Surveying: chain, compass and levelling

In short

Surveying is the measurement of relative positions on, above or below the earth's surface; chain surveying fixes horizontal distances, compass surveying fixes directions, and levelling fixes heights. These three form the foundation course of every civil engineering degree and are the base on which theodolite, total station and GPS work is built. They are examined heavily in GATE, state PSU and SSC-JE papers, and are used daily by site engineers, revenue/cadastral surveyors, irrigation and PWD departments, L&T, NHAI contractors and railway survey teams. All work in India is in SI units, referred to Survey of India benchmarks and mean sea level.

Explained

Principles, classification and accessories

• Two governing principles: (1) always work from the whole to the part - fix a few control points very accurately, then fill in detail, so errors do not accumulate; (2) a new point is fixed by at least two independent measurements (two distances, a distance and an angle, or two angles).
• Plane surveying ignores the earth's curvature - valid up to about 250 km² (an 18 km arc exceeds its chord by only a few millimetres); geodetic surveying accounts for curvature and is done by the Survey of India.
• Classification by purpose: cadastral (land records, revenue survey numbers), topographical, engineering (route, hydrographic), city, mine, archaeological.
• Chain survey accessories: chain or tape, 10 arrows, ranging rods (2 m or 3 m, banded 20 cm red/white), offset rod, cross staff (open, French, adjustable) or optical square for setting out right angles, pegs, plumb bob, field book (single-line or double-line).
• Chains: metric 20 m chain = 100 links and 30 m chain = 150 links (1 link = 0.2 m), brass tallies at every 5 m. Older units: Gunter's chain 66 ft (used for acres), engineer's chain 100 ft, revenue chain 33 ft/16 links, still met in old Indian land records.
• Tapes: linen/cloth (rough), metallic (reinforced, common), steel (accurate, 20/30 m), invar (nickel-steel, very low thermal expansion, for base lines).

Chain surveying - field procedure

1. Reconnaissance and a rough index sketch; select main stations forming well-conditioned triangles (no angle less than 30° or more than 120°; 60° is ideal) so intersections are sharp.
2. Marking stations with pegs/nails; measure the base line (longest line, on level open ground) with the greatest care - all other work is referred to it.
3. Ranging: placing intermediate rods on the line. Direct ranging when the ends are intervisible; reciprocal (indirect) ranging by two surveyors when a hill intervenes; a line ranger (two right-angled prisms) lets one person range alone.
4. Chaining: follower holds zero at the station, leader carries 10 arrows; one arrow is planted per chain length; distance = (chains × length) + fraction.
5. Offsets to detail: perpendicular (short, by cross staff/optical square or 3-4-5 method) and oblique (two tie measurements to a known feature). Offsets are kept short, usually under 15 m.
6. Check line (proof line) and tie line: a check line verifies the accuracy of a triangle; a tie line joins two points on main lines to pick up detail. Every triangle must have a check line.
7. Obstacles: to *chaining but not ranging* (pond) - similar triangles or a rectangle; to *ranging but not chaining* (hill) - reciprocal ranging; to *both* (building) - offset a parallel line and transfer by right angles.
8. Limits of accuracy: ordinary chaining about 1 in 1,000; good work with a steel tape 1 in 5,000 to 1 in 10,000.

Errors and corrections in chaining

• Mistakes (miscounting chains, misreading) are blunders - they are eliminated, not corrected. Cumulative errors have a constant sign (chain too long/short, slope, sag, wrong alignment, chain not straight); compensating errors are equally likely positive or negative (fractional readings, incorrect holding of the chain).
• Too long a chain gives too short a measured length (and vice versa) - the correction is applied with the rule *true length = (wrong length of chain / true length of chain) × measured length*.
• Tape corrections: standardisation (±), slope (always −), sag (always −), temperature (+ if hotter than standard), pull (+ if pull exceeds standard pull), reduction to mean sea level (−).
• Alignment error is always cumulative and makes the length too long; chaining on sloping ground without correction also gives too long a result.

