Module 4
Measurement of Vertical Distances
CE 213 FUNDAMENTALS OF SURVEYING
PREPARED BY: ELIJAH
TASANI
SOURCES OF ERRORS IN LEVELING
1. INSTRUMENTAL ERRORS
a. Instrument out of adjustment
b. Rod not standard length
c. Defective Tripod
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TASANI
SOURCES OF ERRORS IN LEVELING
2. PERSONAL ERRORS
a. Bubble not centered
b. Parallax
c. Faulty Rod Reading
d. Rod not Held plumb
e. Incorrect setting of Target
f. Unequal backsight and foresight distance
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SOURCES OF ERRORS IN LEVELING
3. NATURAL ERRORS
a. Curvature of the Earth
b. Atmospheric Refraction
c. Temperature Variation
d. Wind
e. Settlement of the Instrument
f. Faulty Turning points
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COMMON MISTAKES IN LEVELING
1. Misreading the Rod
2. Incorrect Recording
3. Erroneous Computation
4. Rod not full extended
5. MOving turning points
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Adjustment of the Dumpy level
1. Adjustment of the Cross Hairs
2. Adjustment of the Level Vial
3. Adjustment of the Line of Sight
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TASANI
CURVATURE AND REFRACTION
The effects of earth curvature and atmospheric refraction
are taken into account in leveling work since the
measurements are made in vertical planes and these
effects all occur in the same plane. Due to the earth’s
curvature, a horizontal line departs from a level line by
0.0785 m in one kilometre, varying as the square of the
length of the line. This expression for earth curvature is
based on the mean radius of the earth which is about
6371 km.
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CURVATURE AND REFRACTION
Atmospheric refraction varies with atmospheric
conditions. Under ordinary conditions, it is approximately
equal to 0.0110 m in one kilometre, also varying directly
as the square of the length of the line. This is about oneseventh the effect of curvature of the earth. The point
observed through the level appears to be point B but is
actually point C. The angular displacement resulting from
refraction is variable. It depends upon the angle the line
of sight makes with the vertical and the surrounding
atmospheric conditions.
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TASANI
CURVATURE AND REFRACTION
The combination of the
earths curvature and
atmospheric refraction
causes the telescope’s line of
sight to vary from a level line
by approximately 0.0785
minus 0.0110 or 0.0675 m in
one kilometer, varying as the
square of the sight distance
in kilometers.
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CURVATURE AND REFRACTION
h’ = 0.0675 K2
where h’ is the departure of a
telescope line of sight from a
level line (in meters) and K is
the length of the line of sight (in
kilometers). The value 0.0675
is called the coefficient of
refraction. Its value actually
varies to a certain degree for
different elevations, but is taken
with an average value of 0.0675.
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TASANI
CURVATURE AND REFRACTION
For surveys of ordinary precision, corrections for the combined
effects of curvature and refraction may be omitted. The
correction is only necessary in precise leveling work and
where the difference in length of backsight and foresight
distances is great. If the backsight distance were exactly
equal to the foresight distance for each set up of the
instrument, the errors caused by the atmospheric
refraction and the earth’s curvature would cancel each
other. Since refraction changes rapidly with changes in
temperature, it is advisable to undertake precise leveling
during cloudy days or at mid-afternoon or sunny days when
the ground and air are uniformly warm.
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TASANI
CURVATURE AND REFRACTION
Example. A woman standing on a beach can just see the
top of a lighthouse 24.140 km away. If her eye height
above sea level is 1.738 m, determine the height of the
lighthouse above sea level.
Solution:
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TASANI
CURVATURE AND REFRACTION
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TASANI
LEVELING METHODS: 1. DIFFERENTIAL LEVELING
1. DIFFERENTIAL LEVELING is the process of
determining the difference in elevation between two or
more points some distance apart.
There should be at least two persons to undertake
differential leveling; the rodman who carries and holds
the rod, and the instrument man who sets up the level
and determines the required rod readings. The
instrument man can record the data in a field notebook
or a third person may be employed as recorder. If a
bigger levelling party could be formed, a chief of party, a
pacer, an axeman and utility men may be added to
complete the team.
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TASANI
LEVELING METHODS: 1. DIFFERENTIAL LEVELING
The leveling instrument is set up at any convenient
location along the level route and a backsight is taken
on a leveling rod held vertically on Bma. The backsight
reading added to the known or assumed elevation of the
initial bench mark gives the height of instrument above
datum or
HI = Elev BMa + BS
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TASANI
LEVELING METHODS: 1. DIFFERENTIAL LEVELING
The rodman moves forward along the general direction
of BMb and holds the rod at a convenient turning point
(TP1). The instrument man takes a foresight on the rod.
This foresight reading subtracted from the height of
instrument gives the elevation above datum of the
turning point or
Elev TP1 = HI – FS
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TASANI
LEVELING METHODS: 1. DIFFERENTIAL LEVELING
The level is then transferred and set up at another
convenient location beyond TP1, but still in the general
direction of BMb. The exact location at which the level is
set up is of little importance. The more important thing to
consider is that the level is set up at a location where
backsight and foresight rod readings can be made. A
backsight is then taken on TP, to establish a new height
of instrument (HI2). The rodman finally moves forward to
the location of BMb and a foresight is taken on the rod
held on it. Since the new HI has already be determined,
the elevation of BMb is computed by subtracting the
foresight reading from the height of instrument.
