namibia university of science and...

nAmiBIA UniVERSITY OF SCIEnCE AnD TECHnOLOGY

FACULTY OF NATURAL RESOURCES AND SPATIAL SCIENCES

DEPARTMENT OF GEO-SPATIAL SCIENCES AND TECHNOLOGY

QUALIFICATIONS:

DIPLOMA IN GEOMATICS

BACHELOR OF GEOMATICS

QUALIFICATIONS CODES: QUALIFICATIONS LEVEL:

06DGEM 6 - 06DGEM

07BGEM 7- 07BGEM

COURSE CODE: BSV521S COURSE NAME: BASIC SURVEYING (Level 5)

SESSION: NOVEMBER 2016 PAPER: THEORY

DURATION: 3 HOURS MARKS: 100

FIRST OPPORTUNITY EXAMINATION QUESTION PAPER

EXAMINER: Mr. F. J. Louw

MODERATOR: Mr. E. Sinvula

INSTRUCTIONS 1. You MUST answer Question 1 and ANY THREE OTHER QUESTIONS.

2. Write clearly and neatly.

3. Number the answers clearly.

PERMISSIBLE MATERIALS

1. Calculators may be used as well as other drawing equipment

THIS QUESTION PAPER CONSISTS OF 13 PAGES (Including this Front Page and 4 Data

Sheets)

Basic Surveying BSV521S

Question 1

Answer the following questions on Data Sheet 1, by selecting the correct statement for each:

1.1. In geodetic surveys higher accuracy is achieved, if:

a. The curvature of the earth surface is ignored b. The curvature of the earth surface is taken into account c. The angles between the curved lines are treated as plane angles d. None of the above

1.2. Surveys concerned with the measurements and mapping of natural and artificial features of

the earth, like hills, lakes, rivers, roads, railways, power lines, etc are:

a. Engineering Surveys b. Cadastral Surveys c. Topographic Surveys d. Mining Surveys

1.3. A survey may be executed in several ways by different combinations of instruments and

methods, and some parts of the work may require different treatment from others. The

principle factors to be considered are:

a. The purpose of the survey b. The extent of the survey c. The degree of accuracy required d. All of the above

1.4. The main purposes of surveying is:

a. The art of making measurements of the relative positions of natural and man-made features on the earth's surface, and the presentation of this information either graphically or numerically

b. The determination of the relative positions of points (natural or artificial) on the surface ofthe earth.

c. The setting out on the ground of the positions of the points used in the construction, location of properties, etc

d. band c

1.5. The quality of a Surveyor is:

a. He must have a thorough theoretical and practical knowledge of his work. b. He must be honest and trustworthy and his judgment must be good c. He must have initiative; think clearly and without prejudice, tackling each survey with

energy and perseverance. d. All the above

151 Opportunity Examination of 13 November 2016


1.6. Determining the difference in height between two points relative to a reference plane, or

relative to each other, by means of an instrument that provides a line of sight perpendicular

to that of gravity i.e. a line of sight that is horizontal, is called:

a. Barometric Levelling b. Direct Levelling c. Levelling d. Alloftheabove

1.7. A permanent reference point or mark, of known height is a:

a. Witness Mark b. Reference Mark c. Bench Mark d. None ofthe above

1.8. The imaginary line passing through the optical centre of the object lens, through the

telescope and through the eyepiece, is a:

a. Contour Line b. Collimation Line c. Level Line d. Horizontalline

1.9. The first reading from a level station is:

a. foresight b. back-sight c. intermediate sight d. any sight

1.10. The most common co-ordinate system for referring to the position of any definite point on

the Earth's surface is:

a. Geographical Co-ordinate System b. Plane Rectangular or Grid Co-ordinate System c. Polar Co-ordinate System d. All of the above

1.11. The purpose of observing a Reference Object (R.O.) is:

a. To ensure that the horizontal circle of the instrument has not been disturbed while observing

b. To orient the instrument to Zero South c. To orient the instrument to a trigonometrical beacon d. None of the above



1.12. Basic types of errors in surveying can be divided into two main groups, namely controllable

and uncontrollable errors, of which uncontrollable errors are:

a. Accidental Errors b. Gross Errors c. Systematic Errors d. All of the above

1.13. The basic method of determining a distance is:

a. Taping b. Electronic Distance Measuring c. Staff Tacheometry d. All of the above

