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Surveying is divided into the
The measurement of dimensional
categories:
relationships among points, lines,
and physical features on or near plane surveying (mapping small areas)
the Earth's surface.
geodetic surveying (mapping large
areas of the globe).
Length of Tape / Distance Average: 52.50 paces
PF = 48 m
Ave. No. of Paces Pace Factor =
Line AB 48 m long was paced by a surveyor four times 52.50 paces
51
with the following data: 51, 54, 53, 52. Another line CD Pace Factor: 0.914 m/pace
54
was paced for four times again with the following results: 53
101, 100, 103, 102. 52
a. Determine the pace factor of the surveyor.
b. Determine the actual length of line CD.
A 48 m B
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Length of Tape / Distance Average: 101.50 paces
PF = DistanceCD
Ave. No. of Paces 0.914 m/pace =
Line AB 48 m long was paced by a surveyor four times 101.50 paces
101
with the following data: 51, 54, 53, 52. Another line CD DistanceCD = 92.771 m
100
was paced for four times again with the following results: 103
101, 100, 103, 102. 102
a. Determine the pace factor of the surveyor.
b. Determine the actual length of line CD.
C D
a) b)
Length of Tape / Distance Length of Tape / Distance
PF = PF =
Ave. No. of Paces Ave. No. of Paces A 100m steel tape is used to measure the distance of the line and
found to be 1532.82m long. During measurement, the tape is
51 101 supported at the ends under a pull of 10kg and the observed mean
54 100 temperature is 30ᵒC. The tape is of standard length at 20ᵒC and a
Average: 52.50 paces Average: 101.50 paces tension of 12kg. The cross sectional area of the tape is 0.035cm2. The
53 103
52 102 coefficient of linear expansion is 0.0000116/ᵒC. and the modulus of
elasticity of steel is 2.0x106 kg/cm2. The tape weighs 2.5kg.
48 m DistanceCD
Pace Factor = 0.914 m/pace =
52.50 paces a. Determine the total correction for temperature.
101.50 paces
b. Determine the total correction due to pull/tension.
Pace Factor: 0.914 m/pace Actual Dist: 92.771 m c. Determine the total correction due to sag.
d. What is the correct length of the line?
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A 100m steel tape is used to measure the distance of the line and
found to be 1532.82m long. During measurement, the tape is
supported at the ends under a pull of 10kg and the observed mean
temperature is 30ᵒC. The tape is of standard length at 20ᵒC and a
𝐶 Correction for Temperature tension of 12kg. The cross sectional area of the tape is 0.035cm2. The
𝛼 Coefficient of Thermal Expansion coefficient of linear expansion is 0.0000116/ᵒC. and the modulus of
𝐿 Measured length elasticity of steel is 2.0x106 kg/cm2. The tape weighs 2.5kg.
𝑇 Temperature during measurement
a. Determine the total correction for temperature.
𝑇 Standard temperature b. Determine the total correction due to pull/tension.
c. Determine the total correction due to sag.
d. What is the correct length of the line?
A 100m steel tape is used to measure the distance of the line and
found to be 1532.82m long. During measurement, the tape is
supported at the ends under a pull of 10kg and the observed mean
temperature is 30ᵒC. The tape is of standard length at 20ᵒC and a
tension of 12kg. The cross sectional area of the tape is 0.035cm2. The
𝐶 Correction for Tension
coefficient of linear expansion is 0.0000116/ᵒC. and the modulus of
𝑃 Applied Tension elasticity of steel is 2.0x106 kg/cm2. The tape weighs 2.5kg.
𝑃 Standard Tension
𝐿 Length a. Determine the total correction for temperature.
𝑎 Cross sectional area b. Determine the total correction due to pull/tension.
𝐸 Elastic modulus of the steel c. Determine the total correction due to sag.
d. What is the correct length of the line?
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A 100m steel tape is used to measure the distance of the line and
found to be 1532.82m long. During measurement, the tape is
supported at the ends under a pull of 10kg and the observed mean
temperature is 30ᵒC. The tape is of standard length at 20ᵒC and a
tension of 12kg. The cross sectional area of the tape is 0.035cm2. The
coefficient of linear expansion is 0.0000116/ᵒC. and the modulus of
𝑤 = linear weight of tape elasticity of steel is 2.0x106 kg/cm2. The tape weighs 2.5kg.
