YORK UNIVERSITY
Faculty of Engineering
ENG 2120 / EATS 2620
FUNDAMENTALS OF SURVEYING: LAB 2
Submitted to:
Prof. Wang Jian-Guo
York University, Ontario
Abstract:
This lab mainly focuses on the intrinsic errors of the TRANSIT instrument. The lab splits
in two parts. Both parts of this lab are fairly precise because they are being measured by
very accurate instruments. On the first part we used a two peg test to measure the
deviation of the TRANSIT line of sight from the true horizontal. Every student took turns
measuring the distances and using this data the collimation error was calculated. On the
second part of the lab we set up a circuit loop consisting of 10 stations and measured the
distance between each point. Then we set up the transit in the middle of each point and
students took turns measuring the back sight and fore sight of each point as we traversed
the loop. We then repeated the same procedure backwards. We used the data to calculate
the misclosure .
Introduction:
The main purpose of this lab is to introduce the instruments used in field surveying and
the fundamental skills used in this field and mainly how to work with these instruments.
It also focuses on the intrinsic errors attributed to the TRANSIT. The instruments used in
this lab are levelling rod, TRANSIT (a type of Theodolite), Stadia and fibre glass tape.
The levelling devices are used to ensure measurements are accurate and precise.
The fiber glass tapes are frequently used to measure distances or lengths. Ideally, the tape
is unrolled and laid across a surface between measured points. Suspending the tape in the
air will inevitably cause sag, and cause errors so it is better to hold them tight and straight
not to cause errors. The Stadia or levelling rod is the resolution to long distance
measurements. A TRANSIT and level are used to take measurements using the stadia
rod. The rod is being placed at a distance away, and measurements are read using the
TRANSIT reticle, which make three reading targets. In this lab we are only using the
middle reading. Calculations are made from these readings to determine the distance
between the instrument and the stadia rod.
Levels are used to ensure that instruments are perpendicular and in a straight line to the
floor or surface when getting the data and to insure the data is accurate. The TRANSIT is
placed and locked on a tripod that is height adjustable. The level on the transit was to
ensure the instrument is precisely horizontal and parallel to the floor; a hand level was
used to keep the stadia rod held perpendicular to the floor.
Objective:
To obtain skills to perform spirit levelling and checking the collimation error and
misclosure of a circuit. Establishing surveying skills such as setting up a levelling line,
working with the level, observing and recording measurement from the levelling rods,
recording data, keeping field notes, and field sketching. Being able to analyze the data
collected to calculate accuracy and error deviation.
Field tasks:
1- Two peg test:

a) Identify a line(ca. 40 m) on approximately level ground and place two
levelling plates at both end points, measure the length of the line and find the
middle point on the line;

b)Set up the level over the middle point of the line, hold two levelling rods
vertically on the levelling plates, observe the rods and record the readings;

c)Move the level to either side of the line outside close to the end point ( a few
meters) and reset up the level, measure the distance between the level and the
closer levelling rod, observe the levelling rods and record the readings;

d) Calculate the collimation error.
2- Spirit Levelling(a circuit):
Field Scheme:
a) Identify a circuit along which a group can have 6 (for three person group)
or 8 (for 4 person groups) instrument setups and mark at least two points
on the circuit that can be reoccupied while performing the double-run
levelling;
b) Each of group members should at least perform two instrument setups to
practice the spirit levelling process;
c) A double-run is always required in practice.
Results
Two Peg Test
Table 1: Measurements Taken From the Midpoint
Student
Vincent
B.S.
1.585
F.S.
1.611
F.S.-B.S.
0.026
Luke
1.447
1.462
0.015
Kenneth
1.415
1.441
0.026
Atena
1.481
1.512
0.031
Aaditya
Average
1.502
1.530
0.028
0.0252
Diagram 1: Experimental Setup for Two Peg Test
Transit (level)
Stadia rod
A
A
B
D/2
D/2
D
Table 2: Measurements Taken 4m From the Back Sight
Student
Close
Further
Vincent
1.532
1.519
Further
– Closer
-0.013
Luke
1.501
1.482
-0.019
Kenneth
1.548
1.530
-0.018
Atena
1.453
1.434
-0.019
Aaditya
Average
1.521
1.501
-0.020
-0.0178
Diagram 2: Experimental Setup for Two Peg Test
Stadia rod
A
Transit (level)
B
D
X
D+X
Collimation Error
’’ = 0.0821 (upward deviation from true horizontal)
Spirit Levelling
Table 3: Permissible Misclosure
Nikon AP-7, SOKKIA B21, SOKKIA C300, TOPCON
Zeiss Ni2
AT-G4
5.8 x 10-7 km
7.72 x 10-7 km
Permissible Misclosure
(Cp) (km)
Diagram 3: Circuit for Spirit Leveling
1
A
2
3
8
7
4
6
5
B
Table 4: 1st Traverse of the Circuit Loop
Station
B.S.(m)
B
1.453
4
1.475
3
1.472
2
1.491
H.I. (m)
F.S.(m)
Elev.(m)
1.475
99.978
1.473
99.980
1.495
99.957
101.453
101.452
101.448
1.465
1.423
100.025
1.477
100.013
101.490
A
hi (m)
11.330
0.022
14.540
-0.002
22.565
0.023
14.262
-0.068
11.874
0.012
12.654
0.063
100.000
101.453
1
Distance
(m)
1.482
101.495
8
1.546
1.545
99.950
101.496
7
1.540
1.539
99.957
1.485
100.012
1.472
100.035
1.492
100.028
101.497
6
1.495
5
1.485
101.507
101.520
B
14.750
-0.007
18.358
-0.055
12.621
-0.023
16.750
0.007
Total distance = 149.704 m
Calculated Misclosure (Cm) = -0.028
Diagram 4: Experimental Setup for Spirit Leveling
B.S.