1.14. Observations that are closely grouped and the measurement (average value) is accurate, are:

a. Accurate Observations b. Inaccurate Observations c. Precise Observations d. Accurate and Precise Observations

1.15. The requirement for traverse stations is:

a. Stations should be at inaccessible positions b. A clear line of sight is required between the Stations c. The length of traverse legs must be as short as possible. d. None of the above

1.16. Contours of different elevations may meet only in the case of

a. a vertical cliff b. a saddle c. a ridge d. an inclined plane

1.17. Two contour lines, having the same elevation:

a. cannot cross each other b. can cross each other c. cannot meet d. can meet

1.18. Contour maps can be used for the following:

a. To calculate the water capacities of reservoirs b. To trace a contour gradient for the road alignment c. To ascertain the indivisibility of points d. All the above



1.19. An inverted staff reading means:

a. The levelling staff is held upside down b. The levelling staff is held between the back-sight and the foresight c. The levelling staff is held after the back-sight d. All of the above

1.20. An application of levelling is:

a. Longitudinal section b. Cross section c. Contouring d. All of the above

1.21. The method to calculate a resection is:

a. Bowditch Rule b. Collins' Q-point method c. Blunt's method d. band c

1.22. Fixing the plane coordinates of a point, by setting up on the unknown point, and observing a

distance and direction to a known point, and a direction to another known point is called a:

a. Intersection b. Polar c. Reverse Polar d. Join

1.23. The following correction needs to be applied on distances measured with a Total Station:

a. Atmospheric Corrections b. Conversion to German Legal Metre c. Combined Sea Level and Scale Enlargement Correction d. All of the above

1.24. A traverse that starts at a known point (co-ordinated point) and ends at another know point

(co-ordinated point) is a:

a. Closed Traverse b. Open Traverse c. Loop Traverse d. None of the above



1.25. While viewing through a level telescope and moving the eye slightly, a relative movement

occurs between the image of the levelling staff and the cross hairs. That means the

instrument is:

a. Not Correctly focused b. Said to have parallax c. Free of parallax d. All the above

Question 2

2.1. Use the following information to calculate co-ordinate for point C.

Co-ordinates

Name

A

B

V

-6 836.515

-10 973.129

Angle at A = 38°

Angle at B = 5r

A

151 Opportunity Examination

X

+247 355.618

+247 584.123

c

of 13

B

[25]

(15)

November 2016


2.2. Use the levelling observations given on Data Sheet 2 to calculate final heights using the

"Height of Collimation" method. All checks need to be shown and any misclosures needs to

be distributed. (10}

[25]

Question 3

3.1. Calculate the co-ordinates of points TR1, TR2 and TR3 from the following data, by completing

Data Sheet 3. Adjustment must be done by the Bowditch Rule.

Co-ordinates

Name

b.SWP b. East

Traverse Leg b.SWP to TR1 TR1 to TR2 TR2 to TR3 TR3 to b.East

V X

- 4 680.110 + 62 348.590 + 61753.282 -10 917.978

Oriented Direction 28r 05 ' 41" 260° 06' 22" 262° 18' 42" 243° 32' 31"

Final Horisontal Distance 1824.328m 1 769.365m 1506.927m 1404.871m

(13)

3.2. Obtain orientated directions for the traverse RP1 - Trav1 - Trav2 - RP2 by completing the

direction sheet on Data Sheet 4. Do not calculate the traverse. (12)

[25]

Question 4

4.1. Define the term "Resection". (1)

4.2. The department wants to install a permanent base station on the roof of Poly Heights and

you have done the following observations to determine the co-ordinates for POLY. Use Collins

Q-point method to calculate the co-ordinates. Draw a sketch. (20}

1 51 Opportunity Examination of 13 November 2016

Basic Surveying

Co-ordinates

Name

1'1 Win3 1'1 Eros 1'1 Hohe

y

- 6 423.820 -10 489.690 -11071.260

X

+ 62 884.860 + 60 272.270 + 64 410.770

Final Observed Directions.

