Chain & Compass Surveying
Ranging, Offsetting, WCB vs QB Bearings, Local Attraction & Traverse Computation
Last Updated: April 2026 | GATE CE 2025–2027
📌 Key Takeaways
- Chain surveying measures only linear distances — suitable for small, open areas with well-defined detail.
- Prismatic compass reads WCB (0°–360°, clockwise from N); surveyor’s compass reads QB (N/S ± degrees E/W).
- Fore bearing and back bearing of a line differ by exactly 180° when both stations are free of local attraction.
- Local attraction correction: start from the station where FB − BB = 180°, propagate corrections to other stations.
- Magnetic declination: Eastern declination is added to, Western declination is subtracted from, magnetic bearing to get true bearing.
- Traverse latitudes = d·cosθ; departures = d·sinθ; closing error = √(ΣL² + ΣD²).
- Bowditch (compass) rule distributes closing error proportional to side length; Transit rule distributes proportional to latitude/departure.
1. Chain Surveying — Principles & Instruments
Chain surveying is the simplest form of surveying in which only linear measurements are made. No angular measurements are taken. The area is divided into a network of triangles (triangulation) since a triangle is the simplest plane figure that can be plotted from measured sides alone.
Instruments used:
- Gunter’s chain (1 chain = 20.12 m = 66 ft, 100 links each 0.2012 m) — used in land surveying; areas computed in acres.
- Engineer’s chain (100 ft, 100 links each 1 ft) — used in engineering works.
- Metric chain (20 m or 30 m, 100 links) — most common today; tallies at every 5 m.
- Steel tape (invar tape for precision work, 30 m or 100 m).
- Arrows (marking chain lengths in the field), ranging rods (2 m, painted red & white, 0.5 m bands), pegs, offset staff (3 m or 5 m).
Corrections to Chain Measurements
Temperature correction: CT = α(Tm − T0) × L
Slope correction: Cs = −L(1 − cosθ) ≈ −h²/2L (subtract for slope)
Sag correction: Csag = −w²L³/(24P²) (subtract; w = weight/unit length, P = pull)
Pull correction: CP = (P − P0)L/AE
Chain too long: True length = Measured length × (Actual length/Nominal length)
2. Ranging, Offsetting & Obstacles
Ranging is establishing intermediate points on a survey line. Direct ranging (points visible from both ends) uses the eye to align intermediate ranging rods. Indirect ranging (reciprocal ranging) is used when the two end stations are not intervisible — an intermediate point is found by successive approximation between two observers.
Offsets are lateral measurements from the chain line to locate detail. Perpendicular offsets are most accurate and used when offsets are short (<15 m). Oblique offsets are taken at any convenient angle when the feature is far or perpendicular offset is impracticable.
Obstacles to chaining:
- Obstacle to ranging but not chaining (e.g., rising ground): use reciprocal ranging.
- Obstacle to both ranging and chaining (e.g., pond): use geometric constructions — equilateral triangle method (chain is extended by L·√3) or similar triangle method.
- Obstacle to chaining but not ranging (e.g., river): use similar triangles or the 3-4-5 method to find the width without crossing.
3. Errors in Chaining
| Error Type | Nature | Examples | Proportional to |
|---|---|---|---|
| Cumulative | Always in same direction (+ve or −ve); always add up | Chain too long/short, slope not accounted, temperature, incorrect plumbing in one direction | n (number of lengths) |
| Compensating | Sometimes +ve, sometimes −ve; partially cancel | Incorrect plumbing at random, incorrect estimation of fractions | √n |
The most serious error is using a chain that is too long — every measurement is systematically larger, and the error accumulates. Always test the chain against a standardised length before starting work.
4. Compass Surveying
| Feature | Prismatic Compass | Surveyor’s Compass |
|---|---|---|
| Graduated ring | Moves with needle (graduated 0°–360° CW from S) | Fixed to box (graduated 0°–90° each quadrant) |
| Reading | From opposite end of needle (prism magnifies) | Directly against N end of needle |
| Bearing system | WCB (Whole Circle Bearing) | QB (Quadrantal Bearing) |
| Tripod | Not essential (held in hand) | Essential (mounted on tripod) |
| Accuracy | Lower (±30′ to ±1°) | Higher (±15′) |
5. Bearings — WCB, QB, Fore & Back
WCB ↔ QB Conversion
WCB 0°–90° → QB = N (WCB)° E
WCB 90°–180° → QB = S (180°−WCB)° E
WCB 180°–270° → QB = S (WCB−180°)° W
WCB 270°–360° → QB = N (360°−WCB)° W
Back Bearing from Fore Bearing:
If FB < 180°: BB = FB + 180°
If FB > 180°: BB = FB − 180°
Reduced Bearing (RB) is the acute angle between the survey line and the meridian (same as QB). Magnetic bearing is measured from the magnetic meridian; True bearing from the geographic north; Grid bearing from the grid north used on maps.
6. Magnetic Declination & Local Attraction
Magnetic Declination
True Bearing = Magnetic Bearing + Declination (Eastern, +ve)
True Bearing = Magnetic Bearing − Declination (Western, −ve)
Declination changes with location and time (secular, annual, diurnal variation).
Local attraction is caused by magnetic materials near the compass station — iron ore deposits, steel structures, electric cables, or even steel-toed boots. It deflects the magnetic needle from its true north direction.
