Final Report Traversing

Student ID: 111 4271

iii

Table of Contents

Acknowledgement .................................................................................................................... iv

Control Points, Traversing & Levelling..................................................................................... 1

1. Abstract ............................................................................................................................... 1

2. Aim ..................................................................................................................................... 1

3. Apparatus ............................................................................................................................ 1

4. Control points ..................................................................................................................... 2

4.1. Introduction ................................................................................................................. 2

4.2. Procedure ..................................................................................................................... 2

4.3. Discussion ................................................................................................................... 4

4.4. Conclusion ................................................................................................................... 4

5. Levelling ............................................................................................................................. 5

5.1. Introduction ................................................................................................................. 5

5.2. Procedure ..................................................................................................................... 5

5.3. Results ......................................................................................................................... 7

5.4. Discussion ................................................................................................................... 8

5.5. Precautions ................................................................................................................ 10

5.6. Conclusion ................................................................................................................. 11

6. Trigonometrical Heighting and Coordinates .................................................................... 12

6.1. Introduction ............................................................................................................... 12

6.2. Procedure ................................................................................................................... 12

6.3. Results ....................................................................................................................... 16

6.4. Discussion ................................................................................................................. 24

6.5. Precautions ................................................................................................................ 32

6.6. Conclusion ................................................................................................................. 33

7. Team Organisation ........................................................................................................... 34

8. References ........................................................................................................................ 35


iv

Acknowledgement

I would like to express my sincere gratitude to all those people who have been associated

with this assignment and have helped me with it and made it a worthwhile experience.

I extend my thanks to my friends in my group, namely Stefan Cheung, Zeenaida Hisaindee

and Zafiirah Ramjean, who as a team have worked in great collaboration during the whole

surveying. Working with them has been an enriching experience as well as an opportunity to

learn new things.

I would also like to thank my parents who always provide a continuous support and

encouragement.

Finally, I express our thanks to lecturer, Mr Abdool Hasan Miyan, who gave us this

opportunity to learn the subject in a practical approach and the lab technician Mr Gokool,

who guided us throughout the whole surveying and gave us valuable suggestions and

explanations regarding the subject.


1

Control Points, Traversing & Levelling

1. Abstract

There exist many different levelling methods to determine the heights of points, two of which

are the Differential Levelling and the Trigonometrical Heighting. In this surveying, the

accuracy of these two methods is going to be accessed. By making use of a Total Station,

traversing was carried out to determine the relative positions of survey control points around

the Campus of the University of Mauritius.

2. Aim

The aim of this surveying is to:

Determine the coordinates of the control points by a traverse, by using the three tripod

traversing method and adjusted using the Bowditch method.

Determine the height of the control points by observing using both the

Trigonometrical Heighting and the Levelling method.

To determine which of the 2 above methods were more accurate.

3. Apparatus

The apparatus used for the experiment were as follows:

Automatic level

3 tripods

Graduated staff

2 pendulum bobs

7 pegs

Total station

2 prisms

Hammer


2

4. Control points

4.1. Introduction

A number of survey control points around the University Campus needs to be establish and

their relative positions be determined.

4.2. Procedure

1. A reconnaissance of the campus was first undertaken in order to determine the best

positions of the control points. Figure 1 shows the relative positions of the control

stations.

2. Pegs and nails were used as stations. Wooden pegs were hammered into the soil while the

nails were hammered in the bitumen.

3. After that the distance from the station to nearby strategic points were measured.


3

Figure 1: Reconnaissance map showing relative positions of stations

Road

boundary

Tree Blue

Caravan Station Column

KEY:


4

4.3. Discussion

3 measurements were taken for the position of each station. This was done so that in case the

station was accidentally removed or cannot be found on another day, it could be easily

located.

4.4. Conclusion

The position of the stations was placed in such a way that the distance and angle between 2

stations could be easily measured using the total station. Having established their relative

positions, levelling was carried out in order to determine the height of the stations.