@POLY

Name 1'1 Win3 1'1 Eros 1'1 Hohe

Fin. Observed Direction 70° 00' 00" - Long Leg

215° 04' 16" 292° 06' 30"

BSV521S

4.3. Use the field observations below, which were observed at Koppie to obtain the final observed

directions (No orientation needed). Show in table format. (4)

@Ko~~ie HI= 1.678m

Point/Station Circle Left Circle Right

1'1 Dune 175° 27' 13" 355° 27' 30"

Top 214° 17' 50" 34° 18' 09"

Low 41° 08' 07" 221° 08' 25"

RO 175° 27' 16" 355° 27' 14" [25]

Question 5

5.1. Calculate and apply all corrections to the observations (directions & distances) below. (10)

@WP HI= 1.656m

Point/Station Final Observed Direction Slope Distance Vertical Angle

1'1 OPDAM 284°04'22" 88°46'45"

1'1 DUBIS 49°27'55" 89°22'02"

VRIES 151°59'10" 764.075 8r42'04"


Basic Surveying

Co-ordinates

Name

b. OPDAM

b. DUBIS

WP

Please note:

y

-55 893.240

-36 570.010

-51257.400

BSV521S

X z

+ 113 141.220

+ 124 538.370

+ 111 979.000 1450.150

The Atmospheric Correction and Prism Constant Correction are already applied to all

measured distances.

Combined Sea level & Scale Enlargement Scale Factor= 1+ [(l/ (2R2}- H/R}],

where R = 6 370km.

5.2. Calculate the Y X Z co-ordinates for point House, by using the following information and the

observations at House. (15}

~Hab = H1- Hsig + Sab/Tan (Z} + (1-k}.S2 / (2R}

Where R is earth radius (use R = 6 370 km}, and k is an assumed relative ray curvature factor

(use k = 0.13}.

Ha= Hb- ~Hab

Please note:

ALL corrections are already applied to all measured distances.

@House HI= 1.565m

Point/Station Final Observed Direction Final Hor. Distance Vertical Angle

b. Blauputz 315°11'19" 90°02'24"

Kalk 75°19'23" 926.342 89°27'10" (Target=1.500m}

Co-ordinates

Name

b. Blauputz

Kalk

151 Opportunity Examination

y

+37 057.410

+43 991.910

X

+ 228 354.540

+ 219 483.720

of 13

z

1378.158 (Ground Level}

[25]

November 2016


Student Number:---------- Data Sheet 1

Question 1

Question a b c d

1.1.

1.2.

1.3.

1.4.

1.5.

- -1.6.

1.7.

1.8.

1.9.

1.10.

1.11.

1.12.

1.13.

1.14.

1.15.

1.16. ...... ...... - -1.17.

1.18.

1.19.

1.20.

1.21. - r-- - -1.22.

1.23.

1.24.

1.25.




Question 2.2.

Height of Collimation Levelling Sheet

NOTE: The BOLD and Underlined values are the Inverted Staff Readings.

NOTE: All answers must be rounded off to 3 decimal places

Collimation Reduced Final Point B.S. I.S. F.S. Heights Heights Correction Heights

TSM 201 1.756 1655.253

MH1 2.138

TP2 1.617 0.793

Kerb 1.355

Roofl 1.828

Roof2 2.123

TPS 1.010 2.451

TSM 202 2.234 1654.143




Question 3.1.

Bowditch Rule- Adjustment Sheet

Note: All answers must be rounded off to 3 decimal places

Oriented Directions and

V)

Final Horisontal z

Distances 0

Differences STATION Final Co-ordinates ...,

tJ.Y tJ.X y X

tJ.SWP - 4 680.110 + 62 348.590

Trl Vl c 0 ..., Q) +-' ro Tr2 :::::5 u ro u 1-0 Tr3 z 0 0

tJ.East -10 917.978 + 61753.282

151 Opportunity Examination Page12of13 November 2016



Question 3.2.

Direction Sheet

1 2 3 4 5 6 7

Fin. Obs. Prov. Prov. Join Diff. I Fin Join Dir. I Fin STATION Direction Back Dir. Prov. Corr. Forward Dir. Corr. Dir.

@ RPl

ll Twee 18° 46' 50" 18° 46' 44"

ll Tsaun 128° 24' 35" 128° 24' 28"

Trav1 2or 44' 09" ' . .

@Travl

RP1 21° 44' 26"

Trav2 251° 08' 21"

@Trav2 .