Compass surveying - bearings and local attraction

• A compass gives magnetic bearings; combined with chained distances it produces a traverse. It cannot measure vertical angles and is unsuitable near iron, rails, power lines or reinforcement.
• Whole circle bearing (WCB): 0° to 360° clockwise from magnetic north - read by the prismatic compass. Quadrantal/reduced bearing (RB): 0° to 90° from N or S, e.g. N 35° E - read by the surveyor's compass.
• Prismatic compass: graduated aluminium ring is fixed to the needle (ring stays still, box rotates), figures are inverted, read at the south end through a prism; sighting is through a vertical hair in the vane. Surveyor's compass: graduations on the box, read at the north end, so E and W are interchanged on the dial; needs a tripod and is read from above.
• Fore and back bearings of a line differ by exactly 180°; if the observed difference is not 180°, either local attraction exists at one or both stations, or there is an observational error.
• Local attraction: deflection of the needle by nearby iron/magnetic rock. Detected by finding a line whose FB and BB differ by exactly 180° - both its stations are free from attraction; corrections are then carried round the traverse station by station. Included angles are unaffected when both bearings at a station are equally deflected.
• Magnetic declination: horizontal angle between true (geographic) and magnetic north. *True bearing = magnetic bearing + declination (E) or − declination (W).* Lines of equal declination are isogonic; zero declination is the agonic line. Declination varies secularly, annually, diurnally and irregularly (magnetic storms), so a declination value must be quoted with its date; Survey of India / IGRF model values are used.
• Dip is the vertical inclination of the needle; the needle is counterweighted to keep the card horizontal.
• Traverse computation: latitude L = l cos θ, departure D = l sin θ. For a closed traverse ΣL = 0 and ΣD = 0 ideally; the closing error is adjusted by Bowditch's (compass) rule when angular and linear precision are comparable, and by the transit rule when angles are more precise than distances.

Levelling - instruments and terms

• Levelling determines differences in elevation between points. Level surface: curved, normal to the plumb line everywhere; horizontal plane: tangential to it at a point; datum: surface of zero elevation - in India, mean sea level (Survey of India's vertical datum; the old Great Trigonometrical Survey levelling used MSL at Karachi, the present Indian datum is MSL derived from tide-gauge observations at nine Indian ports - quote the datum stated on the benchmark sheet).
• Reduced level (RL): height of a point above the datum. Benchmark (BM): point of known RL - GTS benchmarks (Survey of India, stone pillars, highest order), permanent BMs (PWD/railway), arbitrary BMs (assumed RL, e.g. 100.000 m) and temporary BMs (closing a day's work).
• Instruments: dumpy level (telescope rigidly fixed), tilting level (fine tilting screw, bubble centred before each reading), automatic/auto level (gravity compensator keeps the line of sight horizontal - fastest and most used on Indian sites), digital level with a bar-coded invar staff (reads and records electronically). Levelling staff: self-reading E-type, telescopic or folding, 4 m or 5 m, least count 5 mm; target staff for long sights.
• Telescope: objective, diaphragm with cross-hairs and stadia hairs, eyepiece. Parallax (image not in the plane of the cross-hairs) is removed by first focusing the eyepiece on the cross-hairs, then the objective on the staff.
• Temporary adjustments at each setting: setting up and approximate levelling with the tripod, levelling up with the foot screws (telescope parallel to two screws, turn both inward/outward; then over the third screw), and elimination of parallax.
• Permanent adjustment: the two-peg test checks whether the line of collimation is parallel to the bubble axis; the collimation error per unit distance is found from readings at the midpoint and from one end.
• Terms: BS (back sight - first reading after setting up, on a point of known RL), FS (fore sight - last reading before shifting), IS (intermediate sight), change/turning point (carries both an FS and a BS), HI (height of instrument = RL of the collimation line).
• Types of levelling: simple, differential (fly) levelling for long distances, profile/longitudinal sectioning and cross-sectioning for roads, canals and railways, check levelling, reciprocal levelling across a river or valley, precise levelling (micrometer/invar staff).

Reduction, errors and contouring

• Height of instrument (collimation) method: RL = HI − staff reading; fast, convenient with many intermediate sights, but intermediate RLs are not checked by the arithmetic check. Check: ΣBS − ΣFS = last RL − first RL.
• Rise and fall method: compare consecutive readings - a smaller following reading is a rise, a larger one a fall; slower, but every reading is checked. Check: ΣBS − ΣFS = ΣRise − ΣFall = last RL − first RL.
• Errors: instrumental (collimation error, defective staff, bubble out of adjustment), natural (curvature, refraction, wind, sun on the bubble, settlement of the tripod or staff) and personal (parallax, staff not vertical - always gives too large a reading, misreading 0.1 m, wrong booking).
• Balancing back sights and fore sights (equal sight distances) cancels collimation error, curvature and refraction; keeping sights under about 100 m and using a staff bubble/waving the staff removes most of the rest.
• Curvature makes staff readings too large; refraction bends the ray downward and makes them too small, taken as 1/7 of curvature.
• Reciprocal levelling eliminates collimation error, curvature and refraction together when the instrument cannot be placed midway (across a river).
• Contour: line joining points of equal RL; contour interval depends on scale, terrain and purpose (typically 0.2-0.5 m for flat building sites, 1-5 m for hilly topography, 10 m and above for small-scale maps). Contours never cross (except an overhanging cliff), close on themselves, are closely spaced on steep ground, and cross a ridge or valley at right angles (V-shape points upstream in a valley).
• Methods of contouring: direct (tracing the contour on the ground - accurate, slow) and indirect (squares/grid method, cross-sections along a line, radial lines from a station - RLs interpolated). Uses: earthwork volumes, reservoir capacity, route alignment, drainage and catchment studies.
• Indian practice and codes: measurement of works to IS 1200; road project surveys to IRC SP:19; BIS specifications cover metric chains, tapes and levelling staves (IS 1492 and IS 1779 series - verify the current revision); maps and vertical control from the Survey of India under the National Map Policy 2005 and the liberalised Geospatial Data Guidelines, 2021; land/cadastral survey under state Land Revenue Acts and the SVAMITVA programme.

