Elementary
El
t
Su ey g
Surveying
Tape corrections
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Correction due to incorrect tape length
• When measuring the distance between two
points:
– With a tape too long,
long add the correction
– With a tape too short, subtract the correction
• When
Wh llaying
i outt a line
li off d
desired
i d length:
l th
– With a tape too long, subtract the correction
– With a tape too short, add the correction
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4
Correction due to incorrect tape length
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Correction due to incorrect tape length
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Correction due to incorrect tape length
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Correction due to incorrect tape length
Corr = TL − NL
⎛ ML ⎞
C I = Corr⎜
⎟
⎝ NL ⎠
CL = ML ± C I
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Correction due to incorrect tape length
• A rectangular lot was measured using a 50‐m
50 m
steel tape which was found out to be 0.025 m
too short
short. If the recorded length and width of
the lot are 180.455 m and 127.062 m,
respectively determine the following:
respectively,
– Actual dimensions of the lot
– Error in area introduced due to the erroneous
length of tape
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Correction due to incorrect tape length
• A building 38 m x 45 m is to be laid out with a
50‐m long metallic tape. If during
standardization the tape is found to be only
49.950 m, determine the following:
– Dimensions to be laid out
out, using the tape
tape, in order
that the building have the desired dimensions
– Using the same tape what should the diagonals
read?
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10
Correction due to slope
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Correction due to slope
• For gentle slopes (less than 20%)
2
h
Ch =
2s
• For steep slopes (between 20% and 30%
h2 h4
Ch =
+ 3
2 s 8s
• For very steep slopes (greater than 30%)
Ch = s (1− cos θ )
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12
Correction due to alignment
• Considered of less importance compared to
the other errors
• Can be calculated using slope correction
formulas
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Correction due to temperature
Ct = αL(T − Ts )
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Problem
• A steel tape known to be of standard length at
20oC, is used in laying out a runway 2,500.00
m long.
long If its coefficient of linear expansion is
0.0000116/oC, determine the temperature
correction and the correct length to be laid
out when the temperature is 42oC.
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Correction due to tension
Cp
(
Pm − Ps )L
=
AE
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Problem
• A heavy 50‐m
50 m tape having a cross‐sectional
cross sectional
area of 0.05 cm2 has been standardized at a
tension of 5.5
5 5 kg.
kg If E = 2.10
2 10 x 106 kg/cm2,
determine the elongation of the tape if a pull
of 12 kg is applied
applied.
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Correction due to sag
Cs =
ω L
2 3
24P
2
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Problem
• A 30‐m
30 m tape is supported only at the ends and
under a steady pull of 8 kg. If the tape weighs
0 91 kg,
0.91
kg determine the sag correction and the
correct distance between the ends of the
tape.
tape
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Correction due to wind
• Error due to wind is similar in effect to error
due to sag
• May be avoided by not conducting survey on a
windy day
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Combined corrections (problem)
• A line was measured to be 2582.35 m usingg a 30‐m
steel tape supported throughout its length under a pull
of 4 kg. The mean temperature during the
measurement is 35oC.
C The tape used has a cross‐
cross
sectional area of 0.03 square centimeters and has a
standard length at 20oC under a pull of 5 kg. The
modulus
d l off elasticity
l
off the
h tape is 2 x 106 kg/cm
k / 2 and
d
the coefficient of thermal expansion is 0.0000116/oC.
– Determine the error due to temperature change
– Determine the error due to tension
– Determine the corrected length of the line
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More problems
• A slope distance of 465
465.82m
82m is measured
between two points with a slope angle of 12o
35’. What is the corresponding horizontal
35
distance between the points?
• A line measured with a 30
30‐m
m steel tape was
recorded as 325.70m. If the tape is found
30 05m long
30.05m
long, during standardization,
standardization what is
the correct length of the line?
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More problems
• A rectangular
g
buildingg 250.00m byy 130.00m is to be
laid out with a 30‐m long steel tape. If during
standardization the tape is found to be 30.03m, what
should be the correct length and width to be laid out?
• A line measured with a 50‐m long steel tape was
g
determined to be 645.22m when the average
temperature during taping was 15.75oC. If the tape is
of standard length at 20oC and the coefficient of
thermal expansion of steel is 0.0000116/1
0 0000116/1oC,
C what is
the correct length of the measured line?
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More problems
• A steel tape
p with a cross‐sectional area of 0.03cm2 is
30.00m long under a pull of 5kg when supported
throughout. It is used in measuring a line 875.63m long
under a steady pull of 10kg.
10kg Assuming E = 2.0
2 0 x 106
kg/cm2, what is the elongation of the tape due to
increase in tension? What is the correct length of the
measured
d line?
l
• A 30‐m steel tape weighs 1.05kg and is supported at its
end points and at the 10‐m and 25‐m marks
marks. If a pull of
6.0kg is applied to the ends of the tape, what is the
correction due to sag for a full tape length?
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Homework
• Using a 25‐m
25 m tape
tape, a square lot was measured
and found to have an area of 1 hectare. If the
total error in area is 4
4.004
004 square meter short
short,
what is the error in each tape length?
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Homework
• A rectangular lot has a correct area of two
hectares. Its length is twice its width. It the
lengths of the sides were measured with a 50‐
50
m tape that is 0.02 m too long, compute the
error in the area of the lot in square meter
meter.
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