE 3
LOCATING STATIONS. Work out the following problems regarding points and
stations along a profile level route.
a.) A turning point along a profile level route measures 126.44m beyond station 8 +
24.50. Determine the stationing of this turning point.
b.) For the illustrated problem given above, determine the stationing of the turning
point if it is instead located 83.45m before the given reference station.
c.) Determine the distance between station 33 + 45.02 and station 26 + 62.75.
EXAMPLE 4
PROFILE LEVELING. Complete the following set of profile level notes and show the
customary arithmetic check.
EXAMPLE 5
PROFILE LEVELING. The figure shows a schematic arrangement of a profile level
route from BM33 to BM34. The values indicated represent backsight, foresight, and
intermediate foresight readings taken on stations along the route. Prepare and
complete profile level notes for the portrayed information. Show the customary
arithmetic check and plot the profile.
EXAMPLE 5
EXAMPLE 5

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FUNDAMENTALS

The accuracy of leveling work may be affected by numerous factors.

a.) Instrument Out of Adjustment

Image Source: https://www.nytimes.com/wirecutter/reviews/the-best-tape-measure/

a.) Bubble Not Centered

a.) Curvature of the Earth

2. Backsight (BS). A backsight is a reading taken on a rod held on a point of known or

BMa 0.68 125.45m

TP1 0.98 3.75

TP2 3.73 3.52

TP3 3.90 1.64

4. The instrument is set up at a convenient location and a backsight is taken on a

6. By the time it is no longer possible to continue with the foresight readings on

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