Total Station Basics: Setup, Measurement and Coordinate Calculation
A total station combines an electronic theodolite, an electronic distance meter (EDM) and a small computer in one instrument. It measures horizontal angles, vertical angles and slope distances, and computes coordinates and levels of points in the field. It has replaced the theodolite and tape on most Indian construction sites for layout, topographic surveys and road alignment work. This article explains how it works, the setup sequence, and the calculations it performs internally, with a worked example you can verify with a calculator.
What a Total Station Measures
| Quantity | Symbol | How it is measured |
|---|---|---|
| Horizontal angle | HA | Electronic encoder on the horizontal circle |
| Vertical (zenith) angle | Z | Encoder on the vertical circle; 0° straight up, 90° horizontal |
| Slope distance | SD | EDM sends infrared or laser signal to a prism and measures phase shift or time |
| Instrument height | hi | Measured with tape from station mark to instrument axis mark |
| Target (prism) height | ht | Read from the graduated prism pole |
From these, the instrument computes horizontal distance, vertical difference, and the easting, northing and elevation of the target. Modern instruments from manufacturers such as Leica, Sokkia, Topcon and Trimble also offer reflectorless mode, in which the EDM measures to a wall or surface directly without a prism, over a shorter range.
Corrections set in the instrument
- Prism constant: an offset in mm that depends on the prism type. Using the wrong constant introduces a fixed error in every distance.
- Atmospheric correction (ppm): the speed of light in air varies with temperature and pressure. Enter the site temperature and pressure so the instrument corrects distances in parts per million.
- Scale factor: used when working in a projected grid coordinate system.
Field Setup Sequence
- Set the tripod over the station mark with the head roughly level.
- Mount the instrument and centre it over the mark using the optical or laser plummet, adjusting the tripod legs.
- Level the instrument with the circular bubble using the legs, then the electronic or plate bubble using the foot screws. Recheck centring and repeat until both are correct.
- Measure the instrument height.
- Create or open a job in the instrument, and enter station coordinates, instrument height, prism constant and atmospheric data.
- Orient the instrument by sighting a back sight point of known coordinates, or by setting a known bearing.
- Measure to each target: sight the prism centre, enter the prism height and record.
Calculations Behind the Display
Horizontal distance HD = SD x sin Z Vertical difference VD = SD x cos Z ΔE = HD x sin(bearing) ΔN = HD x cos(bearing) E(target) = E(station) + ΔE N(target) = N(station) + ΔN RL(target) = RL(station) + hi + VD - ht
Worked example
Station A has coordinates E = 1000.000 m, N = 2000.000 m and RL = 50.000 m. Instrument height is 1.500 m. After orientation, a prism at point P with pole height 1.800 m gives HA (bearing) = 60°00'00", Z = 85°30'00" and SD = 120.000 m.
sin 85°30' = 0.996917 cos 85°30' = 0.078459 sin 60° = 0.866025 cos 60° = 0.500000 HD = 120.000 x 0.996917 = 119.630 m VD = 120.000 x 0.078459 = 9.415 m ΔE = 119.630 x 0.866025 = 103.603 m ΔN = 119.630 x 0.500000 = 59.815 m E(P) = 1000.000 + 103.603 = 1103.603 m N(P) = 2000.000 + 59.815 = 2059.815 m RL(P) = 50.000 + 1.500 + 9.415 - 1.800 = 59.115 m
Because Z is less than 90°, the line of sight points upward and VD is positive, so P is higher than the instrument axis. If Z were greater than 90°, cos Z would be negative and P would be lower.
Area of a Plot from Coordinates
Once corner coordinates are known, the plot area follows from the coordinate (shoelace) formula. Total stations have a built-in area program that uses the same method.
Area = ½ | Σ (Ei x Ni+1 - Ei+1 x Ni) |
| Corner | E (m) | N (m) | Ei x Ni+1 - Ei+1 x Ni |
|---|---|---|---|
| 1 | 0 | 0 | 0 x 0 - 40 x 0 = 0 |
| 2 | 40 | 0 | 40 x 30 - 45 x 0 = 1200 |
| 3 | 45 | 30 | 45 x 35 - 5 x 30 = 1425 |
| 4 | 5 | 35 | 5 x 0 - 0 x 35 = 0 |
| Sum | 2625 |
Area = 2625 / 2 = 1312.5 m²
Typical Site Applications
- Setting out column centres and building grid lines from drawing coordinates using the stake-out program.
- Topographic survey of a plot to prepare contour plans.
- Road and canal alignment, cross sections and chainage marking.
- Monitoring settlement or movement of structures by repeated measurement of fixed targets.
Common Mistakes
- Entering the wrong prism height after the pole was extended or shortened.
- Using the default prism constant with a different make of prism.
- Skipping the back sight check, so a wrong orientation spoils the whole day's work.
- Measuring through vegetation or with the prism pole not vertical.
Summary
A total station measures horizontal angle, zenith angle and slope distance, then computes horizontal distance, height difference and coordinates using simple trigonometry. Careful centring, levelling, correct prism constant and a checked orientation are essential. With coordinates in hand, layout, levels and areas follow directly.