Key points

• Work from whole to part - the first principle of surveying; it controls error accumulation.
• Well-conditioned triangle - all angles between 30° and 120°, so station positions are sharply fixed.
• Check line - an independent measured line used to verify a chain triangle on the plot.
• Cumulative vs compensating error - constant sign (slope, sag, wrong chain length) vs random sign.
• Too long a chain - gives measured length too small; correct by multiplying by (L′/L).
• Sag and slope corrections - always subtractive; alignment error always makes length too long.
• WCB - 0°-360° clockwise from north (prismatic compass); RB - 0°-90° from N or S (surveyor's compass).
• FB − BB = 180° - if not, suspect local attraction or an observation error.
• Local attraction - needle deflected by nearby iron; included angles stay correct if both bearings are equally deflected.
• Declination - angle between true and magnetic north; changes with place and time, so it is always dated.
• Bowditch rule - distributes closing error in proportion to line lengths; transit rule in proportion to latitudes/departures.
• Reduced level - height above datum (mean sea level in India, via Survey of India benchmarks).
• HI method - fast, no check on intermediate sights; rise and fall - every reading checked.
• Arithmetic check - ΣBS − ΣFS = ΣRise − ΣFall = last RL − first RL.
• Combined curvature and refraction - 0.0673 d² metres (d in km), subtracted from the staff reading.
• Balancing sights - equal BS and FS distances cancel collimation, curvature and refraction.
• Reciprocal levelling - the mean of two reciprocal observations gives the true difference in level.
• Contour interval - constant on one map; closer contours mean steeper ground.

Formulas and examples

1. Incorrect chain. A 20 m chain was found to be 20.08 m long during a survey. The measured length of a line was 1,500 m and the measured area of a plot 2.5 hectares.

• Correct length = (20.08/20) × 1,500 = 1.004 × 1,500 = 1,506 m.
• Correct area = (1.004)² × 2.5 = 1.008016 × 2.5 = 2.520 ha.
• The chain being too long, the measured values were too small, so both corrections are additive.

2. Local attraction in a compass traverse.

• AB differs by exactly 180°, so A and B are free from local attraction.
• B is correct, so the BB of BC should be 139°30′ + 180° = 319°30′; observed 318°00′ → correction at C = +1°30′.
• Corrected FB of CD = 215°15′ + 1°30′ = 216°45′; its BB should be 36°45′, which is what D observed → correction at D = 0.
• Included angle ABC = BB of AB − FB of BC = 239°00′ − 139°30′ = 99°30′.
• If the declination is 1°20′ E, the true bearing of AB = 59°00′ + 1°20′ = 60°20′.

3. Levelling - both reduction methods. BS 1.455 on a BM of RL 100.000; IS 2.350; IS 0.980; FS 2.885 (change point); BS 1.250; IS 1.775; FS 2.045.

• ΣBS = 2.705, ΣFS = 4.930 → ΣBS − ΣFS = −2.225.
• ΣRise = 1.370, ΣFall = 3.595 → ΣRise − ΣFall = −2.225.
• Last RL − first RL = 97.775 − 100.000 = −2.225 m - all three agree, so the reduction is arithmetically correct.

4. Curvature, refraction and reciprocal levelling.

• Sight length 2.5 km: combined correction = 0.0673 × 2.5² = 0.0673 × 6.25 = 0.421 m, to be *subtracted* from the staff reading.
• Visible horizon from a 30 m tower: d = √(30/0.0673) = √445.8 = 21.1 km.
• Reciprocal levelling across a river, A and B 800 m apart. Level near A: staff A = 1.485, staff B = 2.360 → difference 0.875 m (B lower). Level near B: staff A = 1.925, staff B = 2.695 → difference 0.770 m.
  • True difference = (0.875 + 0.770)/2 = 0.8225 m, B lower than A.
  • Combined error = (0.875 − 0.770)/2 = 0.0525 m; curvature + refraction over 0.8 km = 0.0673 × 0.64 = 0.0431 m, so the collimation error ≈ 0.0094 m in 800 m (about 0.0012 m per 100 m).

