Principle of Levelling
The principle of leveling is based on establishing a horizontal line of sight and determining the vertical distances of points above or below this line. A leveling instrument is used to provide the horizontal line of sight, while a graduated leveling staff measures the height between the line of sight and various points on the ground.
In Figure above, point O represents the center of the Earth. Points A and A’ are two positions on the ground whose difference in elevation needs to be measured. The leveling instrument is positioned at point C. The line CO is the vertical plumb line, and BB’ represents the line of sight, which is horizontal and perpendicular to CO.
The readings on the leveling staff held at points A and A’ are noted as AB and A’B’, respectively. The equation used to calculate the difference in elevation between A and A’ is:
OA+AB=OA′′+A′′A′+A′B′
As This simplifies to:
AB−A′B′=A′′A′=
where δh is the difference in the staff readings, representing the change in elevation between the two points.
To eliminate the effect of the Earth’s curvature, the distances from the instrument station to the two staff positions are kept equal. This ensures that any error caused by the Earth’s curvature is minimized.
Important Considerations
- Earth’s Curvature: To mitigate the effects of the Earth’s curvature, surveyors typically ensure that the distances from the instrument to both staff positions are equal. This practice helps cancel out curvature-related errors, which will be discussed in more detail later.
- Instrument Setup: Proper levelling of the instrument is crucial for accurate measurements.
- Staff Positioning: The levelling staff must be held perfectly vertical at each point for precise readings.
- Multiple Setups: For longer distances or significant elevation changes, multiple instrument setups may be necessary to maintain accuracy.
- By understanding and applying this principle, surveyors can accurately determine elevation differences across various terrains and distances, enabling precise topographic mapping and engineering design.
Technical Terms Used in Leveling
Level Surface
A surface that is parallel to the average curved surface of the Earth is called a level surface. Every point on this surface is equally distant from the center of the Earth. It is always perpendicular to the plumb line at any location. An example of this is the still surface of water in a lake.Level Line
A level line is a line that lies on a level surface, meaning every point on this line is at the same distance from the center of the Earth. The edge or cross-section of calm water in a lake is an example of a level line.Horizontal Surface
A surface that touches the level surface at one specific point(tangential) is known as a horizontal surface. It is perpendicular to the plumb line at the point of contact.Horizontal Line
A horizontal line is a straight line that lies on a horizontal surface. It touches the level line at a single point and is tangential to it.Vertical Line
A vertical line is a line that is perpendicular to a level line. The plumb line, which points straight toward the center of the Earth, is an example of a vertical line.Vertical Plane
A vertical plane is a flat surface that contains a vertical line.Vertical Angle
The vertical angle is the angle formed between a sloping (inclined) line and a horizontal line within a vertical plane.Datum Surface
A datum surface is an imaginary level surface from which the heights or depths of points are measured. It serves as a reference level for all measurements.
- Mean Sea Level (MSL)
The Mean Sea Level is calculated by averaging the water level at a location over a 19-year period. This serves as the base reference for determining the elevations of different points in a region. In India, the Survey of India uses Mumbai’s sea level as the standard for this purpose. Reduced Level (RL)
The Reduced Level is the height (above) or depth (below) a specified datum or reference point. It is also referred to as the elevation of a point. If a point is below the datum, it is assigned a negative elevation.Line of Sight
The line of sight refers to the path along which light travels through the optical center of the instrument’s objective lens, passing through the eyepiece to the observer’s eye.Line of Collimation
The line of collimation is the line that extends through the optical center of the instrument’s objective lens and intersects the crosshairs, continuing onward. This line is used for precise measurements.Plane of Collimation
The plane of collimation is the horizontal plane in which a properly adjusted leveling instrument rotates about its vertical axis.Optical Center of a Lens
The optical center is a point within a lens where light rays pass through without bending or being displaced laterally. It is positioned so that its distances from the lens’ curved surfaces are proportional to their radii.Axis of the Telescope
The axis of the telescope is the line that connects the optical center of the objective lens and the center of the eyepiece.Bench Mark (BM)
A bench mark is a permanent and stable reference point with a known elevation above the chosen datum. It is used as a base point for leveling operations.
