instruments & analysis of measurement of distances

Principle of chain surveying

Chain surveying is the simplest method of surveying in which only linear measurements are made in the field. The area is divided into a network of triangles whose sides are measured; details are located by offsets from the survey lines.

• The principle is triangulation in its simplest form — a triangle is the only figure that can be plotted from its sides alone.
• Triangles should be well-conditioned — no angle less than about 30° or greater than about 120° (ideally equilateral) — so that plotting errors are small.

Suitability: small, fairly level, open areas with simple details. Unsuitable for large areas, crowded or wooded areas, or undulating ground.

Instruments

Chains

Chains are robust and easily repaired but change length (stretching, bending of links, wear) and are heavy.

Tapes

Accessories

• Arrows (chaining pins) — mark ends of each chain length.
• Ranging rods — 2 m or 3 m long, painted in alternate red and white (or black and white) bands of 20 cm, with a pointed shoe — mark stations and range lines.
• Offset rods — with a hook to pull the chain through obstructions and notches for setting out right angles.
• Pegs — mark survey stations.
• Plumb bob — transfer points and chaining on slopes.
• Cross staff (open, French, adjustable), optical square and prism square — to set out perpendicular offsets (optical and prism squares use reflection to give 90°).
• Line ranger — to locate intermediate points on a line between two stations.
• Clinometer / Abney level — to measure slopes.

Survey stations and lines

• Main stations — at the ends of main survey lines; subsidiary (tie) stations — on main lines, to run tie lines.
• Base line — the longest line running through the middle of the area, on which the framework is built; measured most accurately.
• Main survey lines — sides of the main triangles.
• Check (proof) lines — run from a station to a point on the opposite side (or between points on two sides) to check the accuracy of the framework.
• Tie lines — join tie stations to locate interior details and provide checks.

Selection of stations: mutually visible adjacent stations; well-conditioned triangles; minimum number of lines; lines through level ground and close to details (short offsets); avoid obstacles to chaining and ranging; lines not crossing busy roads frequently.

Ranging

Ranging is the process of establishing intermediate points on a straight line between two end points.

• Direct ranging — when the ends are intervisible: intermediate ranging rods are aligned by eye (or line ranger).
• Indirect (reciprocal) ranging — when the ends are not intervisible (e.g. due to a rise in ground): two persons with rods on intermediate points alternately align each other with the far end until both are in line.

Chaining on sloping ground

1. Direct method (stepping): the tape is held horizontal in short steps and the end is transferred to the ground by a plumb bob.
2. Indirect methods: measure the slope distance $L$ and:
   • Angle measured: horizontal distance $=L\cos \theta$; correction $=L(1-\cos \theta )$.
   • Difference in level $h$ measured: horizontal distance $=\sqrt{L^2-h^2}$; slope correction $\approx \frac{h^2}{2L}$.
   • Hypotenusal allowance: at each chain length on a slope $\theta$, the arrow is placed ahead by $100(\sec \theta -1)$ links per chain, so that the horizontal distance recorded is directly correct.

Errors in chaining

Sources: incorrect length of chain or tape (standardisation), bad ranging (always makes measured length too long), bad straightening (too long), non-horizontality on slopes (too long), sag (too long), temperature variations (either sign), variation in pull (either sign), displacement of arrows, and personal mistakes (miscounting chains, wrong reading of tallies, wrong booking).

Errors such as bad ranging, bad straightening, sag and slope are positive (cumulative) errors — the measured length is too long.

Tape corrections

Erroneous length of chain

If the true (designated) length of a chain is $L$ and its actual length is $L^{\prime }$:

Offsets

Offsets are lateral measurements from survey lines to locate details.

• Perpendicular offsets — at right angles to the chain line (set by eye, cross staff, optical/prism square).
• Oblique offsets — at any angle; two oblique offsets from two points on the chain line fix a detail by intersection.
• Long offsets need accurate right angles; short offsets can be set by eye. The limiting length of offsets depends on the scale and the accuracy of setting the right angle.

Obstacles in chaining

Field book

The field book records measurements. In single-line booking a single central line represents the chain line; in double-line booking the chainages are written between two parallel lines. Records include station names, chainages, offsets with sketches of details, and remarks. Entries start from the bottom of the page and go upwards.

