---
title: "Use and working principle of subtense bar"
subject: "Surveying II"
chapter: 2
key: "semester_4/surveying_ii:subtense-bar-use-working-principle"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/subtense-bar-use-working-principle
site: BCT Engineering
---

# Use and working principle of subtense bar

Surveying II · Chapter 2: Tacheometry

- Asked in: 2065 Kartik (old course), 6 marks
- Video: [Subtense Bar Method | Tachymetry Methods of Horizontal Distance Measurement | Surveying](https://www.youtube.com/watch?v=gbuOsFrpkI4) — Jonas' Class Notes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/subtense-bar-use-working-principle
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2

## Question

What is the use of subtense bar? Write the working principles of subtense bar.

## Short answer

A subtense bar is used for indirect horizontal distance measurement over difficult terrain and for checking tapes. It is a 2 m horizontal bar set perpendicular to the line of sight; the small horizontal angle β subtended at the theodolite gives horizontal distance D = (l/2) cot(β/2).

## Answer

#### Use of the subtense bar
A subtense bar is used for the **indirect measurement of horizontal distances** where chaining is difficult or slow: across rivers and valleys, and over marshy, steep, densely vegetated or rough ground, or in traffic. It is also used for setting out, for measuring base lines or traverse sides, and for checking tape measurements. With a 1" theodolite it gives results of about 1 in 3000 to 1 in 10,000 on short lines.

#### Working principle
A **subtense bar** is a horizontal bar of fixed length $l$ (usually 2 m) with targets at its ends. It is mounted on a tripod and set perpendicular to the line of sight with the help of a small sighting telescope on the bar. The small horizontal angle $\beta$ subtended by the targets at the theodolite is measured (to seconds, by repetition), and the distance is computed from it.

```text
 Theodolite                       Subtense bar
     O  <------------ D ---------->  A |
       \  beta                       | l (2 m)
         \_____________________________ B
```
#### Horizontal distance
From the isosceles triangle $OAB$:

$$
\frac{l}{2}=D\tan\frac{\beta}{2}\ \Rightarrow\ D=\frac{l}{2}\cot\frac{\beta}{2}\ \approx\ \frac{l}{\beta}\ (\beta\ \text{in radians})
$$

Because the bar is horizontal and $\beta$ is measured in the horizontal plane, $D$ is the horizontal distance directly, even when the line of sight is inclined; no slope correction is needed. If the difference in level is wanted, the vertical angle $\alpha$ to the bar is also read, and $V=D\tan\alpha$.

## Check yourself

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

1. What is a subtense bar used for?
   A. Indirect measurement of horizontal distance across difficult ground
   B. Measuring levels
   C. Measuring magnetic bearing
   D. Measuring areas
   Answer: A. It avoids chaining over rivers, steep or marshy ground. (Key point: Use)

2. How is the bar set up?
   A. Vertical, along the line
   B. Horizontal, perpendicular to the line of sight, on a tripod
   C. Parallel to the line of sight
   D. Held by hand
   Answer: B. A small telescope on the bar is sighted to the instrument to set it normal. (Key point: Bar setup)

3. What is the horizontal-line-of-sight distance formula?
   A. D = l tan β
   B. D = 2l cot β
   C. D = (l/2)cot(β/2), about l/β in radians
   D. D = l/(2 cosβ)
   Answer: C. l/2 = D tan(β/2). (Key point: Distance formula)

4. If the line is inclined at α, the horizontal distance is?
   A. (l/2)cot(β/2) sinα
   B. (l/2)cot(β/2)/cosα
   C. (l/2)cot(β/2)
   D. (l/2)cot(β/2) cosα
   Answer: D. The bar formula gives the inclined distance, which is resolved by cosα. (Key point: Inclined sight)

## Related in Surveying II

- [Subtense bar principle and formula](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asubtense-bar-principle-formula) — Surveying II, chapter 2, asked 2×
- [Subtense bar principle, fixed hair derivation](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asubtense-bar-fixed-hair-derivation) — Surveying II, chapter 2
- [Subtense bar principle, increasing precision](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asubtense-bar-principle-precision) — Surveying II, chapter 2
- [Subtense bar and tacheometer gradient A-B](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asubtense-bar-3m-level-difference-gradient) — Surveying II, chapter 2
- [Subtense bar, level difference and gradient A-B](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asubtense-bar-tacheometer-level-diff-gradient) — Surveying II, chapter 2
- [Subtense bar and tacheometer, A-B distance and level](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Asubtense-bar-2m-theodolite-c-ab) — Surveying II, chapter 2

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