𝐿 = distance between supports
𝑃 = Applied Tension a. Determine the total correction for temperature.
b. Determine the total correction due to pull/tension.
c. Determine the total correction due to sag.
d. What is the correct length of the line?
A rectangular lot having a dimension of 200.3m by TOO LONG TOO SHORT
150.5m was measured by a 30m tape which is MEASURE ADD SUBTRACT
0.02m too long. LAY-OUT SUBTRACT ADD
a. What is the correct width of the lot. S L A M S
b. Find the correct length of the lot. too Short Laying-out Add Measured Subtract
c. Determine the error in the area.
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A rectangular lot having a dimension of 200.3m by TOO LONG TOO SHORT
150.5m was measured by a 30m tape which is MEASURE ADD SUBTRACT
0.02m too long. LAY-OUT SUBTRACT ADD
a. What is the correct width of the lot. S L A M S
b. Find the correct length of the lot. too Short Laying-out Add Measured Subtract
c. Determine the error in the area.
The distance of line XY was measured four times and recorded as follows: An angle was carefully measured five times with a
TRIAL DISTANCE (m) theodolite by observers A and B on two separate
1 100.1 days. The calculated results are as follows:
2 100.3
3 100.2
Observer A Observer B
4 100.4
Mean = 40°16’25” Mean = 40°16’20”
Error = ± 1.2” Error = ± 3.6”
a. Determine the probable value of the distance.
b. Compute the probable error of the mean.
c. Compute the precision of measurement.
Determine the best value of the angle.
Relative
Probable Precision
Error – is (Error) – total
a quantity amount
which of error
defines a rangein within
a givenwhich
measurement
there is arelated to the
50% chance Most Probable Value (MPV) – refers to a quantity which, based on available data,
magnitude
that the trueofvalue
the measured quantity
of the measured to indicate
quantity lies the accuracy
inside of measurement.
or outside the limits thus set. has more chances of being correct than has any other.
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Problem 7:
A civil engineer used a 100 m tape which is of standard length at
A 40-m steel tape is suspended in the air between a leveling 32°C in measuring a certain distance and found out that the length of
instrument and vertical rod, which is placed exactly at the 40m the tape have diff. lengths at diff. tensions were applied as shown.
mark, under a pull of 12 kg. The slope of the measured line is α= 0.0000116/°C
2°30’. The tape weighs 1 kg, standard pull of 8 kg, cross- LENGTH OF TAPE TENSION APPLIED
sectional area of 0.039 cm2, and E = 2x106 kg/cm2. 99.986 m 10 kg
99.992 m 14 kg
a. Determine the correction for sag of the tape.
100.003 m 20 kg
b. Determine the horizontal distance between the theodolite and
rod in meters. a. What tension must be applied to the tape at a temperature of 32°C
c. What additional pull must be applied to eliminate the effect of so that it would be of standard length?
sag? b. What tension must be applied to the tape at temperature of 40.6°C
so that it would be of standard length?
Problem 9:
TN
In 1990 the magnetic bearing of line AB MN2019 MN1990
measured by a compass instrument
Problem 8: was N550 40’W. The declination of the
A
needle at that time was 20 30’E. Secular Variation
A line was measured with a 50m tape. There were 2
tallies, 8 pins and the distance from the last pin to the a. What is the true bearing of the 2°30’
B
line?
end of the line was 2.25m. Find the length of the line
in meters? b. If the new declination at present was
3020’W, determine the new magnetic
bearing of the same line.
c. Find the secular variation per year.
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Problem 11:
Problem 10: A compass instrument was used to determine the interior angles of a
In a compass survey made fifty years TN
MN1986 MN1936 triangle and their corresponding number of times measured are as
ago, the observed magnetic bearing of a follows.
reference line XY was S 50018’ E when STATION ANGLES NO. OF
the magnetic declination was 8015’ East. 12° 10’
8° 15’ MEASUREMENT
Lately in 1986, a new survey was made A 410 5
and the declination in the same survey
X Azimuthmagnetic
site changed to 12010’ West. Determine B 770 6
the following descriptions of line XY: 500 18’
Azimuthtrue
TB
a. True bearing MB1986 C 630 2
b. New magnetic bearing
c. Magnetic azimuth from south in 1986 Y
a. Find the correct value of angle A.
d. True azimuth of line XY b. Find the correct value of angle B.
c. Find the correct value of angle C.