5

5. Levelling

5.1. Introduction

Levelling is carried out in order to determine the height of the station with respect to the

Benchmark whose height is 312.200m. The two-peg test was carried out in order to determine

whether there was any collimation error in the apparatus. If the error is ± 2mm, the apparatus

can still be used but then proper adjustments should be made to the recorded values.

5.2. Procedure

1. One of the pegs was hammered into the ground.

2. Using the tape, a distance of 30m was measured from the 1st peg and the other peg

was hammered at the other end.

3. The tripod was then set up equidistant from the two pegs, that is, at 15m from each

peg.

4. The legs were securely tightened. The legs of the tripod were firmly pressed into the

ground with the tripod base plate being roughly horizontal.

5. The automatic level was then mounted on the tripod and was levelled.

6. This was done by first aligning the level parallel to 2 foot screws. The screws were

then rotated in opposite directions at the same time. The bubble moved in the same

line as the movement of the left thumb. This is known as the left thumb’s rule.

7. The instrument was then rotated by 180 degrees to check if the bubble still lies in the

centre, else it should be readjusted by halving the difference.

8. The other foot screw was then used to move the circular bubble in the opposite axis

until the bubble was centred.

9. The level was then checked in other directions and the above procedures were

repeated as necessary.


6

10. The graduated staff was held vertically over the first peg and the reading of the

intersection of the cross-hair with the image of the staff (backsight, b) was noted.

11. The same staff was then held vertically over the second peg and a further reading was

made (foresight, f). The difference between the two readings is the difference in

height between the two points:

h = b - f

12. The instrument was then displaced at unequal distances between the pegs and steps 4-

10 were repeated.

After the two-peg test was carried out the collimation error was checked, it was found that the

apparatus could still be used. After that, the height of the stations was determined as follows:

13. The graduated staff was placed over the Benchmark and the instrument was placed at

a distance approximately equal but of less than 30m from the benchmark and station

E.

14. The instrument was levelled as described in the two-peg test.

15. The staff reading was noted and this value is known as the backsight reading.

16. The staff was then placed on station E and this time the foresight was noted.

17. The instrument was then displaced while leaving the staff in place. After it has been

levelled, another backsight reading was taken.

18. The procedures were repeated to find the height of all the stations and the final

foresight was taken on the same Benchmark such that a closed loop was formed.

19. The readings were noted in the record sheet.


7

5.3. Results

Two-peg test

Distance from

1st peg (m)

Backsight (m) Foresight (m) Rise (m) Fall (m)

15.00 1.425

1.101 0.324

19.70 1.516

1.192 0.324

Table 1: Two-peg test to determine collimation error

Back

Sight

Inter

Sight

Fore

Sight

Rise Fall Red'd

Level

Corr. Adj

Level

Remarks

1.223

312.200

BM

1.308

1.362

0.139 312.061

STN E

1.372

1.245 0.063

312.124

CP 1

0.625

1.261 0.111

312.235

STN A

1.342

1.408

0.783 311.452

CP 2

0.526

1.849

0.507 310.945

STN B

1.331

1.372

0.846 310.099

CP 3

1.293

1.395

0.064 310.035

CP 4

1.856

0.831 0.462

310.497

STN C

2.196

0.752 1.104

311.601

CP 5

1.255

1.309 0.887

312.488

STN D

1.549

0.294 312.194

BM

Table 2: Record sheet showing all recorded values as well as the rise, fall, reduced and

adjusted levels


8

5.4. Discussion

Concerning the two-peg test, if h is positive, this means there is a rise in elevation in moving

from the first to the second peg. Else, there is a depression in moving from the first to the

second peg. It can be observed that the difference in height between the two pegs is 0.324m

and that the same value has been obtained for both apparatus setup. Since they are both equal,

this shows that the level used did not have any collimation error.

However if the difference in height calculated was not equal and the error lied between -

2mm and 2mm inclusive, then proper corrections should have to be made to the reading in

order to obtained the true value. If the error does not lie within that range, then it is not

recommended to use the instrument.

For the levelling, in order to check if all arithmetic calculations had been properly done, the

differences between the total backsights and foresights, total rises and falls, starting and

finishing reduced levels are calculated. If all arithmetic calculations are correct, all these

differences should be equal.