Worked examples

Frequently tested points

• Chain surveying: only linear measurements; well-conditioned triangles (30°–120°); small open level areas.
• Metric chains 20 m (100 links) and 30 m (150 links); Gunter's chain 66 ft; engineer's chain 100 ft; revenue chain 33 ft.
• Invar tape — very low thermal expansion — base line measurement.
• Ranging rods 2–3 m with 20 cm bands; optical/prism squares for right angles.
• Base line, check lines (for checking), tie lines (details and checks).
• Reciprocal ranging when ends are not intervisible.
• Hypotenusal allowance $100(\sec \theta -1)$ links per chain.
• Bad ranging, bad straightening, sag, slope → measured length too long.
• Corrections: standardisation ±, temperature ±, pull ±, sag −, slope −, MSL −; normal tension balances pull and sag.
• True length $(L^{\prime }/L)\times$ measured; area $(L^{\prime }/L{)}^2$; volume $(L^{\prime }/L{)}^3$.

Electronic distance measurement (EDM)

EDM measures distances by electromagnetic waves instead of tapes. It gives high accuracy over long distances quickly, across rough terrain, rivers and traffic.

Principle — phase comparison

A carrier wave (microwave, infrared or light) is modulated with a measuring wave of known wavelength $\lambda$. The wave travels from the instrument to a reflector and back (double path). The instrument measures the phase difference between transmitted and received waves, which gives the fractional part of a wavelength ($\Delta \lambda$); the integer number of wavelengths ($n$) is resolved by transmitting several frequencies.

Pulse (time-of-flight) method — the time taken by a short laser pulse to travel to the target and back gives $D=\frac{vt}{2}$ — used in reflectorless EDM and laser scanners.

Types of EDM

Reflectors

• Corner cube prisms (retro-reflectors) return the beam parallel to its incoming direction — single or multiple prisms for longer ranges; mounted on poles or tribrachs.
• Reflective sheets (targets) for short ranges; reflectorless measurement to walls, rock faces and inaccessible points.
• Each prism has a prism constant (offset) that must be set in the instrument.

Errors and corrections

Accuracy specification: stated as $\pm (a\text{mm}+b\text{ppm})$ — a constant part plus a part proportional to distance (e.g. ±(2 mm + 2 ppm)).

Reductions

EDM measures slope distance $S$. With the zenith angle $z$ (or vertical angle $\alpha$):

Further reductions: to mean sea level (or ellipsoid) and to the map projection grid (scale factor) for control surveys.

Total station

A total station is an integrated electronic surveying instrument combining:

1. An electronic (digital) theodolite — measures horizontal and vertical angles electronically.
2. An EDM — measures slope distances.
3. A microprocessor — computes horizontal distances, height differences, coordinates, etc.
4. Data storage — internal memory, cards or data collectors, with USB/Bluetooth transfer.
5. Display and keyboard (often both faces) with onboard software programs.
6. Laser plummet, electronic level (dual-axis tilt compensator), guide lights.

Functions and onboard programs

Setting up and orientation

1. Set up the tripod over the station; centre with the laser/optical plummet.
2. Level using the circular bubble and electronic level (tilt compensator corrects residual tilt).
3. Enter station data — station coordinates, instrument height, prism height, prism constant, atmospheric correction (temperature and pressure).
4. Orientation (backsight) — sight a known backsight point (or enter a known azimuth) to set the horizontal circle to the correct bearing.
5. Measure detail/control points or stake out.

Advanced total stations and related technology

• Robotic (motorised) total stations — automatic target recognition and tracking; one-person operation, machine control.
• Reflectorless total stations — measure to surfaces without prisms.
• Imaging total stations — integrated cameras for documentation and photogrammetric measurement.
• Terrestrial laser scanners — capture dense point clouds (millions of points) for 3D modelling, as-built surveys, heritage documentation.
• Integration with GNSS ("smart stations") and CAD/GIS/BIM software.

Advantages and limitations

Applications

Topographic and detail surveys; control traverses; construction layout (buildings, bridges, highways, tunnels); cadastral boundary surveys; deformation monitoring of dams, bridges, slopes and buildings; as-built surveys; volume computations of stockpiles and excavations; mining; accident reconstruction.