Trav1 7r 07' 53"

RP 178° 41' 44"

@RP2

ll Sand 122° 04' 21" 122° 04' 30"

ll Naub 25r 49' 50" 25r 50' o1"

Trav2 358° 41' 19"


nAmiBIA Un i VERSITY OF SCIEnCE AnD TECHnOLOGY

FACULTY OF NATURAL RESOURCES AND SPATIAL SCIENCES

DEPARTMENT OF GEO-SPATIAL SCIENCES AND TECHNOLOGY

QUALIFICATIONS:

DIPLOMA IN GEOMATICS

BACHELOR OF GEOMATICS

QUALIFICATIONS CODES: QUALIFICATIONS LEVEL:

06DGEM 6- 06DGEM

07BGEM 7- 07BGEM

COURSE CODE: BSV521S COURSE NAME: BASIC SURVEYING (Level 5)

SESSION: NOVEMBER 2016 PAPER: THEORY

DURATION: 3 HOURS MARKS: 100

FIRST OPPORTUNITY EXAMINATION MEMORANDUM

EXAMINER:

MODERATOR:

Mr. F. J. Louw

Mr. E. Sinvula

INSTRUCTIONS 1. The model answers are used as guidelines only.

2. The information presented by the students will be evaluated on

merit.

TH IS MEMORANDUM CONSISTS OF 18 PAGES (Including this Front Page and 4 Data Sheets)

I ~


Question 1

Answer the following questions on Data Sheet 1, by selecting the correct statement for each :

1.1. In geodetic surveys higher accuracy is achieved, if:

a. The curvature of the earth surface is ignored b. The curvature of the earth surface is taken into account c. The angles between the curved lines are treated as plane angles d. None of the above

1.2. Surveys concerned with the measurements and mapping of natural and artificial features of

the earth, like hills, lakes, rivers, roads, railways, power lines, etc are:

a. Engineering Surveys b. Cadastral Surveys c. Topographic Surveys d. Mining Surveys

1.3. A survey may be executed in several ways by different combinations of instruments and

methods, and some parts of the work may require different treatment from others. The

principle factors to be considered are:

a. The purpose of the survey b. The extent of the survey c. The degree of accuracy required d. All of the above

1.4. The main purposes of surveying is:

a. The art of making measurements of the relative positions of natural and man-made features on the earth's surface, and the presentation of this information either graphically or numerically

b. The determination of the relative positions of points (natural or artificial) on the surface of the earth.

c. The setting out on the ground of the positions of the points used in the construction, location of properties, etc

d. band c

1.5. The quality of a Surveyor is:

a. He must have a thorough theoretical and practical knowledge of his work. b. He must be honest and trustworthy and his judgment must be good c. He must have initiative; think clearly and without prejudice, tackling each survey with

energy and perseverance. d. All the above

1st Opportunity Memorandum Page 2 of 18 November 2016


1.6. Determining the difference in height between two points relative to a reference plane, or

relative to each other, by means of an instrument that provides a line of sight perpendicular

to that of gravity i.e. a line of sight that is horizonta l, is called:

a. Barometric Levelling b. Direct Levelling c. Levelling d. All of the above

1.7. A permanent reference point or mark, of known height is a:

a. Witness Mark b. Reference Mark c. Bench Mark d. None of the above

1.8. The imaginary line passing through the optical centre of the object lens, through the

telescope and through the eyepiece, is a:

a. Contour Line b. Collimation Line c. Level Line d. Horizontalline

1.9. The first reading from a level station is:

a. foresight b. back-sight c. intermediate sight d. any sight

1.10. The most common co-ord inate system for referring to the position of any definite point on

the Earth's surface is:

a. Geographical Co-ordinate System b. Plane Rectangular or Grid Co-ordinate System c. Polar Co-ordinate System d. Al l of the above

1.11. The purpose of observing a Reference Object (R.O.) is :

a. To ensure that the horizontal circle of the instrument has not been disturbed while observing

b. To orient the instrument to Zero South c. To orient the instrument to a trigonometrica l beacon d. None of the above

151 Opportunity Memorandum Page 3 of 18 November 2016


1.12. Basic types of errors in surveying can be divided into two main groups, namely controllable

and uncontrollable errors, of which uncontrollable errors are:

a. Accidental Errors b. Gross Errors c. Systematic Errors d. All of the above

1.13. The basic method of determining a distance is:

a. Taping b. Electronic Distance Measuring c. Staff Tacheometry d. All of the above