∑backsight = 14.327m

∑foresight = 14.333m

D1 = ∑backsight - ∑foresight = -0.006m

∑rise = 2.627m

∑fall = 2.633m

D2 = ∑rise - ∑fall = -0.006m

Final Reduced level = 312.194m

Starting Reduced level = 312.200m

D3 = Final – Starting Reduced level = -0.006m

Since D1 = D2 = D3 = -0.006m, this shows that the arithmetic calculations are correct.


9

In addition, the difference between the Final and Starting reduced level is known as the close.

In this case, the close is -0.006m. In theory, the close should have been 0.000m but in

practice, there are many factors, such the earth curvature, refraction and wind, which affect

the surveying and hence affecting the final reduced level.

According to the following formula, the permissible error over the covered distance is:

√

Where,

e is the error in mm,

m is a constant which can be taken to be 12mm in this experiment,

d is the distance covered in km.

The distance covered was 0.36131km and this was calculated from the horizontal distance

between each station using the Total Station.

Therefore the permissible error in this surveying is:

√

Since the error obtained is 0.006m (less than 0.007m), the misclosure can be accepted since

there are several factors which affect this value such as the earth curvature, refraction as well

as the weather conditions.


10

5.5. Precautions

Distances between the staff and the automatic level must not be so great in order to be

able to read the graduations accurately. It is recommended to use a distance not exceeding

30m between the automatic level and the backsight or foresight.

It must be ensured that the tripod screws and hinges are kept tight.

When the instrument was removed from the box, it was lifted by the centre and not by the

eyepiece or objective end of the telescope.

The level should be covered when not in use to prevent sunlight from causing the bubble

to expand otherwise it would be practically impossible to level the instrument.

The automatic level should not be carried in a vertical or near-vertical position, as the

compensator would swing about and be prone to damage.

In order to obtain the correct reading from the graduated staff, the latter was rocked

backward and forward. The person looking through the instrument continuously read the

staff and selected the lowest value.


11

5.6. Conclusion

From the two-peg test, it can be deduced that the automatic level did not have any collimation

error.

Concerning the levelling, the misclosure was -0.006m which was within the range of the

permissible error of ±0.007m. As such the height of each station was as follows:

Station Height (m)

A 312.235

B 310.945

C 310.497

D 312.488

E 312.061

Table 3: Height of stations above mean sea level


12

6. Trigonometrical Heighting and Coordinates

6.1. Introduction

The Total Station is an apparatus used to measure horizontal angles as well as zenith angles.

It can have a 3km range with a single prism. In addition, it can also be used to measure

distances. Using the three tripod traversing method, coordinates of control points can be

found and using trigonometrical heighting method, the height of these points can also be

found. In this surveying, the coordinates and height of the established control points are going

to be determined using these two methods.

6.2. Procedure

1) The tripod was mounted over station A at a comfortable height and in such a way that

its base plate was approximately horizontal.

2) The plumb bob was suspended from the centre beneath the base plate.

3) One of the legs of the tripod was firmly fixed into the ground by stepping on the small

footrest and using the other two legs the tripod was adjusted such that the plumb bob

was approximately over the station A. The two legs were also firmly pressed into the

ground.

4) Then the total station was mounted on the plate and using the 3 tribrach levelling

screws, it was levelled using the same procedure as that used to level the automatic

level.

5) By looking through the optical plummet, the total station was positioned exactly over

the station. The central fixing screw on the tripod was then tightened to prevent the

total station from moving.

6) Then fine levelling was done by aligning the total station parallel to 2 tribrach screws,

A and B and by using the thumb’s rule, the 2 screws were adjusted such that the

bubble in the horizontal plate vial was brought to the centre.


13

Figure 2: Thumb’s rule

7) Once this had been accomplished, the apparatus was turned until the level was parallel

to the screws B and C. The bubble was adjusted to the centre by turning only the

screw C

8) Once this had been levelled, the apparatus was rotated back to the first orientation and

this time only screw A was used to adjust the bubble again.

