Essential Concepts in Land Surveying and Mapping
Definition of Land Surveying
Surveying is the science that deals with the determination of relative positions and heights, as well as the size and shape of any part of the Earth’s surface, including all detail. It also involves the projection of measured data or detail onto a map at a suitable scale. Surveying may also include determining relative heights of different points on the Earth’s surface.
Understanding Maps and Plans
A map is a generalized and reduced representation, on a flat surface, of a part of the Earth’s curved surface.
What Are Coordinates?
Coordinates are a system of magnitudes used to fix the position of a point, line, or plane.
Achieving Accurate Leveling
- Observation lines to points or the staff must not exceed 60m.
- At a setup, all lines must be of equal length, except when taking intermediate readings.
- Observation lines need to be more than one meter above the ground. Rays lower than one meter are subject to refraction caused by warmer air closer to the ground than higher up.
- Benchmarks can also be determined underneath roofs, against the soffit of bridges and columns, etc., by using the staff either straight up or upside down. These readings are theoretically negative.
Field Methods to Eliminate Leveling Errors
- Make a balanced setup in the field between the two staves.
- If the surveyor knows the extent of the error, an error per meter can be calculated and then applied over the distance from the level to the staff.
- Perform a balanced setup: First, position the instrument close to one staff; take backsight and foresight readings to determine the height difference. Then, move the instrument close to the second staff; again, take backsight and foresight readings and calculate the height difference. Finally, determine the mean between the two differences.
Errors Affecting Leveling Accuracy
- Incorrectly recording staff numbers.
- Exchanging backsight and foresight columns.
- Errors in addition and subtraction.
- The staff not remaining in the same place for backsight and foresight readings.
- Tubular bubble not level.
- The level is not in proper adjustment.
- The staff is not held vertically.
- The tripod and staff are not on stable ground.
- Parallax error.
What is a Traverse in Surveying?
A traverse consists of consecutive survey lines. A traverse always starts and ends at known points, where the starting point’s coordinates are established. Therefore, a traverse is defined by its coordinates, directions, and distances.
Traverse Purpose and Accuracy
- To provide adequate control points for a survey.
- To establish points for future surveys.
Traversing vs. Leveling: Staff & Instrument Positions
In leveling, the staff is positioned at the point of interest, while the instrument’s position is fixed. Conversely, in traversing, the instrument is positioned at the point of interest, and the staff (or target) is moved.
Factors Influencing Traverse Accuracy
- Instrument Accuracy: On engineering sites, single-second instruments are not always necessary due to relatively short distances compared to triangulation surveys, where distances can range from short to tens of kilometers and accuracy is paramount.
- Surveyor’s Experience: Greater knowledge, discipline in the study area, and skillful instrument handling reduce the likelihood of errors and blunders.
- Accuracy of Start and End Points: High-quality start and end points contribute significantly to the overall accuracy of the traverse.
- Type of Survey:
- Monitoring structures requires extremely high accuracy (parts of millimeters, e.g., 0.0001m).
- Cadastral surveys require lesser accuracy (to the nearest half-centimeter).
- Detail surveys can be to the nearest 0.1m.
Elements of Traverse Calculation
- Coordinates
- Directions
- Distances
Level Adjustment for Collimation Error Elimination
- The tubular bubble must be perpendicular to the vertical axis of the instrument.
- The observation line must be parallel to the axis of the tubular bubble.
Detecting Collimation Error in the Field
Field Corrections in Surveying
- Scale and sea-level correction
- Slope correction
- Temperature correction
Methods for Expressing Map Scales
- Word Scale: A verbatim statement of scale, convenient for small-scale maps but less effective for large-scale maps (e.g., ‘one centimeter represents one kilometer’).
- Ratio Scale: Expressed as a ratio where units on both sides are the same (e.g., 1:1,250 or 1:500). This implies that one unit on the map represents the stated number of the same units on the ground.
- Fraction Scale: The ratio expressed as a fraction (e.g., 1/1250 or 1/500). Also known as a Representative Fraction (RF).
- Graphic or Line Scale: A visual representation of the scale as a divided straight line of a convenient length, facilitating easy reading of distances on the map.
Understanding Contour Lines
Contour Lines
A contour line is a line that joins points of the same elevation. It is a visual representation of a specific terrain on a map, as seen from above.
Contour Interval
A contour interval is the perpendicular distance between two subsequent contour lines.
Key Characteristics of Contour Lines
- The angle of inclination influences the horizontal distance between contour lines.
- Contours never cross one another.
- Contour lines are always closed.
- Contour lines must have a height value.
- A contour index (or index contour) can also be used; this is a slightly thicker line than other contours, spaced at regular intervals.
Map Projection Properties
- Conformity: A map is conformal when its scale at any point is the same in all directions. This occurs when meridians (lines of longitude) and parallels (lines of latitude) intersect perpendicularly.
- Distance: A map that maintains distance accurately reflects distances from the center of the projection to any other part of the projection.
- Direction: Maintaining direction on a map means that angles reflect minimal distortion or deviation from any point on a line to another point.
- Scale: Scale is the ratio between a distance on a map and the corresponding distance on the ground.
- Area: Maintaining area on a map means that all areas on the map have the same ratio to their corresponding areas on the ground.
Classes of Map Projections
- Cylindrical Projections (e.g., Gauss Conformal Projection or Transverse Mercator Projection)
- Conical Projection
- Zenithal Projection
Note: The projection system used in South Africa is the Transverse Mercator projection, also known as the Gauss Conformal projection.
Gauss Conformal Projection Characteristics
- The land is divided into sections, each two degrees of longitude in width. The specific section for the work must be indicated.
- The central meridian is always an odd-numbered line of longitude (e.g., Lo 27°, Lo 29°) and projects as a straight line.
- The origin of each section is the intersection of the central meridian and the equator.
- Distances are measured clockwise from the south (0°). The direction from A to B is denoted as AB=∝, and the direction from B to A is BA= ∝± 180°.
- A perceived direction projects as a curved line, similar to the equal meridians.
What Does “Lo” Stand For?
Data Types Collected in Surveying
Surveying is the science that deals with the determination of relative positions and heights, as well as the size and shape of any part of the Earth’s surface, including all detail. It also involves the projection of measured data or detail onto a map at a suitable scale.