06/09/2019
Measurement of Horizontal Distances
MODULE
09
Trial
1
2
3
4
5
6
Line
AB
BA
AB
BA
AB
BA
Taped Distance
45.0m
Measurement of Horizontal Distances
MODULE
09
A 45m course, AB, on level ground was paced by a surveyor for the
purpose of determining his pace factor. The number of paces for each
trial taken are shown in the table below.
A 45m course, AB, on level ground was paced by a surveyor for the
purpose of determining his pace factor. The number of paces for each
trial taken are shown in the table below.
Trial
1
2
3
4
5
6
Number of Paces
50
53
51
53
52
53
Line
AB
BA
AB
BA
AB
BA
Taped Distance
45.0m
Number of Paces
50
53
51
53
52
53
If the surveyor then took 771, 770, 768, 770, 772, and 769 paces in
walking an unknown distance CD, what is the length of line CD?
Determine his pace factor.
0.865m/pace
SURVEYING
SURVEYING
666.346m
CIVIL ENGINEERING CORRELATION COURSES
1
CIVIL ENGINEERING CORRELATION COURSES
2
MODULE
Measurement of Horizontal Distances
09
A line AB cannot be measured directly because of an
obstruction on the line. Accordingly, the two lines AC and CB
were measured as 2,400.850m and 1,320.420m, respectively.
Point C was set at a perpendicular distance of 155m from
point D on line AB. Using approximate slope correction
formula for steep slopes, determine the length of AB.
A rectangular lot was measured using a 50m steel tape which
was found to be 0.025m too short. The recorded length and
width are 180.455m and 127.062m, respectively. Determine
the actual dimension of the lot.
L = 180.365m, W = 126.998m
3,707.13m
SURVEYING
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
3
Measurement of Horizontal Distances
MODULE
09
CIVIL ENGINEERING CORRELATION COURSES
4
1
06/09/2019
Measurement of Horizontal Distances
MODULE
Measurement of Horizontal Distances
MODULE
09
09
A steel tape with a coefficient of linear expansion of 11.6 x
10-6/°C is known to be 50m long at 20°C. The tape was used
to measure a line which was found to be 532.28m long when
the temperature was 35°C. What is the correct length of the
line?
A heavy 50m tape having a cross-sectional area of 0.05cm2,
has been standardized at a tension of 5.5kg. If E = 2.10 x
106kg/cm2, determine the change in the length of the tape if
a pull of 12kg is applied.
+0.0031m
532.37m
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SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
5
CIVIL ENGINEERING CORRELATION COURSES
6
Measurement of Horizontal Distances
MODULE
09
Measurement of Horizontal Distances
MODULE
09
A line was determined to be 2395.25m when measured with
a 30m steel tape supported throughout its length under a
pull of 4kg and at a mean temperature of 35°C. Determine
the correct length of the line if the tape used is of standard
length at 20°C under a pull of 5kg. The cross-sectional area
of the tape is 0.03cm2, its coefficient of linear expansion is
11.6 x 10-6/°C, and the modulus of elasticity of steel is 2.0 x
106kg/cm2.
The angle between two intersecting fences is to be
determined with a tape. A point on each fence is established
30.0m from the point of intersection. If the distance between
the established points is 12.20m, what is the intersection
angle?
23°27’50”
2395.627m
SURVEYING
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
7
CIVIL ENGINEERING CORRELATION COURSES
8
2
06/09/2019
Measurement of Horizontal Distances
MODULE
Errors, Accuracy, and Precision
MODULE
09
09
In the figure shown, lines NQ and PR are established
perpendicular to the line MNP, and points Q and R are lined
up with the distant point M. If NQ = 318.55m, and PR =
475.62m, and NP = 210.38m, determine the length of MN
which represents the width of the river?
A surveying instructor sent out five groups of students to
measure a distance between two points marked on the
ground. The students came up with the following five
different values: 250.25m, 250.15m, 251.04m, 250.50m, and
251.22m. Assuming these values are equally reliable and that
variations result from accidental errors, determine the most
probable value of the distance measured.
250.632m
426.67m
SURVEYING
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
9
CIVIL ENGINEERING CORRELATION COURSES
10
Errors, Accuracy, and Precision
MODULE
Errors, Accuracy, and Precision
MODULE
09
09
The following values were determined in a series of tape
measurements of a line: 1000.58m, 1000.40m, 1000.38m,
1000.48m, 1000.40m, and 1000.46m. What is the most
probable value of the measure length?
The angles about a point Q have the following observed
values: 130°15’20”, 142°37’30”, and 87°07’40”. Determine the
most probable value of the second angle.
142°37’20”
1000.45m
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SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
11
CIVIL ENGINEERING CORRELATION COURSES
12
3
06/09/2019
Errors, Accuracy, and Precision
MODULE
Errors, Accuracy, and Precision
MODULE
09
09
The following values were determined in a series of tape
measurements of a line: 1000.58m, 1000.40m, 1000.38m,
1000.48m, 1000.40m, and 1000.46m. What is the probable
error of the mean?
The following values were determined in a series of tape
measurements of a line: 1000.58m, 1000.40m, 1000.38m,
1000.48m, 1000.40m, and 1000.46m. What is the probable
error of a single measurement?
±0.05m
±0.02m
SURVEYING
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
13
CIVIL ENGINEERING CORRELATION COURSES
14
Errors, Accuracy, and Precision
MODULE
09
The following values were determined in a series of tape
measurements of a line: 1000.58m, 1000.40m, 1000.38m,
1000.48m, 1000.40m, and 1000.46m. What is the relative
precision of a single measurement?
The three sides of a triangular tract of land is given by the
following measurements and corresponding probable errors:
a
=
162.54 ± 0.03m
b
=
234.26 ± 0.05m
c
=
195.70 ± 0.04m
Determine most probable value of the perimeter.
1:20000
592.50m
SURVEYING
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
15
Errors, Accuracy, and Precision
MODULE
09
CIVIL ENGINEERING CORRELATION COURSES
16
4
06/09/2019
Errors, Accuracy, and Precision
MODULE
Errors, Accuracy, and Precision
MODULE
09
09
The three sides of a triangular tract of land is given by the
following measurements and corresponding probable errors:
a
=
162.54 ± 0.03m
b
=
234.26 ± 0.05m
c
=
195.70 ± 0.04m
Determine the probable error of the perimeter.
The two sides of a rectangular lot were measured with
certain estimated probable errors as follows:
W
=
253.36 ± 0.06m
L
=
624.15 ± 0.08m
Determine the most probable value of the area.
158,134.64m2
±0.071m
SURVEYING
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
17
CIVIL ENGINEERING CORRELATION COURSES
18
Errors, Accuracy, and Precision
MODULE
09
The two sides of a rectangular lot were measured with
certain estimated probable errors as follows:
W
=
253.36 ± 0.06m
L
=
624.15 ± 0.08m
Determine the probable error of the area.
±42.58m2
SURVEYING
CIVIL ENGINEERING CORRELATION COURSES
19
5