Levelling is the operation in surveying used to determine the difference in elevation between two or more points on the earth's surface. It is fundamental to all engineering surveys — from road alignment to building layout, from dam construction to drainage network design. The reduced level (RL) of each point relative to a datum is determined by levelling.
Terms and Definitions
| Term | Definition |
|---|---|
| Datum | Reference surface of zero elevation; in India: Mean Sea Level at Mumbai (Chart Datum) |
| Reduced Level (RL) | Height of a point above the datum |
| Bench Mark (BM) | Fixed reference point of known RL; established by trigonometric or levelling surveys |
| Backsight (BS) | First reading taken on a staff held at a point of known RL; after instrument setup |
| Foresight (FS) | Last reading at an instrument position; before moving to next setup |
| Intermediate Sight (IS) | Any reading between BS and FS at a given instrument position |
| Turning Point (TP)/Change Point (CP) | Point where both FS and BS are taken (before and after moving instrument) |
| Height of Instrument (HI) | RL of the line of sight = RL of benchmark + BS reading |
Types of Levels (Instruments)
| Instrument | Type | Accuracy | Use |
|---|---|---|---|
| Dumpy Level | Fixed telescope, bubble tube | ±3–5 mm/km | General construction surveying |
| Auto Level (Automatic Level) | Automatic compensator — self-levelling within ±15' | ±1–2 mm/km | Most common; highways, buildings, engineering surveys |
| Digital Level | Electronic bar-code staff reader | ±0.3–0.5 mm/km | Precise control surveys, benchmarking |
| Theodolite (trigonometric) | Vertical angles measured | ±5–20 mm/km | Hills, towers, inaccessible points |
Types of Levelling
1. Simple / Direct Levelling
One instrument setup; BS from known point, FS to unknown point. HI = RL_BM + BS; RL_new = HI − FS.
Used for short distances within the instrument's range (< 100 m).
2. Differential (Fly) Levelling
Multiple instrument setups across a long traverse. Used to transfer RL from a known BM to a distant point. Accuracy check: Closing error = RL_final − RL_known; distribute as per BIS specification.
3. Profile Levelling (Longitudinal Section)
Levels taken along the centreline of a proposed road, canal, or pipeline at regular intervals (usually 20–30 m).
Used for: Design of road vertical profile, cut-and-fill analysis, gradient calculation.
4. Cross-Section Levelling
Levels taken at regular distances perpendicular to the centreline. Used for earthwork volume calculation using prismoidal formula.
5. Reciprocal Levelling
Used when a long sight across a valley, river, or wide obstruction is required. Two instrument setups — once on each bank:
True difference in elevation = (h1 + h2) / 2
where h1 and h2 are differences observed from each bank. Eliminates effects of Earth's curvature, atmospheric refraction, and instrument/staff errors.
6. Precise Levelling
Follows strict procedures for first-order control surveys: staff read to nearest 0.1 mm; backsight = foresight distance balance; no sights >50 m; double-run (forward and backward); allowable error = ±4√K mm (K in km).
Booking and Calculation Methods
Method 1: Height of Instrument (HI) Method
HI = RL of BM + BS reading (once per instrument station)
RL = HI − Staff reading (for each IS and FS)
Check: Σ BS − Σ FS = RL last TP − RL first BM
Limitation: Error in HI affects all RL calculations for that setup; intermediate points not independently checked.
Method 2: Rise and Fall Method
Rise (+) or Fall (−) = difference between consecutive staff readings.
RL = Previous RL + Rise (or − Fall)
Check: Σ BS − Σ FS = Σ Rise − Σ Fall = RL last TP − RL first BM
Advantage: Each RL is independently calculated; errors do not propagate.
Worked Example — Levelling Booking
Field Data
BM RL = 100.000 m
| Station | BS | IS | FS |
|---|---|---|---|
| BM | 1.255 | — | — |
| A | — | 0.850 | — |
| B | — | 1.340 | — |
| CP1 | 0.980 | — | 2.105 |
| C | — | 0.560 | — |
| D | — | — | 1.220 |
HI Method Solution
| Station | BS | IS | FS | HI | RL |
|---|---|---|---|---|---|
| BM | 1.255 | — | — | 101.255 | 100.000 |
| A | — | 0.850 | — | — | 100.405 |
| B | — | 1.340 | — | — | 99.915 |
| CP1 | 0.980 | — | 2.105 | 100.130 | 99.150 |
| C | — | 0.560 | — | — | 99.570 |
| D | — | — | 1.220 | — | 98.910 |
Check: ΣBS − ΣFS = (1.255 + 0.980) − (2.105 + 1.220) = 2.235 − 3.325 = −1.090
RL_D − RL_BM = 98.910 − 100.000 = −1.090 ✓
Errors in Levelling
Instrumental Errors
- Line of collimation not horizontal (most important): Balanced BS=FS distances eliminates this
- Staff not graduated uniformly
- Tripod settlement
Natural Errors
- Earth's curvature: c = 0.0785 × d² (m) where d in km; always makes RL appear higher than actual
- Atmospheric refraction: r = 0.0112 × d²; refraction makes RL appear lower; net correction: c−r = 0.0673 × d²
- At d = 1 km: correction = 0.0673 m = 67.3 mm (significant for precise surveys)
Personal Errors
- Incorrect staff reading
- Staff not held vertical (use circular bubble on staff)
- Wrong booking
IS 1619 — Levelling Standard for India
IS 1619 specifies: Classification of levelling, field procedures, closing errors, and corrections for first-, second-, and third-order levelling networks:
| Order | Allowable Closing Error | Application |
|---|---|---|
| First order (Geodetic) | ±4√K mm (K in km) | National BM network, dams, critical projects |
| Second order | ±8√K mm | State-level control, large projects |
| Third order | ±12√K mm | General engineering surveys |
Frequently Asked Questions
What is the significance of balanced backsight and foresight distances in levelling?
If backsight distance = foresight distance, the systematic error from a non-horizontal line of collimation is automatically cancelled, as the error is proportional to the horizontal distance. This is the most important procedural rule in levelling. Modern auto levels with compensators reduce (but do not eliminate) this error, making equal BS-FS distances still best practice.
What is the closing error in a levelling loop and how is it adjusted?
After completing a levelling loop (returning to the starting BM or closing on another BM of known RL), the difference between calculated RL and known RL is the closing error. If within allowable limits, it is distributed over the route proportional to the distance from the starting point (Bowditch rule for levelling) or uniformly.