9) This process was repeated until the apparatus was level over both sets of screws.

When the bubble settled in the centre in both directions, it meant that the apparatus

was fine levelled. It was then checked in every direction.

10) Two prisms were then placed at Station E and B and were levelled in the same way

the total station was levelled.

11) The prisms were then directed at the total station

12) The following values were recorded:

a. The horizontal angle

b. The vertical angle

c. The horizontal distance

13) Two rounds of readings were taken for the horizontal and vertical angles.


14

14) At first, the total station was switched on. The telescope screw was unlocked and the

telescope was rotated until a beep sound was heard.

15) The total station was then directed at target E on face left and both the telescope screw

and the clamp screw were tightened to prevent movement of the apparatus.

16) The horizontal angle was set to 00˚ 00ˈ 00"

17) The vertical angle and the horizontal distance were also noted.

18) By unlocking the clamp screw, the apparatus was rotated towards Target B. Next, the

telescope screw was unlocked and the telescope was directed at Target B. Then both

screws were tightened again.

19) The horizontal and vertical angles as well as the horizontal distance were noted.

20) In order to obtain the reading on face right, the telescope and clamp screws were

again unlocked and the total was rotated by 180˚ followed by the rotation of the

telescope by the same amount. The screws were then tightened again.

21) From target B, the horizontal angle, vertical angle and the horizontal distance were

noted.

22) Then the apparatus was rotated back towards Target E and again the horizontal and

vertical angles as well as the horizontal distance were noted.

23) Thereafter, the second round of values was taken. This was first done by the setting

the horizontal angle to zero at some fictitious point on the left of target E.

24) The apparatus was rotated to target E and the necessary values as mentioned above

were noted. Subsequently the steps 18 to 22 were repeated to obtain the second round

of values.

25) The instrument and target heights were measured using a measuring tape.

26) Afterwards, by leaving the tribrach in place, the total station as well as the 2 prisms

were removed and were swapped in an anticlockwise direction, that is, the prism at E

was placed at A, the instrument was moved from A to B and the prism at B to C. It

has to be noted that the tripod from E had to be moved to C while the rest remained in

place.


15

27) The prism at C had to be levelled again and the steps from 14 to 24 were then carried

out and the values noted for target A and C.

28) The procedures were repeated for each station until a closed traverse loop was

formed.


16

6.3. Results

The following tables shows the values recorded using the Total Station.

Station A

From

Stn

Target Face Left Face Right Mean Red'd to RO Comments

◦ ˈ " ◦ ˈ " ◦ ˈ " ◦ ˈ "

Horizontal angle

Round 1

A E 00 00 00 180 00 31 00 00 16 00 00 00

B 98 59 06 278 38 03 98 48 35 98 48 19

Round 2 Mean

A E 60 16 44 240 16 27 60 16 36 00 00 00 00˚ 00ˈ 00"

B 159 04 41 339 05 12 159 04 57 98 48 21 98˚ 48ˈ 20"

Red'd to horizontal

Vertical angle

Round 1

A E 90 15 44 269 45 42 90 15 01 -00 15 01

B 91 08 29 268 50 30 91 08 60 -01 08 60

Round 2 Mean

A E 90 14 49 269 46 05 90 14 22 -00 14 22 -00˚ 14ˈ 42"

B 91 09 22 268 50 51 91 09 16 -01 09 16 -01˚ 09ˈ 08"

Table 4: Horizontal and vertical angles from Station A to Targets E and B

Horizontal Distance

From Station Target Round Face left (m) Face right (m)

A E 1 61.539 61.538

B 1 72.917 72.917

A E 2 61.538 61.535

B 2 72.917 72.917

Table 5: Horizontal distance from Station A to targets E and B


17

Instrument Height at A (m) 1.540

Target Height at E (m) 1.445

Target Height at B (m) 1.412

Mean Horizontal distance from A to E (m) 61.538

Mean Horizontal distance from A to B (m) 72.917

Table 6: Instrument and targets height when Total Station was at A

Station B

From

Stn


◦ ˈ " ◦ ˈ " ◦ ˈ " ◦ ˈ "

