Understanding Triangulation and Trilateration

Oct 7, 2024

Lecture Notes on Triangulation and Trilateration

Introduction to Surveying

  • Focus on Module 6: Triangulation and Trilateration
  • Basic measurements in surveying: Angle and Distance
  • Measurement methods: Chain tape, invar tape, EDMI (Electronic Distance Measurement Instrument)
  • Angle measuring devices: Compass (less accurate) and Theodolite (more accurate)
  • Total Station: Combines theodolite and EDMI for complete measurement

Triangulation

Definition

  • Triangulation: A network of triangles used to establish a control network.
  • Coverage of terrain using triangles to create a map.

Importance of Triangulation

  • Cost-effective angle measurement using theodolites compared to distance measurement.
  • Only one accurate base length needs to be measured, while other lengths can be computed from angles.
  • Establishes a network of control points to determine coordinates of points on the ground.

Triangulation Process

  1. Measure one accurate base length (the base measurement).
  2. Measure all internal angles using the theodolite.
  3. Compute coordinates of points using the known base and measured angles.

Length Measurement Techniques

  • Small Base Lengths (e.g., 100m or less): Can measure using tape or chain on flat ground.
  • Long Base Lengths (e.g., 2km+): Use base extension methods in hilly terrain if EDMI is not available.

Control Networks

Types of Control

  1. Horizontal Control: Establishing horizontal coordinates (X, Y).
  2. Vertical Control: Establishing vertical coordinates (Z) or reduced levels (RL).

Applications of Control Networks

  • Making maps using control points.
  • Setting out operations, e.g., for tunnels in construction.

Triangulation Figures

Types of Figures

  1. Single Chain of Triangles: Simple, straightforward mapping (e.g., river boundaries).
  2. Braced Quadrilateral: Allows for multiple computation routes, making it more flexible.
  3. Three Centered Figure: Involves occupying a center point; useful in complex terrains.

Selection Criteria for Figures

  • Need for a figure that allows computations through multiple routes.
  • Ensure the angles are well-conditioned (between 30° and 120°).
  • Cover the entire area for effective mapping.

Framework of Triangulation in India

Grid Iron System

  • A network of control points established throughout the country.
  • Originated from the Great Trigonometrical Survey of India, which started over 200 years ago.

Centered System

  • Used for smaller countries with networks covering the entire area.

Order of Triangulation

  • Primary Order: Highly accurate, used for establishing the size and shape of the Earth.
  • Secondary and Tertiary Orders: Less accurate networks that refine control for specific areas or projects.

Conclusion

  • Reviewed the significance of triangulation, methods, figures, and the framework established in India.
  • Prepared for future lectures on practical applications of surveying methods.