Introduction to Leveling
Leveling is a vital branch of surveying aimed at determining the relative heights or elevations of different points on, above, or below the earth's surface. It's the foundation for establishing grades for construction, drainage, and mapping.
Types of Leveling
Direct Leveling
Also known as spirit leveling. The most accurate and commonly used method. It measures vertical distances directly using a leveling instrument and a graduated rod.
Learn more →Trigonometric Leveling
Calculates differences in elevation indirectly from measured vertical angles and horizontal or inclined distances.
Learn more →Barometric Leveling
Involves determining differences in elevation by measuring differences in atmospheric pressure. Because atmospheric pressure decreases as elevation increases, instruments like an aneroid barometer are used to find the elevation of a point. It's less accurate than direct leveling.
Stadia Leveling
A variation of trigonometric leveling where distances are measured using stadia hairs within the instrument's telescope, combined with vertical angles. It's faster but generally less accurate than standard direct leveling.
Direct Leveling
Direct leveling determines the difference in elevation between points by taking readings on graduated rods placed on those points, using a level instrument set up between them.
Figure: Concept of Direct Leveling
Key Terms
- Benchmark (BM): A point of known elevation.
- Backsight (BS): A rod reading taken on a point of known elevation (like a BM) to establish the height of the instrument.
- Height of Instrument (HI): The elevation of the line of sight.
HI = Elev + BS - Foresight (FS): A rod reading taken on a point whose elevation is to be determined.
- Elevation (Elev): The height of a point relative to a datum.
Elev = HI - FS
Profile Leveling
The objective is to determine the elevations of a series of points located at measured intervals along a defined line (e.g., center line of a road or stream). This produces a profile showing the ground surface.
Trigonometric Leveling
This method is used when direct leveling is impractical, such as measuring the height of a steep hill or a distant object. It relies on measuring the vertical angle to the object and the horizontal (or slope) distance to its base.
Figure: Trigonometric Leveling Principle
Basic Calculation
If you know the horizontal distance (D) and the vertical angle (α), you can calculate the vertical component (V).
V = D × tan(α)
To find the total elevation of the observed point, you must add the height of the instrument (h.i.) and subtract the target reading if applicable.
Corrections
For long distances, corrections for Earth's curvature (Cr) and atmospheric refraction (Re) must be considered. The combined correction is often denoted as C.
The Two-Peg Test
A simple but essential field procedure used to determine if the line of sight of a leveling instrument is truly horizontal when the bubble is centered. It checks and allows for the adjustment of the instrument's collimation error.
The test involves setting up the level at two different positions relative to two solid points (pegs) A and B.
- Setup 1 (Midway): Set the instrument exactly midway between Peg A and Peg B. Take rod readings on both. The difference between these readings is the true difference in elevation because any instrument error affects both readings equally.
- Setup 2 (Near one peg): Move the instrument close to Peg A (or B). Take readings on A and B again.
- Analysis: Calculate the apparent difference in elevation from Setup 2. Compare it to the true difference from Setup 1.
- Adjustment: If they don't match, the line of sight is inclined. The difference reveals the error, and the instrument's crosshairs can be adjusted to correct it.
Principle:
When the instrument is exactly midway between two points, any error in the horizontal line of sight affects the reading on both rods equally. Subtracting the readings cancels out this error, giving the true difference in elevation.
Quick Knowledge Check
1. Which type of leveling relies on measuring vertical angles and distances?
2. What is the primary purpose of the Two-Peg Test?