Horizontal angle

Round 1

B A 00 00 00 180 00 53 00 00 27 00 00 00

C 87 08 43 267 09 22 87 09 03 87 08 36

Round 2 Mean

B A 51 06 45 231 07 04 51 06 55 00 00 00 00˚ 00ˈ 00"

C 138 15 09 318 15 41 138 15 25 87 08 31 87˚ 08ˈ 33"

Red'd to horizontal

Vertical angle

Round 1

B A 88 52 33 271 07 49 88 52 22 01 07 38

C 90 13 58 269 45 36 90 14 11 -00 14 11

Round 2 Mean

B A 88 52 27 271 07 43 88 52 40 01 07 20 01˚ 07ˈ 29"

C 90 14 21 269 45 21 90 14 30 -00 14 30 -00˚ 14ˈ 21"

Table 7: Horizontal and vertical angles from Station B to Targets A and C


18

Horizontal Distance


B A 1 72.925 72.926

C 1 113.561 113.561

B A 2 72.926 72.926

C 2 113.560 113.561

Table 8: Horizontal distance from Station B to targets A and C

Instrument Height at B (m) 1.444

Target Height at A (m) 1.562

Target Height at C(m) 1.446

Mean Horizontal distance from B to A (m) 72.926

Mean Horizontal distance from B to C (m) 113.561

Table 9: Instrument and targets height when Total Station was at B


19

Station C

From

Stn


◦ ˈ " ◦ ˈ " ◦ ˈ " ◦ ˈ "

Horizontal angle

Round 1

C B 00 00 00 180 00 32 00 00 16 00 00 00

D 95 38 55 275 38 54 95 38 54.5 95 38 38.5

Round 2 Mean

C B 24 24 15 204 25 04 24 24 39.5 00 00 00 00˚ 00ˈ 00"

D 120 02 48 300 03 31 120 03 9.5 95 38 30 95˚ 38ˈ 34"

Red'd to horizontal

Vertical angle

Round 1

C B 89 45 51 270 14 31 89 45 40 00 14 20

D 87 59 43 271 59 35 88 00 04 01 59 56

Round 2 Mean

C B 89 45 41 270 14 05 89 45 48 00 14 12 00˚ 14ˈ 16"

D 87 59 59 271 59 38 88 00 11 01 59 50 01˚ 59ˈ 53"

Table 10: Horizontal and vertical angles from Station C to Targets B and D

Horizontal Distance


C B 1 113.563 113.564

D 1 56.338 56.338

C B 2 113.564 113.563

D 2 56.339 56.339

Table 11: Horizontal distance from Station C to targets B and D


20

Instrument Height at C (m) 1.441

Target Height at B (m) 1.450

Target Height at D(m) 1.400

Mean Horizontal distance from C to B (m) 113.564

Mean Horizontal distance from C to D (m) 56.339

Table 12: Instrument and targets height when Total Station was at C

Station D

From

Stn


◦ ˈ " ◦ ˈ " ◦ ˈ " ◦ ˈ "

Horizontal angle

Round 1

D C 00 00 00 179 59 17 -00 00 22 00 00 00

E 107 29 27 287 30 07 107 29 47 107 30 09

Round 2 Mean

D C 31 58 07 211 59 02 31 58 35 00 00 00 00˚ 00ˈ 00"

E 139 28 24 319 28 25 139 28 25 107 29 50 107˚ 29ˈ 59"

Red'd to horizontal

Vertical angle

Round 1

D C 91 58 44 268 02 16 91 58 14 -01 58 14

E 90 21 09 269 40 50 90 20 10 -00 20 10

Round 2 Mean

D C 91 58 20 268 01 56 91 58 12 -01 58 12 -01˚ 58ˈ 13"

E 90 21 21 269 37 40 90 21 51 -00 21 51 -00˚ 21ˈ 01"