PREPARED BY: ELIJAH
TASANI
LEVELING METHODS: 1. DIFFERENTIAL LEVELING
If the terminal point (BMb) is still some distance away
such that more turning points have to be established
before it could be foresighted, the procedure of reading
a backsight, the rodman moving ahead to establish
another turning point, and reading a foresight is
repeated. This is done as many times as necessary until
the elevation of BMb is finally obtained. The four
illustrative problems given in this lesson should provide
the student a clearer idea as to how differential levelling
is undertaken, how the notes are kept, and how the
customary arithmetic check is made.
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TASANI
LEVELING METHODS: 2. DOUBLE-RODDED LEVELING
2. DOUBLE-RODDED LEVELING. Double-rodded
differential leveling is a method of determining
differences between points by employing two level
routes simultaneously. This method differs from
conventional differential leveling in that two turning
points are established such that at each setup of the
leveling instrument, two sets of independent backsights
and foresights are taken.
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TASANI
LEVELING METHODS: 2. DOUBLE-RODDED LEVELING
This method has an advantage of providing a
continuous check on the process of determining ground
elevations while the work is in progress. It is extremely
useful when there is an urgent need to undertake
differential leveling in a short period of time where no
established bench marks are available for checking
results. Double-rodded leveling is also useful when
running a long line of levels which do not close back on
the initial bench mark.
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TASANI
LEVELING METHODS: 2. DOUBLE-RODDED LEVELING
Although this method of leveling can be run with a single
rod and only one rodman, it is preferable to employ two
rods and two rodmen to speed up the process of
leveling. When using the method, It is advisable to use
sets of turning points which are near each other and
having elevation differences of at least one-half meter or
more. This technique eliminates the possibility of making
the same mistake in reading the meter marks on both
rods. It is also advisable to swap rods on alternate
setups of the instrument to minimize systematic errors.
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TASANI
LEVELING METHODS: 2. DOUBLE-RODDED LEVELING
Upon completion of the leveling operation, it will be
observed that the two computed elevations of the
terminal bench mark will vary slightly from each other.
The discrepancy is due usually to errors of observation,
and the correct elevation is determined by taking the
average value. However, when the discrepancy between
two final elevations is sufficiently large, it is advisable to
repeat the leveling process. It should also be expected
that the discrepancy will increase as the length of the
line increases.
PREPARED BY: ELIJAH
TASANI
LEVELING METHODS: 2. DOUBLE-RODDED LEVELING
Just as in conventional differential leveling, there is a need to perform
the customary arithmetic check before leaving the survey site. This
arithmetic check is made by adding separately all the backsight
readings and all the foresight readings. It should be noted that the
backsight readings are considered as positive values and foresight
readings as negative values. Since there are two sets of level lines,
the algebraic sum of the backsight and foresight readings is divided
by two. The quotient thus obtained is then added algebraically to the
elevation of the initial bench mark. If the resulting sum is equal to the
elevation of the terminal bench mark, it can be safely assumed that
the process of adding and subtracting has been done correctly.
PREPARED BY: ELIJAH
TASANI
LEVELING METHODS: 2. DOUBLE-RODDED LEVELING
Again, it is stressed that the arithmetic check does not
provide any measure of verifying mistakes in observing
and recording of data. It does not also tell us if the field
observations and techniques employed were undertaken
satisfactorily.
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TASANI
LEVELING METHODS: 3. THREE-WIRE LEVELING.
3. THREE-WIRE LEVELING. A more precise method of
differential leveling can be attained by the three-wire
method of leveling. It is a method of determining
differences in elevation wherein three horizontal hairs
(or threads) are read and recorded rather than from a
single horizontal hair. The leveling instrument used
should be equipped with stadia hairs in addition to the
regular vertical and horizontal hairs. For each backsight
and foresight, all three horizontal hairs are read to the
nearest millimeter and the average of the three readings
is taken as the correct value.
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TASANI
LEVELING METHODS: 3. THREE-WIRE LEVELING.
Since three-wire leveling is employed for high precision
work, only precise leveling rods should be used. It is
preferable to employ rods which use graduated strips of
invar. To attain fast and accurate plumbing, the rod
should have an attached rod level. It is also important to
calibrate the rod before using them in the field. The
backsight and corresponding foresight distances should
always be maintained at equal lengths.
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TASANI
LEVELING METHODS: 3. THREE-WIRE LEVELING.
The level is set up at station L and the rod is held
vertically at station P.The horizontal distance between
the instrument and the rod is shown as HD, and the
vertical distance between the line of sight and station P
is taken as the mean of the three hair readings.
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TASANI
LEVELING METHODS: 3. THREE-WIRE LEVELING.
Where:
a= Upper stadia hair reading
b= lower stadia hair reading
c= horizontal cross-hair reading or rod reading on P
s= stadia intercept or the difference between the upper stadia hair reading and the lower stadia
hair reading
m= mean of three hair readings
HD= horizontal distance from the level to the rod held at P
K= Stadia interval factor
C= instrument constant
HI= height of the line of sight above datum or mean sea level
Elev of P= unknown elevation of station P
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TASANI
LEVELING METHODS: 3. THREE-WIRE LEVELING.
The following equations are used in
three-wire leveling:
The stadia intercept, s,
provides an indirect measure of the
distance from the center of the
leveling instrument to the rod
sighted. In determining the
horizontal distance, the stadia
interval factor, K, and the instrument
constant, C, must first be known or
given. For most leveling instruments,
K is usually equal to 100 and C is
zero.
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TASANI
References
[1] Johny Pilapi La Putt Surveyin Lab Manual
[2] Colorado Department of Transportation Survey Manual
PREPARED BY: ELIJAH
TASANI