1.14. Observations that are closely grouped and the measurement (average value) is accurate, are:

a. Accurate Observations b. Inaccurate Observations c. Precise Observations d. Accurate and Precise Observations

1.15. The requirement for traverse stations is:

a. Stations should be at inaccessible positions b. A clear line of sight is required between the Stations c. The length of traverse legs must be as short as possible. d. None of the above

1.16. Contours of different elevations may meet only in the case of

a. a vertica l cliff b. a saddle c. a ridge d. an inclined plane

1.17. Two contour lines, having the same elevation:

a. cannot cross each other b. can cross each other c. cannot meet d. can meet

1.18. Contour maps can be used for the following:

a. To calculate the water capacities of reservoirs b. To trace a contour gradient for the road alignment c. To ascertain the indivisibility of points d. All the above



1.19. An inverted staff reading means:

a. The levelling staff is held upside down b. The levelling staff is held between the back-sight and the foresight c. The levelling staff is held after the back-sight d. All of the above

1.20. An application of levelling is:

a. Longitudinal section b. Cross section c. Contouring d. All of the above

1.21. The method to calculate a resection is:

a. Bowditch Rule b. Collins' Q-point method c. Blunt's method d. band c

1.22. Fixing the plane coordinates of a point, by setting up on the unknown point, and observing a

distance and direction to a known point, and a direction to another known point is called a:

a. Intersection b. Polar c. Reverse Polar d. Join

1.23. The following correction needs to be applied on distances measured with a Total Station:

a. Atmospheric Corrections b. Conversion to German Legal Metre c. Combined Sea Level and Scale Enlargement Correction d. All of the above

1.24. A traverse that starts at a known point (co-ordinated point) and ends at another know point

(co-ordinated point) is a:

a. Closed Traverse b. Open Traverse c. Loop Traverse d. None of the above



1.25. While viewing through a level telescope and moving the eye slightly, a relative movement

occurs between the image of the levelling staff and the cross ha irs. That means the

instrument is:

a. Not Correctly focused b. Said to have parallax c. Free of parallax d. All the above

See Data Sheet 1 for answers:

[25]

Question 2

2.1. Use the following information to calculate co-ordinate for point C. (15)

Co-ordinates

Name y X

A -6 836.515 +247 355.618

B -10 973.129 +247 584.123

Angle at A = 38°

Angle at B =5r

c

A

B



8

A

-10 973.129 +247 584.123

+247 355.618

Direction= 273° 09' 42"

-6 836.515 Distance = 4 142.920m

L1 y = -4 136.614 L1X = +228.505

= 38° 00' 00" =5roo·oo" = 95° 00' 00"

Angle at A

Angle at 8

Angle {A+ B)

Angle at C = 180° 00' 00"- 95° 00' 00" = 85° 00' 00"

Direction A to C = 235° 09' 42"

Direction 8 to C = 150° 09 ' 42"

Angle at C = 85° 00' 00" - Check

Distance A to C = 3 487.817m

Distance 8 to C = 2 560.379m

Polar A to C

Direction= 235° 09' 42"

Distance = 3 487.817m

Polar 8 to C

Direction= 150° 09' 42"

Distance= 2 560.379m

c y - 9 699.201 X+ 245 363.160

A

c

8

c

Y- 6 836.515

L1Y =- 2 862.686 y- 9 699.201

Y-10 973.129

L1 y = + 1 273.928 y - 9 699.201

X+ 247 355.618 L1X = - 1 992.460

X+ 245 363.158

X+ 247 584.123

L1X = - 2 220.957

X+ 245 363.162

2.2. Use the levelling observations given on Data Sheet 2 to ca lculate final heights using the

"Height of Collimation" method. All checks need to be shown and any misclosures needs to

be distributed. {10}


[25]



Question 3

3.1. Calculate the co-ordinates of points TR1, TR2 and TR3 from the following data, by completing

Data Sheet 3. Adjustment must be done by the Bowditch Ru le.