5. Area from offsets. Offsets of 2.5, 3.8, 4.6, 5.2, 4.9, 4.0, 3.1 m taken at 10 m intervals along a chain line.

• Simpson: A = (10/3)[(2.5 + 3.1) + 4(3.8 + 5.2 + 4.0) + 2(4.6 + 4.9)] = (10/3)[5.6 + 52.0 + 19.0] = (10/3)(76.6) = 255.33 m².
• Trapezoidal: A = 10[(2.5 + 3.1)/2 + 3.8 + 4.6 + 5.2 + 4.9 + 4.0] = 10[2.8 + 22.5] = 253.00 m².
• Simpson's rule assumes a parabolic boundary and is the more accurate for a curved edge; it needs an even number of intervals.

Where it is used

• Cadastral and revenue survey: village maps, survey numbers, boundary demarcation and partition cases by state revenue departments and licensed surveyors; chain/tape measurements are still the legal record in many districts.
• Roads, canals and railways: longitudinal sections and cross-sections for formation levels and earthwork quantities under IRC SP:19 and railway engineering codes; NHAI and PWD project reports.
• Building construction: transferring RLs from a site benchmark to plinth, floor and lintel levels, checking formwork and sill levels, setting out column grids by 3-4-5 offsets - the core daily work of a junior site engineer at L&T, Shapoorji Pallonji, Tata Projects.
• Irrigation and water supply: contour mapping for canal alignment, reservoir capacity from contour areas, gravity main profiles, flood-level surveys by state WRDs and CWC.
• Mining, forestry and utilities: surface traverses with compass and chain in thickly wooded or magnetically clear terrain where satellite signals are blocked.
• Job roles and exams: site/survey engineer, chainman and surveyor grades in SSC-JE, RRB-JE, state PSU and PWD recruitment; the practical surveying viva is a standard part of the civil engineering degree.

Interview questions

• Q: State the two fundamental principles of surveying. A: Work from the whole to the part, and fix each new point by at least two independent measurements.
• Q: A 30 m chain is 30.06 m long - is the measured distance too long or too short? A: Too short; the correction is additive, true length = (30.06/30) × measured length.
• Q: What is a well-conditioned triangle and why does it matter? A: One with no angle below 30° or above 120°; its sides intersect at a sharp angle, so a small measurement error shifts the station very little.
• Q: Difference between a prismatic compass and a surveyor's compass? A: The prismatic reads whole circle bearings on an inverted graduated ring attached to the needle, read through a prism at the south end; the surveyor's compass reads quadrantal bearings from the box top at the north end, with E and W interchanged.
• Q: How do you detect and correct local attraction? A: Find a line whose fore and back bearings differ by exactly 180° - both its stations are unaffected; then work round the traverse applying station corrections to the remaining bearings.
• Q: Does local attraction affect the included angles of a traverse? A: No, provided both bearings at a station are deflected equally, because the deflection cancels when the difference is taken.
• Q: Why is the rise and fall method preferred for precise work? A: It provides a complete arithmetic check on every reading including intermediate sights, whereas the HI method checks only the back sights and fore sights.
• Q: Why should back sight and fore sight distances be equal? A: Equal distances cancel collimation error and the effects of curvature and refraction.
• Q: What is the combined curvature and refraction correction and its sign? A: 0.0673 d² metres with d in kilometres, subtracted from the observed staff reading.
• Q: What is a change point? A: A staff station on which both a fore sight and the following back sight are taken, used to transfer the level when the instrument is shifted.
• Q: How do you remove parallax? A: Focus the eyepiece on the cross-hairs against a bright background first, then focus the objective on the staff.
• Q: If a staff is not held vertical, is the reading too large or too small? A: Too large - the true vertical reading is the observed reading times cos of the tilt; a staff bubble or waving the staff and taking the minimum reading corrects it.

Common mistakes

• Inverting the (L′/L) ratio - remember a long chain gives short measurements, so the correction is additive.
• Forgetting that area is corrected by the square of the ratio and volume by the cube.
• Adding a fore sight instead of subtracting it in the HI method, or applying the arithmetic check only to back sights.
• Converting WCB to RB carelessly - in the second quadrant RB = 180° − WCB (S…E) and in the fourth RB = 360° − WCB (N…W).
• Applying a local attraction correction at a station already proved free of attraction, instead of starting from that station.
• Using Simpson's rule with an even number of offsets (odd number of intervals) instead of the trapezoidal rule for the last strip.
• Taking a reading without centring the bubble or removing parallax, and failing to record a temporary benchmark before closing a day's work.

Related topics

Theodolite, total station and GPS · Curves and setting out · Photogrammetry and drone surveys · GIS and remote sensing · Earthwork volumes and mass haul · Building construction and site layout