F.S.
Transit (level)
Stadia rod
Station 1
Station A
D/2
D/2
D
Table 5: Elevation Differences for 1st Traverse of the Circuit Loop
Station
B
Elev.
100.000
4
99.978
Difference
0.022
-0.002
3
99.980
2
99.957
0.023
-0.068
1
100.025
0.012
A
100.013
0.063
8
99.950
7
99.957
6
100.012
5
100.035
B
100.028
-0.007
-0.055
-0.023
0.007
-0.028
Table 6: 2nd Traverse of the Circuit Loop
Station
B.S.(m)
B
1.473
5
1.485
H.I. (m)
F.S.
(m)
Elev.(m)
1.486
1.491
1.489
99.983
1.497
99.977
1.500
99.976
101.474
1.499
8
1.497
101.476
101.473
A
1.450
1.454
100.019
1.491
99.978
101.469
1
1.494
101.472
2
1.496
1.493
99.979
1.498
99.977
1.520
99.967
101.475
3
1.510
4
1.490
101.487
101.457
B
16.750
0.013
12.621
0.004
18.358
0.006
14.750
0.001
12.654
-0.043
11.874
0.041
14.262
-0.001
22.565
0.002
14.540
0.010
11.330
-0.020
99.987
101.472
7
hi (m)
100.000
101.473
6
Distance
(m)
1.470
Total Distance = 149.704 m
Calculated Misclosure (Cm) = 0.013
99.987
Table 7: Elevation Differences for 2nd Traverse of the Circuit Loop
Station
B
Elev.
100.000
5
99.987
6
99.983
Difference
0.013
0.004
0.006
7
99.977
8
99.976
A
100.019
0.001
-0.043
0.041
1
99.978
2
99.979
-0.001
0.002
3
99.977
4
99.967
B
99.987
0.010
-0.020
0.013
Table 8: Average of the Elevation Differences for Both Traversals
Station
B
1st Run
Height
Difference
2nd Run
Height
Difference
0.022 -0.020
Average
Height
Difference
0.001
4
-0.002 0.010
0.004
0.023 0.002
0.0125
-0.068 -0.001
-0.0345
0.012 0.041
0.0265
0.063 -0.043
0.01
3
2
1
A
8
-0.007 0.001
-0.003
7
-0.055 0.006
-0.0245
-0.023 0.004
-0.0095
6
5
0.007 0.013
0.01
B
Calculated Misclosure (Cm) = -0.0075 m
= - 7.5 x 10-6 km
Therefore, if we refer to Table 3, “Permissible Misclosure,” we see that
|Cm| > Cp for both instruments.
Table 9: Adjustment of Level Circuits
Station
B
Elevation
Correction Correction
Diff. (m) Length(m) (m)
Diff. (m)
0.001
11.33
0.0013
0.0023
0.004
14.54
0.0021
0.0061
0.0125
22.565
0.00092
0.01342
-0.0345
14.262
0.0
-0.0345
0.0265
11.874
0.0011
0.0276
0.01
12.654
0.0009
0.0109
4
3
2
1
A
8
-0.003
14.75
0.0
-0.003
-0.0245
18.358
0.0
-0.0245
-0.0095
12.621
0.0
-0.0095
0.00118
0.01118
0.0075
0
7
6
5
0.01
B
SUM
-0.0075
16.75
Calculations:
Two Peg Test
Table 1
Average
= ¼ ∑ (F.S. – B.S.)