Table 13: Horizontal and vertical angles from Station D to Targets C and E


21

Horizontal Distance


D C 1 56.347 56.349

E 1 58.936 58.936

D C 2 56.349 56.346

E 2 58.936 58.937

Table 14: Horizontal distance from Station D to targets C and E

Instrument Height at D (m) 1.390

Target Height at C (m) 1.448

Target Height at E(m) 1.428

Mean Horizontal distance from D to C (m) 56.348

Mean Horizontal distance from D to E (m) 58.936

Table 15: Instrument and targets height when Total Station was at D


22

Station E

From

Stn


◦ ˈ " ◦ ˈ " ◦ ˈ " ◦ ˈ "

Horizontal angle

Round 1

E D 00 00 00 180 00 20 00 00 10 00 00 00

A 150 55 42 330 55 21 150 55 32 150 55 22

Round 2 Mean

E D 54 16 02 234 16 56 54 16 29 00 00 00 00˚ 00ˈ 00"

A 205 11 04 25 11 55 205 11 30 150 55 01 150˚ 55ˈ 11"

Red'd to horizontal

Vertical angle

Round 1

E D 89 37 45 270 22 03 89 37 51 00 22 09

A 89 40 41 270 18 50 89 40 56 00 19 04

Round 2 Mean

E D 89 37 44 270 22 06 89 37 49 00 22 11 00˚ 22ˈ 10"

A 89 41 01 270 19 29 89 40 46 00 19 14 00˚ 19ˈ 09"

Table 16: Instrument and targets height when Total Station was at E

Horizontal Distance


E D 1 58.948 58.948

A 1 61.539 61.539

E D 2 58.947 58.947

A 2 61.540 61.538

Table 17: Horizontal distance from Station E to targets D and A


23

Instrument Height at E (m) 1.424

Target Height at D (m) 1.395

Target Height at A(m) 1.540

Mean Horizontal distance from E to D (m) 58.948

Mean Horizontal distance from E to A (m) 61.539

Table 18: Instrument and targets height when Total Station was at E


24

6.4. Discussion

Redundant observations were carried out in order to detect any blunders which might have

occurred either due to misreading or misalignment of the apparatus.

The instrument and target heights, the vertical angle as well as the horizontal distance would

be used to calculate the height of each stations using trigonometry. On the other hand, the

horizontal angle and the horizontal distance would be used to calculate the position of each

station in term of coordinates in the horizontal plane.

In order to calculate the height of each station above the mean sea level, the relative position

of station E from the differential levelling method was taken as a reference.

The principle behind the trigonometrical heighting is illustrated in the diagram below:

Figure 3: Principle of trigonometrical heighting

Benchmark (known height)

∆h

Horizontal distance, H

∆h

Instrument

height, I

Target

height, T

Difference

in level

Ɵ


25

The height of station E a.m.s.l is 312.061m.

From

station

Instrument

height (m)

To

station

Vertical angle Horizontal

distance

(m)

Target

height

(m)

∆h (m)

Height

of point

(m) ◦ ᶦ "

E 1.424 A 00 19 09 61.539 1.540 0.3428071 312.288

A 1.540 B -01 09 08 72.917 1.424 -1.4667046 310.949

B 1.444 C -00 14 21 113.564 1.446 -0.4740468 310.473

C 1.441 D 01 59 53 56.346 1.400 1.9657311 312.480

D 1.390 E -00 21 00 58.941 1.428 -0.3603403 312.081

Table 19: Height of station using trigonometrical heighting

Note that the mean of the horizontal distance in both directions were taken. For example, the

mean of the horizontal distance from A to B and that from B to A were calculated.

The height of each station using the differential heighting and the trigonometrical heighting is

summed up in the table below:

Height(m)

Station Differential

Levelling

Trigonometrical

Heighting

Difference (m)

A 312.235 312.288 -0.053

B 310.945 310.949 -0.004

C 310.497 310.473 0.024

D 312.488 312.480 0.008

E 312.061 312.081 -0.020

Table 20: Height of stations above mean sea level


26

Sources of error using Differential Levelling:

Parallax error might have been occurred if the level was not properly focused. Hence,

whenever the observer was changed, the automatic level had to be focused again.

