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Surveying

Future Geodetic Engineer! Surveying - the art and science of precise measurements. Field work, instruments, and computation techniques!

1. Types of Surveys ๐Ÿ“

Survey Type Purpose Precision Required
Cadastral Property boundaries, land titles High (legal purposes)
Topographic Elevation, terrain features Medium-High
Construction Setting out buildings, roads Very High (mm level)
Hydrographic Water body depths, shorelines High (navigation safety)
Geodetic Large area control networks Highest (sub-mm)

2. Leveling ๐Ÿ“Š

Determining elevation differences between points.

Basic Leveling Equation

Elevation B = Elevation A + BS - FS

HI = Elevation A + BS

BS (Backsight)

Reading on known elevation point. Always ADDED to elevation.

FS (Foresight)

Reading on unknown point. Always SUBTRACTED from HI.

HI (Height of Instrument)

Elevation of line of sight = Known Elev + BS

Leveling Errors

  • Curvature: c = 0.0785Dยฒ (meters, D in km)
  • Refraction: r = 0.011Dยฒ (meters, D in km)
  • Combined (c-r): 0.0675Dยฒ โ‰ˆ 0.07Dยฒ
  • At 1 km: c-r โ‰ˆ 0.07m = 7cm error!

3. Traverse Surveying ๐Ÿ”„

Angular Closure

Interior angles sum = (n-2) ร— 180ยฐ

Exterior angles sum = (n+2) ร— 180ยฐ

Error distribution: Equally distribute angular error to all angles

Linear Closure

Departure = Distance ร— sin(Bearing)

Latitude = Distance ร— cos(Bearing)

ฮฃDep = 0 and ฮฃLat = 0 for closed traverse

Precision = Linear error / Total distance (e.g., 1:5000)

Adjustment Methods

  • Compass Rule: Correction โˆ Distance (for equal angular & linear precision)
  • Transit Rule: Correction โˆ Lat/Dep (for higher angular precision)
  • Least Squares: Most rigorous, minimizes sum of squares

4. Area Computation ๐Ÿ“

Double Meridian Distance (DMD)

Area = ยฝ ฮฃ(DMD ร— Lat)

  • First DMD = First Departure
  • Next DMD = Prev DMD + Prev Dep + Curr Dep
  • Last DMD = Last Departure (check!)

Coordinate Method

2A = ฮฃ(Xn(Yn+1 - Yn-1))

Or: 2A = ฮฃ(Yn(Xn-1 - Xn+1))

Faster for coordinate-based surveys

5. Surveying Instruments ๐Ÿ”ญ

Total Station

Electronic theodolite + EDM combined. Measures angles and distances simultaneously.

Accuracy: 1-5mm + 1-3ppm for distance; 1" for angles

GNSS Receiver

Satellite-based positioning. RTK mode: cm-level accuracy in real-time.

Static survey: mm accuracy with post-processing

Level

Automatic/digital level for height determination. Self-leveling compensator.

Precision levels: ยฑ0.3mm per km double-run

6. Practice Questions ๐Ÿ“š

Common Board Exam Questions

Q1: In a 5-sided closed traverse, what should be the sum of interior angles?

A: (n-2) ร— 180ยฐ = (5-2) ร— 180ยฐ = 3 ร— 180ยฐ = 540ยฐ

Q2: The BS reading is 2.543m and FS is 1.876m. If BM elevation is 100.000m, what is the elevation of the new point?

A: HI = 100.000 + 2.543 = 102.543m. New Elev = 102.543 - 1.876 = 100.667m

Q3: What is the combined curvature and refraction error at 2km?

A: c-r = 0.0675 ร— Dยฒ = 0.0675 ร— 4 = 0.27m

๐Ÿ”ฅ GE Challenge ๐Ÿ”ฅ

Master field surveying! Leveling, traversing, area computation, instruments - precise measurements in any terrain!

Measure twice, mark once - the surveyor's creed!