Surveying and Traversing Study Notes

SECTION A (20 marks)

Each question in this section consists of four (4) marks.

1. Main Objective of Conducting a Traverse

• To determine a series of connected points in terms of horizontal coordinates.

• To establish and describe the relative positions of points in a specific survey area.

• To measure angles and distances for accurate mapping of terrain or construction projects.

• To create a control network that can be used for various engineering applications such as designing, mapping, and construction.

2. Reducing WCB to Quadrant Bearing

(i) For WCB 075° 20' 50" :

• Since WCB is in the 1st quadrant, it is directly reducible.

• Quadrant Bearing = 075° 20' 50"
  
  (ii) For WCB 200° 00' 00" :

• This is in the 3rd quadrant. To convert, subtract 180°.

• Quadrant Bearing = 200° - 180° = 20° 00' 00" S.

3. Bearing of Line QR

• Line PQ has a bearing of 120° 00' 00".

• At point Q, line QR makes a clockwise angle of 120° 00' 00".

• To find the bearing of line QR:
    - Start bearing of PQ: 120° 00' 00"
    - Add the clockwise angle to this bearing:
    - Bearing of QR = 120° + 120° = 240° 00' 00".

4. Causes of Changes in Magnetic North Direction

• Variations in the Earth's magnetic field due to geological formations.

• Movement of molten iron within the Earth’s outer core.

• Changes in the magnetic pole positions caused by solar winds and cosmic radiation.

• Geomagnetic jerks or secular variation affecting the magnetic field orientation over time.

5. Distinction Between True North and Local North

• True North:
    - Geographical north pole, located at 90°N latitude.
    - Fixed point on the Earth’s surface used for navigation and mapping.
    - Utilizes the lines of longitude for accurate navigation.

• Local North:
    - Refers to the direction specified by a local magnetic compass.
    - Subject to the local magnetic declination and can vary significantly over short distances.
    - Not a fixed point; instead influenced by local magnetic anomalies.

6. Origin of Rectangular Coordinate System in Surveying

• The origin is located at the extreme South-west to:
    - Establish a universal reference point to minimize coordinate values for calculations.
    - Maximize the use of positive coordinates for eastings (x) and northings (y).
    - Facilitate ease of calculations in large surveying areas by using increasing coordinates from the origin.

7. Importance of Areas and Volumes in Civil Engineering (Earthworks)

• Essential for determining the quantity of materials required for construction projects.

• Critical for calculating excavation and fill volumes to ensure leveling and stability of structures.

• Helpful in economic evaluations for budgeting and resource allocation concerning earth movements.

• Useful in planning drainage systems and assessing geological conditions.

8. Methods of Estimating Areas of Irregular Figures

• Grid Method:
    - Overlaying a grid of known dimensions over the figure and counting the full and partial squares.

• Planimeter Method:
    - Utilizing a planimeter tool that traces the perimeter of the shape to directly compute the area.

9. Definition of Map Reading

• The process of interpreting and understanding various symbols, lines, and colors on a map to extract information about the location, terrain, and features depicted.

10. Indicators in a Map

(i) Parallel Straight Line Contour:

• Indicates a uniform slope; the contours are evenly spaced implying an equal gradient across the terrain.
  (ii) Congested Contours:

• Indicates a steep gradient or abrupt changes in elevation; contours are closely spaced suggesting significant vertical changes over a short horizontal distance.

SECTION B

Each question in this section carries ten (10) marks.

11. Unusual Meanings of Map Elements

(i) Blue Colour:

• Represents water bodies such as rivers, lakes, and oceans on the map.

• Often used to highlight the aquatic features of the landscape.
  (ii) Symbol:

• A graphic representation used to convey specific information regarding features such as roads, parks, or landmarks.

• Different symbols denote different categories of data and help in quick identification.
  (iii) Network of Lines with Figures at the Center:

• Often indicates a road or transportation network; can represent junctions or significant points of interest on the map.

• Highlights connectivity and access routes between locations.
  (iv) Green Colour:

• Represents vegetation areas such as forests, parks, and agricultural fields.

• Signifies ecological zones and land use types regarding greenery and environmental aspects.

12. Calculating Accuracy and Correction of Angular Misclosure for a Traverse

An engineer conducted a 10 station traverse with:

• Angular Misclosure = 20"

• Linear Misclosures:
    - $dE = 0.12m$
    - $dN = 0.20m$

• Total Length of Traverse = 750 m.

a) Calculate the Accuracy of the Traverse

• Accuracy calculated using the formulas:
    - Linear accuracy defined as $ext{Accuracy} = rac{ ext{Length of Traverse}}{ ext{Total Misclosure}}$
    - Total Misclosure = $ext{linear misclosure} = ext{dE} + ext{dN} = 0.12 + 0.20 = 0.32m$

• Applying the formula:
  $ext{Accuracy} = rac{750m}{0.32m} = 2343.75$

b) Calculate the Correction of Angular Misclosure for Each Angle

• Total angles in a traverse of ten stations = 10 - 2 = 8.

• Correction per angle = $ext{Total Angular Misclosure} / ext{Number of Angles} = rac{20"}{8} = 2.5"$

13. Interior Angles of a Triangular Dam

Given Bearings:

• AB: 123° 14' 07"

• BC: 259° 38' 20"

• AC: 197° 18' 32"

Calculation of Interior Angles

• To find the interior angles of the triangle, use the following relationship:
  $ext{Angle A} = 180° - ext{(Bearing AB - Bearing AC)}$

• Calculate:
    - Bearing B = $ext{Bearing BC - Bearing AB}$
    - Bearing C = $ext{Bearing AC - Bearing AB}$

14. Chronological Steps to Calculate the Traverse

• Determine the starting point and establish a known coordinate for the starting station.

• Measure the angles and distances between stations using appropriate surveying tools.

• Record the coordinate changes at each station based on measurements taken.

• Calculate the misclosures by comparing actual coordinates against expected coordinates.

• Adjust the measurements for any angular and linear misclosure.

• Compile all collected data for analysis to ensure accuracy and precision in final readings.