The observer might have misjudged the lowest value while reading the staff. However

there was less chance of misjudgement since for each reading, two different observers

had read and confirmed the value on the graduated staff.

Sources of error using Trigonometrical Heighting:

It was not possible to fine-level the Total Station due to a defect in the apparatus and

hence the apparatus could only be approximately levelled. Due to the large distance,

the any variation in the vertical angle had a significant effect on the vertical distance.

One of the prisms could not be fine-levelled due to a defect.

The height of the instrument and the target from the station could not be measured

accurately since the apparatus was found just above the station.


27

Bearing

Using the horizontal angles from tables 4, 7, 10, 13 and 16, the angular misclosure was first

calculated.

Since there were 5 stations, the loop formed is a pentagon. Therefore, the sum of the internal

angles was calculated using the following formula:

∑ ( )

( )

In practice, the sum of the internal angles was:

9 ˈ " ˈ " 9 ˈ " 9ˈ 9" ˈ "

= 540 00ˈ 37"

As such the angular misclosure was:

ˈ " ˈ "

Consequently, angular adjustment had to be carried out.

"

"

Therefore 7" had to be subtracted from 3 stations and 8" had to be subtracted from 2 stations.

A fictitious bearing from station A to station E (reference) was taken to be 351˚ 11ˈ 47".


28

Thereupon, the bearing of each station was calculated as shown in the table below:

˚ ˈ " ˚ ˈ "

Station A 351 11 47

Angle at Stn A 98 48 20 Sub 7" 98 48 13

Stn A - Stn B 98 48 13 (Add 351˚ 11ˈ 47") - 360˚ 90 00 00

Stn B - Stn A 90 00 00 Add 180˚ 270 00 00

Angle at Stn B 87 08 33 Sub 7" 87 08 26

Stn B - Stn C 270 00 00 Add 87˚ 08ˈ 26" 357 08 26

Stn C - Stn B 357 08 26 Sub 180˚ 177 08 26

Angle at Stn C 95 38 34 Sub 7" 95 38 27

Stn C - Stn D 177 08 26 Add 95˚ 38ˈ 27" 272 46 53

Stn D - Stn C 272 46 53 Sub 180˚ 92 46 53

Angle at Stn D 107 29 59 Sub 8" 107 29 51

Stn D - Stn E 92 46 53 Add 107˚ 29ˈ 51" 200 16 44

Stn E - Stn D 200 16 44 Sub 180˚ 20 16 44

Angle at Stn E 150 55 11 Sub 8" 150 55 03

Stn E - Stn A 20 16 44 Add 150˚ 55ˈ 03" 171 11 47

Stn A - Stn E 171 11 47 Add 180˚ 351 11 47



29

Figure 4: Sketch to indicate the bearing and the angle between the stations

72.922m

113.563m 61.539m

90˚ 00ˈ 00" 270˚ 00ˈ 00"

357˚ 08ˈ 26"

177˚ 08ˈ 26"

272˚ 46ˈ 53"

92˚ 46ˈ 53" 200˚ 16ˈ 44"

351˚ 11ˈ 47"

171˚ 11ˈ 47"

20˚ 16ˈ 44"

98˚ 48ˈ 20"

98˚ 48ˈ 13"

87˚ 08ˈ 33"

95˚ 38ˈ 34"

87˚ 08ˈ 26"

95˚ 38ˈ 27"

107˚ 29ˈ 59"

107˚ 29ˈ 51"

150˚ 55ˈ 11"

150˚ 55ˈ 03"


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Coordinates of each station

Finally the traverse computation was used to calculate the coordinates of each station.

In the traversing, the coordinates of station A was taken to be (1000, 1000).