= ¼ ((1.611 – 1.585) + (1.462 – 1.447) + (1.441 – 1.415) + (1.512–1.481)
+ (1.530 – 1.502))
= ¼ (0.025 + 0.015 + 0.026 + 0.031 + 0.028)
= 0.0252
Table 2
Average
= ¼ ∑ (Further. – Closer)
= ¼ ((1.519 – 1.532) + (1.482 – 1.501) + (1.530–1.548) + (1.434 – 1.453)
+ (1.501 – 1.521))
= ¼ (-0.013 - 0.019 - 0.018 - 0.019 – 0.020)
= -0.0178
Collimation Error
’’
= [(a2 - b2) – (a1 – b1)] x (206265/D)
= [(Further – Closer) – (F.S. – B.S.)] x (206265/D)
= [(Table 2 Average) – (Table 1 Average)] x (206265/D)
= [(-0.0178) – (0.0252)] x (206265/30)
= -295.6465 (seconds)
= 0.0821 (upward deviation from true horizontal)
Spirit Levelling
Permissible error
The permissible error is only calculated for the Nikon AP-7, SOKKIA B21, Zeiss Ni2,
the calculation for the SOKKIA C300, TOPCON AT-G4 is similar.
Cp
= 1.5mm * sqrt(D)
= (1.5/1000000) * sqrt(149.704)
= 5.8 x 10-7 km
Due to the many calculations required for this section, we have decided to show several
sample calculations taken for Station 4 and 3 of Table 4, “1st Traverse of the Circuit
Loop.”
i)
Elevation (Elev.)
Sample Calculation
Reference Level = 100m
Elev4 = HIB4 - F.S.
= 101.453 – 1.475
= 99.978
Elev3 = HI43- F.S.
= 101.453 - 1.473
= 99.980
ii) Height of the Instrument (HI)
Sample Calculation
HI43
= Elevation + B.S.
= 99.978 + 1.475
= 101.453
HI32
= Elevation + B.S.
= 99.980 + 1.472
= 101.452
iii) Difference in Elevation (hi)
Sample Calculation
Hi43
= F.S. – B.S.
= 1.473 – 1.475
= -0.002
hi32
= F.S. – B.S.
= 1.495 – 1.472
= 0.023
Misclosure
The misclosure is only calculated for Table 4 “1st Traverse of the Circuit Loop.” The
calculation for Table 4 is similar.
Misclosure
= ∑ hi
= (-0.002 + 0.023 – 0.068+0.012+ 0.063 – 0.007 – 0.055 - 0.023 + 0.007)
= -0.028 m
Misclosure of Averaged Double Runs
Refer to Table 8, “Average of the Elevation Differences for Both Traversals.” The average
is only calculated for the height difference between stations B and 4.
iv) Average
Sample Calculation
Average
= (1st Run Height Difference + 2nd Run Height Difference) / 2
= (0.022 – 0.020) / 2
= 0.001 m
Misclosure
Misclosure
= ∑ hi
= (0.001 + 0.004 + 0.0125 - 0.0345 + 0.0265 + 0.01 – 0.003 – 0.0245 –
0.0095 + 0.01)
= -0.0075 m
Discussion
For the first part of the lab (Two Peg Test), we calculated the collimation error in our
setups. Prior to taking readings from the transit, the instrument must be correctly aligned
to the horizontal, using the leveling bubble. The collimation error reveals how deviated
our leveling instrument was to the horizontal. Fortunately, the collimation error in our
measurements were very minimal. This means that we leveled the instrument very
precisely, prior to taking readings.
In the Spirit Leveling portion of the lab, we had to calculate the misclosure of our
leveling circuit setup. Misclosure is the sum of the differences between Foresight and
Backsight. Theoretically, in a circuit-loop setup, the value of misclosure should be zero.
Unfortunately our results were unsuccessful, in the sense that our misclosure value was
greater than the permissible misclosure. There are several reasons for this:
Total Distance
The total distance may have been measured inaccurately. This may be due to the stations
not being perfectly horizontal to each other, in other words the stations may not have
been aligned correctly. Also while using the fibreglass tape, there was no way to secure
the tape in place while making measurements; this resulted in a parallax error. Constantly
pulling the tape back and forth caused these errors.
Stadia
The stadia had to be moved back and forth many times between stations and although the
transit was levelled each time this constant moving and turning of the transit may have
caused the instrument to render slightly wrong results.
Human Error
We must also take into account the human component of this experiment. The human eye
can only resolve things to a given accuracy and the rest is a logical guess. For example
when reading measurements off of the fibreglass tape, we can only be sure of the distance
to the millimetre level and the rest is a guess. Errors of this nature may have added up
and accumulated to produce wrong results. Also there is no guarantee that the surveyer
(student) will read the right measurement each time. Due to the many readings that were
taken it is likely that a wrong reading was taken along the circuit.
Conclusion
In this experiment we learned how to two different levelling techniques: the Two Peg
Test and Spirit Levelling. We also furthered our familiarity with the various measuring
instruments, in particular the Transit. Our results for the Spirit Levelling section of the
lab were not perfect. However, this can be attributed to inexperience and the introduction
of new levelling strategies with which we were not acquainted. Over the course of this
lab, we have increased our knowledge of fundamental levelling principles and know what
types of errors to be cautious of when performing such tasks. To improve results it is
necessary to take precautions to ensure that results are accurate and also be aware of the
various errors that may occur for a particular technique so that means of correcting may
be established.