Co-ordinates

Name

{j.SWP {j.East

Traverse Leg {j.SWP to TR1

TR1 to TR2

TR2 to TR3 TR3 to {j.East

y X

- 4 680.110 + 62 348.590 + 61753.282 -10 917.978

Oriented Direction

28r OS' 41"

260° 06' 22"

262° 18' 42"

243° 32' 31"

Final Horisontal Distance

1824.328m

1 769.365m

1506.927m

1404.871m

{13)

3.2. Obtain orientated directions for the traverse RP1 - Trav1 - Trav2 - RP2 by completing the

direction sheet on Data Sheet 4. Do not calculate the traverse. (12)


[25]

Question 4

4.1. Define the term "Resection" . (1)

Resection is the fixing of the plane coordinates of a point by observing directions to at least

three known or control points.

4.2. The department wants to install a permanent base station on the roof of Poly Heights and

you have done the following observations to determine the co-ordinates for POLY. Use Coll ins

Q-point method to calculate the co-ordinates. Draw a sketch . (20)


Basic Surveying

Co-ordinates

Name

b. Win3 b. Eros b. Hohe

y

- 6 423.820 -10 489.690 -11 071.260

X

+ 62 884.860 + 60 272.270 + 64 410.770

Final Observed Directions.

@POLY

Name

b. Win3 b. Eros b. Hohe

b. Win3 -

POLY

Fin. Observed Direction 70° 00' 00" - Long Leg

215° 04' 16" 292° 06' 30"

b.Eros

b.Hohe

BSV521S

L1 Hohe

L1 Eras

y - 11 071.260 y -10 489.690

X+ 64 410.770 X+ 60 272.270

Direction = 352° 00' 03 " Distance= 4 179.163m

L1 y = -581.570 L1X = + 4 138.500

Direction POLY to q = 250° 00' 00" Angle a = 34° 55 ' 44" Angle 6 = 42° 06' 30" Angle a1 = 145° 04 ' 16" Angle 61 = 13r 53' 30" I of Angles = 360° 00' 00" Angle {a1 + 61} = 7r 02 ' 14" Angle q = 180° OO' OO"- 7r 02' 14" = 10r 57' 46"

Direction L1 Eras to q

Direction L1 Hohe to q

Check Angle q

1st Opportunity Memorandum

= 309° 53' 33" = 206° 55 ' 47" = 1or 57'46"

Distance = 2 455.392m Distance = 2 875.554m

Page 9 of 18 November 2016


Direction= 309° 53' 33"

Distance = 2 455.392m fJ Eras Y -10 489.690 X+ 60 272.270

!JY=-1883.897 !JX= +1574.764

Direction= 206° 55' 47"


q y -12 373.587

fJ Hohe Y- 11 071 .260 fj y = -1 302.331

q y -12 373.591

M ean q Y - 12 373.589 X+ 61 847.034

X+ 61 847.034

X+ 64 410.770 !JX = -2 563.737

X+ 61 847.034

fJ Win3 q

Y+ 53 689.320 y -12 373.589

X+ 103 390.460 X+ 61 847.034

Direction = 80° 06' 19"

!JY = +5 949.769 !JX = +1 037.826

Join q to fJ Win3 = 80° 06' 19" Observe POLY to fJ Win3 = 70° 00' 00" Orientation Correction = +10° 06' 19"

Direction fJ Eras to POLY Direction fJ Ho he to POLY

= 45° 10' 35"

= 12r 12' 49"

Angle {a1 + 61} Angle a2 Angle 62

I of Angles

= 1r o2' 14" = 53° 10' 32" = 49° 47' 14 " = 180° 00' 00"

fJ Eras to POLY Distance = 3 274.884m fJ Ho he to POLY Distance = 3 432.800m

Direction= 45° 10' 35"


Direction= 122° 12' 49" Distance= 2 875.554m

POLY Y - 8166.881

151 Opportunity Memorandum

fJ Eras Y -10 489.690 fj y = +2 322.811

POLY Y- 8166.879

fJ Hohe Y- 11 071 .260

!JY = +2 904.377 POLY Y- 8166.883

X+ 62 580.822

Page10of18

X+ 60 272.270 !JX = +2 308.553

X+ 62 580.823

X+ 64 410.770 !JX = -1 829.822

X + 62 580.822

November 2016


4.3. Use the field observations below, which were observed at Koppie to obtain the final observed

directions (No orientation needed). Show in table format. (4}

@Ko~~ie HI= 1.678m

Point/Station Circle Left Circle Right

b. Dune 175° 27' 13" 355° 27' 30"