Detection: Measure FB and BB of every line. If BB − FB = ±180°, both stations are free from local attraction. If the difference ≠ ±180°, at least one station is affected.
Correction procedure: Find a line whose FB and BB differ by exactly 180° — both end stations are unaffected. Take these as starting points. Calculate what the bearing at the affected station should be based on the unaffected end, and find the error. Apply the same error correction to all bearings observed from that station.
7. Traverse Computation
Latitude, Departure & Closing Error
Latitude = d · cos θ (+ for N, − for S)
Departure = d · sin θ (+ for E, − for W)
Closing error: e = √(ΣL² + ΣD²)
Direction of closing error: tan δ = ΣD / ΣL
Accuracy = 1 in (Perimeter / e)
Bowditch Rule (Compass Rule)
Correction to L of line AB = (eL × length of AB) / Perimeter
Correction to D of line AB = (eD × length of AB) / Perimeter
Use when angular and linear measurements have equal precision.
Transit Rule
Correction to L = (eL × |LAB|) / Σ|L|
Correction to D = (eD × |DAB|) / Σ|D|
Use when angular measurements are more precise than linear measurements.
8. Worked Examples (GATE CE Level)
Example 1 — Local Attraction Correction
The following bearings were observed with a prismatic compass:
| Line | FB (°) | BB (°) |
|---|---|---|
| AB | 45°30′ | 224°00′ |
| BC | 96°00′ | 277°00′ |
| CD | 29°30′ | 210°30′ |
Step 1: Check each line: Line CD: BB − FB = 210°30′ − 29°30′ = 181° ≠ 180°. Line AB: 224°00′ − 45°30′ = 178°30′ ≠ 180°. Line BC: 277° − 96° = 181° ≠ 180°. None differ by exactly 180°.
Step 2: The error at each station is constant. Check end-to-end: for line CD, if C is affected by +1° and D is free, then CD FB should be 29°30′ − 1° = 28°30′. Try systematically — find the station combination where applying one correction makes all lines consistent. (Full solution in theodolite traversing topic.)
Key principle: The difference (BB − FB − 180°) gives the algebraic sum of errors at the two stations of that line. Work from a line where at least one end station has no error.
Example 2 — WCB/QB Conversion (GATE 2019 type)
A line has WCB = 295°30′. Find its QB and back bearing in WCB.
Solution: WCB 295°30′ is in 270°–360° range → QB = N(360° − 295°30′)W = N64°30’W.
Back bearing WCB: FB = 295°30′ > 180°, so BB = 295°30′ − 180° = 115°30′.
Example 3 — Traverse Closing Error
A closed traverse ABCD has the following data: AB: length=200m, bearing=N30°E; BC: 150m, S60°E; CD: 200m, S30°W; DA: 150m, N60°W. Find the closing error.
Solution:
ΣL = 200cos30° − 150cos60° − 200cos30° + 150cos60° = 173.2 − 75 − 173.2 + 75 = 0
ΣD = 200sin30° + 150sin60° − 200sin30° − 150sin60° = 100 + 129.9 − 100 − 129.9 = 0
Closing error = √(0² + 0²) = 0 — perfectly closed traverse (as expected for a rectangle).
Common Mistakes
- Adding instead of subtracting Western declination: True bearing = Magnetic bearing − (West declination). Always check the sign convention before converting.
- Confusing prismatic and surveyor’s compass graduation: Prismatic compass is graduated clockwise from South (0° at S, 90° at W, 180° at N, 270° at E) but the readings represent WCB from North due to how the prism inverts the image.
- Ignoring chain length error sign: If the chain is too long, measured distance is less than true distance — apply positive correction. Opposite for short chain.
- Applying Bowditch rule when transit rule is required: Use Bowditch when both linear and angular accuracy are equal (e.g., chain survey). Use Transit rule when theodolite angles are precise but taping is rough.
- Missing the closing error direction: The direction of closing error is tan⁻¹(ΣD/ΣL). The correction is applied in the opposite direction, not just split equally.
Frequently Asked Questions
What is the difference between WCB and QB in compass surveying?
WCB (Whole Circle Bearing) measures angles from North in a clockwise direction, ranging 0° to 360°. QB (Quadrantal Bearing) measures from North or South towards East or West, ranging 0° to 90° in each quadrant. For example, a WCB of 135° equals QB of S45°E. The prismatic compass uses WCB; the surveyor’s compass uses QB.
What is local attraction in compass surveying and how is it corrected?
Local attraction is the deflection of the magnetic needle at a station due to local magnetic influences like iron ore, steel structures, or electric cables. To detect it, check the fore bearing and back bearing of each line — if they differ by exactly 180°, the station is free of local attraction. Corrections start from unaffected stations and propagate through the traverse.
What are the errors in chaining and how are they classified?
Errors in chaining are classified as: (1) Compensating errors — occur randomly, cancel out partially, proportional to √n; (2) Cumulative errors — always add up in the same direction, proportional to n (e.g., wrong chain length, slope, temperature). Cumulative errors are more serious and must be corrected systematically.
What is magnetic declination and how does it affect bearings?
Magnetic declination is the horizontal angle between the true north and magnetic north at a location. If magnetic north is east of true north, the declination is Eastern and is added to magnetic bearing to get true bearing. If west, it is Western and subtracted. True bearing = Magnetic bearing ± Declination.