From

Station

Bearing Distance

(m)

∆E

Adjustment

(m)

∆N

Adjustment

(m)

Easting

(m)

Northing

(m)

To

station

◦ ' "

A 90 00 00 72.922 72.922 0.000 1072.928 999.989 B

-0.006 0.011

B 357 08 26 113.563 -5.665 113.422 1067.273 1113.395 C

-0.010 0.017

C 272 46 53 56.344 -56.278 2.734 1011.000 1116.121 D

-0.005 0.008

D 200 16 44 58.942 -20.429 -55.289 990.577 1060.823 E

-0.005 0.009

E 171 11 47 61.539 9.418 -60.814 1000.000 1000.000 A

-0.005 0.009


∑distance = 363.310m

East Misclosure, ∑∆E = -0.032m

North Misclosure, ∑∆N = 0.053m


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Using Bowditch adjustment, the East and North correction were calculated using the

following formula:

Calculation of Coordinates:

( )

( )

Each partial coordinates was then added to the coordinates of the previous point to obtain the

next coordinates.

Where,

∆EAB and ∆EAB are the partial coordinates,

and are the adjustments

After the correction, there was no misclosure.

∆NAB

∆EAB

(EA, NA)

(EB, NB)


32

6.5. Precautions

The total station was always covered using its protective cover when not in use

whenever it was left in the sun.

Care was taken to position the apparatus exactly in its place in its casing to prevent

damage to the apparatus when the casing was closed.

The instrument should never be transported on the tripod, since this causes stress to

tripod tribrach and instrument base.

Roadside reflectors, windows, or other reflective objects in the path of or behind the

prism can often cause erroneous measurements. Therefore, it should be checked that

no such objects are found in the path of the electromagnetic waves to the prism.

Figure 5: (a) A proper method of transporting the total station in the field

(b) Total station in an open case

[Courtesy Leica Geosystems, Inc]


33

6.6. Conclusion

Due to the significant errors which arose in trigonometrical heighting, it was concluded that

the differential levelling method was more accurate than the trigonometrical heighting

method. Furthermore when the height of the stations using trigonometrical heighting was

calculated, the reference height at station E was obtained from the differential levelling

method. Hence the height of the stations above mean sea level were found to be more

accurate using the differential levelling method and the final accepted height of the stations

were as follows:

Station Height (m)

A 312.235

B 310.945

C 310.497

D 312.488

E 312.061

Table 24: Height of stations using differential levelling method

The summary of the final accepted coordinates of the stations are found table 23.

Station Coordinates

A (1000.000,1000.000)

B (1072.928, 999.989)

C (1067.273, 1113.395)

D (1011.000, 1116.121)

E (990.577, 1060.823)

Table 23: Summary of final accepted coordinates


34

7. Team Organisation

My group consisted of Zeenaida Hisaindee, Stefan Cheung and Zafiirah Ramjean and myself.

The work was equally shared among us and it was pleasing to see that everyone was doing

their part with great dedication and care. The high team spirit and team chemistry made the

practical a fruitful one.

The surveying was carried out in two days. On the first day, the differential levelling was

done. Two staffs were used in order to speed up the practical since time was extremely

limited due to the workload and the fact that other groups would be also using the apparatus

after us. We had levelled and noted the readings in turn. There was always two of us noting

and cross-checking the reading on the staff while the rest would be holding the staffs, one

acting as the backsight and the other one as the foresight. The levelling, noting and holding

the staff was done on a rotating basis so that each one of us could have a grasp of the

practical procedures.

Then on the second day, we had booked the full day to carry out the Traverse and

Trigonometrical Heighting. Each one of us has levelled the total station or the prism at least

once. Whenever, readings were being taken, two of us would be cross-checking the recorded

values while the other two were positioned at the targets in order to make that no one bumped

against the levelled prisms by accident.

This clearly shows that the team was well organised and that the workload was equitably

shared among the four of us.


35

8. References

Markham Starr, Operation Manual for a Sokkia Powerset 3000 Total Station to be

Used in the Measurement of Watercraft

http://vcampus.uom.ac.mu/researchweek/conference2009/map.htm

Geodetic Survey Section, Survey and Mapping Office, Lands Department, September

2000, Accuracy Standards of Control Survey

http://vcampus.uom.ac.mu/researchweek/conference2009/map.htm

Documents

Final Report Traversing