Top 214° 17' 50" 34° 18' 09"

Low 41° 08' 07" 221° 08' 25"

RO 175° 27' 16" 355° 27' 14"

~

@ Ko~~ie

Mean Observe RO Fin. Observed

Direction Correction Direction

b. Dune 175° 27' 22" 00" 175° 27' 22"

Top 214°18'00" +02" 214°18'02"

Low 41° 08' 16" +05" 41°08'21"

RO 175° 27' 15" +07" ;17§0~7' ~~"

RO Correction: 22" -15" = +07" +07"/3 = +2.333"

[25]

Question 5

5.1. Calculate and apply all corrections to the observations (directions & distances) below. (10}

@WP HI= 1.656m

Point/Station Final Observed Direction Slope Distance Vertical Angle

b. OPDAM 284°04'22" 88°46'45"

b. DUBIS 49°27'55" 89°22'02"

VRIES 151°59'10" 764.075 8r42'04"


Basic Surveying

Co-ordinates

Name

f1 OPDAM

f1 DUBIS

WP

Please note:

V

-55 893.240

-36 570.010

-51257.400

X

+ 113 141.220

+ 124 538.370

+ 111 979.000

BSV521S

z

1450.150

The Atmospheric Correction and Prism Constant Correction are already applied to all

measured distances.

Combined Sea level & Scale Enlargement Scale Factor= 1+ [{// {2R2) - H/R)L

where R = 6 370km.

i@WP

Name Fin. Observed Join Difference Oriented

Direction Direction I Correction Direction

iLl OPDAM 284°04'22" 284° 04' 27" +07"

iLl DUBIS 49° 27' 55" 49° 27' 59" +04"

Vries 151° 59' 10" {06") 151°59' 16"

Correction = +11''/2 = +06"

Distance WP to Vries

HO =SO. Sin Z

= 764.075 . Sin 8r42 '04" = 763.460m

HD = 763.460m x 0.999 986 4 (GLM}

= 763.450m

1+ [(y /(2R2) - H/R}}

= 1+ [(-51257.400//(2. 6 370 ood; - (1450.150/6 370 ooo)J = 1+ {0.000 032 375 - 0.000 227 653} = 1 - 0.000 195 278 = 0.999 804 722

Final Distance WP to Vries = 763.450m x 0.999 804 722 = 763.301m



5.2. Calculate the Y X Z co-ordinates for point House, by using the following information and the

observations at House. (15)

LlHab = H1- Hsig + Sab/Tan (Z) + (1-k).$2/ (2R)

Where R is earth radius (use R = 6 370 km), and k is an assumed relative ray curvature factor

(use k = 0.13).

Please note:

ALL corrections are already applied to all measured distances.

@House HI= 1.565m

Point/Station Final Observed Direction Final Hor. Distance Vertical Angle

b. Blauputz

Kalk

Co-ordinates

Name y

90°02'24"

926.342 89°27'10" (Target=l.500m)

X z b. Blauputz

Kalk

+37 057.410

+43 991.910

+ 228 354.540

+ 219 483.720 1378.158 (Ground Level)

!JBiauputz Kalk

y +37 057.410 y +43 991 .910

[j y = -6 934.500

Measured Angle @ House

Angle @ !JBiauputz

Angle@ Kalk

Direction Kalk to House

Direction = 266° 11 1 57" Distance = 926.342m

151 Opportunity Memorandum

X+ 228 354.540 X+ 219 483.720

!JX = +8 870.820

= 120° 08' 04"

=4° 04 1 49"

= 55° 471 07"

= 266°11 I 57"

Direction. = 32r 59' 04 " Distance= 11 259.606m

Kalk Y +43 991.910 X+ 219 483.720 [j y = - 924.304 !JX = - 61.406

House Y +43 067.606 X+ 219 422.314

Page 13 of 18 November 2016


LJHab =HI- Hsig + Sab/Tan{Z} + {1-k}. Sab 2/{2R}

=1.565 -1.500 + 926.342/Tan{89°27'10"} +{1-0.13}.926.3422/{2 .6370000}

= 0.065 + 8.848 + 0.059

=8.972m

Ha = Hb - LJHab

= 1 378.158m - 8.972m

Height of ST1= 1 369.186m


[25)


