---
title: "Classification of triangulation system"
subject: "Surveying I"
chapter: 8
key: "semester_3/surveying_i:classification-triangulation-system"
source: https://www.bctengineer.com/q/semester_3/surveying_i/classification-triangulation-system
site: BCT Engineering
---

# Classification of triangulation system

Surveying I · Chapter 8: Triangulation and Trilateration

- Asked in: 2075 Chaitra, 4 marks; 2068 Chaitra, 6 marks (asked 2 times)
- Video: [Classification of triangulation || Types of triangulation || Triangulation Survey || advance survey](https://www.youtube.com/watch?v=UpuSu41MhO0) — Mukesh Kumar
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/classification-triangulation-system
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-8

## Question

Explain the classification of triangulation system.

## Short answer

Triangulation systems are classified by accuracy into first, second, and third order. First order (primary) has sides 30–150 km, average error <1″, for national geodetic frameworks. Second order (secondary) has sides 8–30 km, error 3″. Third order (tertiary) has sides 1.5–10 km, error 6″ for engineering surveys.

## Answer

The triangulation system is classified into **first order (primary)**, **second order (secondary)** and **third order (tertiary)** triangulation, according to the accuracy of the work. The classification depends on the length of the base line and sides, the closure of the triangles and the probable error of the computed lengths.

#### 1. First order (primary) triangulation
- It forms the main framework of a country and is used for geodetic work, for determining the shape and size of the earth, and for control of the whole area.
- Highest accuracy: long sides (30 to 150 km), base line 5 to 15 km, average triangular error less than 1".
- Stations are on hilltops or towers; signals and precise theodolites are used.

#### 2. Second order (secondary) triangulation
- Based on the primary stations as control; it divides the primary network into smaller parts.
- Sides 8 to 30 km, base line 1.5 to 5 km, average triangular error 3". Used for regional surveys and for fixing points for topographic mapping.

#### 3. Third order (tertiary) triangulation
- Based on the secondary net; it gives closely spaced stations for engineering surveys (towns, roads, dams, bridges, tunnels).
- Sides 1.5 to 10 km, base line 0.5 to 3 km, average triangular error 6". Less precise instruments are acceptable.

| Item | First order (primary) | Second order (secondary) | Third order (tertiary) |
|---|---|---|---|
| Length of base line | 5 to 15 km | 1.5 - 5 km | 0.5 - 3 km |
| Length of sides of triangles | 30 - 150 km | 8 - 30 km | 1.5 - 10 km |
| Average triangular error (closure) | less than 1" | 3" | 6" |
| Maximum triangular error | 3" | 8" | 12" |
| Probable error of base line | 1 in 1,000,000 | 1 in 500,000 | 1 in 250,000 |
| Discrepancy between two measures of the base | 5 mm $\sqrt{K}$ | 10 mm $\sqrt{K}$ | 20 mm $\sqrt{K}$ |
| Probable error of computed distances | 1 in 60,000 to 1 in 250,000 | 1 in 20,000 to 1 in 50,000 | 1 in 5,000 to 1 in 20,000 |

($K$ is the distance in km. The figures are the common textbook values; Survey Department practice may differ slightly.)

#### Classification by figure
The triangulation system can also be classified by the type of figure used: (i) a chain of single triangles, (ii) a chain of braced quadrilaterals, and (iii) a chain of polygons with a central station. The best-conditioned figures have all angles between 30 and 120 degrees.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. On what basis is triangulation classified into first, second and third order?
   A. The type of theodolite colour and make
   B. The accuracy of the work (base line and side lengths, triangle closure, probable error)
   C. The number of stations in the net
   D. The season in which the survey is done
   Answer: B. The order depends on the accuracy achieved, which is judged by base line and side lengths, closure of triangles and the probable error of computed lengths. (Key point: Basis of classification)

2. What is first order (primary) triangulation mainly used for?
   A. Detailed town and dam surveys
   B. Plotting small plane-table sketches
   C. Geodetic work, shape and size of the earth, and control of the whole area
   D. Fixing boundaries of single plots
   Answer: C. Primary triangulation forms the main framework of a country with highest accuracy and is used for geodetic work. (Key point: Use of first order)

3. Which set of side lengths correctly matches first, second and third order respectively?
   A. 1.5-10 km, 8-30 km, 30-150 km
   B. 8-30 km, 30-150 km, 1.5-10 km
   C. 30-150 km, 1.5-10 km, 8-30 km
   D. 30-150 km, 8-30 km, 1.5-10 km
   Answer: D. Accuracy and side length decrease with order: 30-150 km, 8-30 km, then 1.5-10 km. (Key point: Side lengths by order)

4. What are the average triangular errors (closure) for first, second and third order?
   A. less than 1", 3", 6"
   B. 3", 6", 12"
   C. 6", 3", less than 1"
   D. less than 1", 8", 12"
   Answer: A. The permissible average closure grows with decreasing order: below 1", 3" and 6". (Key point: Average triangular error)

## Related in Surveying I

- [Types of triangles; first-order specification](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atriangle-types-first-order-spec) — Surveying I, chapter 8

## Related in other subjects

- [Q-system of rock mass classification](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Aq-system-classification) — Engineering Geology II, chapter 6, asked 7×
- [MIT classification system](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amit-classification-grain-size) — Soil Mechanics, chapter 3, asked 2×
- [Describe one classification system, limits](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adescribe-classification-system-limits) — Soil Mechanics, chapter 3
- [Channel in communication system and its classification](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Achannel-classification) — Communication Systems, chapter 1