Student Number: Memorandum Data Sheet 1

Question 1

Question a b c d

1.1. X

1.2. X

1.3. X

1.4. X

1.5. X

1.6. X

1.7. X

1.8. X ...... - ...... ...... 1.9. X

1.10. X

1.11. X

1.12. X

1.13. X

1.14. r-- - - r--

X

1.15. X

1.16. X

1.17. X

1.18. X

1.19. X

1.20. X ...... 1.21.

X

1.22. X

1.23. X ...... - .... 1.24.

X

1.25. X ...... - ...... ......

151 Opportunity Memorandum Page15of18 November 2016



Question 2.2.

Height of Collimation Levelling Sheet

NOTE: The BOLD and Underlined values are the Inverted Staff Readings.

NOTE: All answers must be rounded off to 3 decimal places

Collimation Reduced Final Point B.S. 1.5. F.S. Heights Heights Correction Heights

TSM 201 1.756 1657.009 1655.253 0.000 1655.253

MH1 2.138 1654.871 -0.005 1654.866

TP2 1.617 0.793 1657.833 1656.216 -0.005 1656.211

Kerb 1.355 1656.478 -0.010 1656.468

Roof1 1.828 1659.661 -0.010 1659.651

Roof2 2.123 1659.956 -0.010 1659.946

TPS 1.010 2.451 1656.392 1655.382 -0.010 1655.372

TSM 202 2.234 1654.158 -0.015 1654.143

4.383 -0.458 5.478 11601.742 11596.722

-5.478 -5.020 -0.015/3

-1.095 11596.722 -1.095 =-0.005




Question 3.1.

Bowditch Rule- Adjustment Sheet

Note: All answers must be rounded off to 3 decimal places

Oriented Directions and

(./')

Final Horisontal z

Distances 0

Differences STATION Final Co-ordinates .......

l:J.Y l:J.X y X

~SWP - 4 680.110 + 62 348.590 28r OS' 41" -1743.729 +536.265

1824.328m +0.005 -0.006

Tr1 -6 423.834 +62 884.849 Vl

260° 06' 22" c -1743.050 -304.019 ·a 1 769.365m ....... +0.005 -0.006 Q)

+-' ro Tr2 -8 166.879 +62 580.824 ~

262° 18' 42" u ro -1493.380 -201.603

1506.927m u +0.004 -0.005 I-0 Tr3 -9 660.255 +62 379.216 z

243° 32' 31" 0 -1257.726 -625.930 0

1404.871m +0.003 -0.004 -10 917.978 +61 753.282

~East -10 917.978 + 61753.282 'i.l:J.Y= 'i.l:J.X=

5=6 505.491m -6 237.885 -595.287 DV= -6 237.868 DX=-595.308

dY = +0.017 dX = -0.021

Linear Misclosure = 0.027

Class A =0.256

Traverse is Class A

1st Opportun ity Memorandum Page 17 of 18 November 2016



Question 3.2.

Direction Sheet

1 2 3 4 5 6 7

Fin. Obs. Prov. Prov. Join Diff. I Fin Join Dir. I Fin STATION Direction Back Dir. Prov. Corr. Forward Dir. Corr. Dir.

@ RPl

ll Twee 18° 46' 50" -06" 18° 46' 44"

ll Tsaun 128° 24' 35" -07" 128° 24' 28"

Trav1 201° 44' 09" -06" 201° 44' 03" (-OS") (201° 43' 58")

-13"12

=-06"

@Travl

RP1 21° 44' 26" 21° 44' 03" -23"

Trav2 251° 08' 21" -23" 251° 07' 58" (-10") (251 ° 07' 48")

@Trav2

Trav1 71° 07' 53" 71° 07' 58" +OS"

RP 178° 41' 44" +OS" 178° 41' 49" (-15") 178° 41 ' 34"

@RP2

ll Sand 122° 04' 21" +09" 122° 04' 30"

ll Naub 2sr 49' so" +11" 2sr so· o1"

Trav2 358° 41' 19" 188° 41' 49" +10" 358° 41' 29" (+OS") (358° 41' 34")

+20"12

=+10"

29" - 49" =-20"14

= -05"

151 Opportunity Memorandum Page18of18 November 2016

namibia university of science and...

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