---
title: "Methods of tacheometry, tangential horizontal distance"
subject: "Surveying II"
chapter: 2
key: "semester_4/surveying_ii:tacheometry-methods-tangential-horizontal-distance"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/tacheometry-methods-tangential-horizontal-distance
site: BCT Engineering
---

# Methods of tacheometry, tangential horizontal distance

Surveying II · Chapter 2: Tacheometry

- Asked in: 2075 Bhadra, 2+4 marks
- Video: [Methods of Tacheometry - Civiconcepts](https://www.youtube.com/watch?v=l0ak6X3XxRI) — Civiconcepts - Bhushan Mahajan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/tacheometry-methods-tangential-horizontal-distance
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2

## Question

Mention different methods of tachometric surveying. Discuss measurement of horizontal distance by tangential method.

## Short answer

Methods include stadia (fixed and movable hair), tangential, and subtense bar. In the tangential method, horizontal distance D is computed as D = s / (tan α2 – tan α1) where s is vane spacing and α1, α2 are measured vertical angles.

## Answer

#### Methods of tacheometric surveying

1. **Stadia method**
   - *Fixed hair method:* stadia hairs are at a fixed interval; the staff intercept changes with distance. Staff may be held vertical or normal to the line of sight. This is the most common method.
   - *Movable hair method:* the interval between the hairs is varied to read a fixed staff intercept (rarely used).
2. **Non-stadia methods**
   - *Tangential method:* two vanes on a staff and two vertical angles are measured.
   - *Subtense bar method:* a bar of known length and the horizontal angle subtended by it.
3. **Others:** Optical wedge and EDM (total station) methods are also used.

#### Horizontal distance by the tangential method

Two vanes on the staff are a known distance $s$ apart. The vertical angles to the vanes are measured from the instrument at A. The staff is held at B and D = horizontal distance AB.

**Case 1: both angles of elevation** ($\alpha_1$ lower vane, $\alpha_2$ upper vane)

```text
                          * upper vane
                     _.-' |  s
                _.-'      * lower vane
        a2 _.-' a1  . '   |
   A _.-'-------------------- B
   |<--------- D -------->|
```

$$
\begin{aligned}
s &= D\tan\alpha_2 - D\tan\alpha_1 \\
D &= \frac{s}{\tan\alpha_2 - \tan\alpha_1}
\end{aligned}
$$

**Case 2: both angles of depression** ($\beta_1$ to the upper vane, $\beta_2$ to the lower vane, $\beta_2 > \beta_1$)

$$
D = \frac{s}{\tan\beta_2 - \tan\beta_1}
$$

**Case 3: one elevation $\alpha$ (to the upper vane) and one depression $\beta$ (to the lower vane)**

$$
s = D\tan\alpha + D\tan\beta \quad\Rightarrow\quad D = \frac{s}{\tan\alpha + \tan\beta}
$$

In each case the RL of the staff station is found from the vertical component $V = D\tan\alpha$ to a vane of known height: $RL_{B} = RL_{A} + h_i \pm V - h_{vane}$, with $+V$ for elevation and $-V$ for depression, and $h_{vane}$ the height of that vane above the staff foot.

The method is less accurate than the stadia method because small errors in the angles affect $D$ directly, but it needs no stadia hairs.

## Check yourself

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

1. Which is a non-stadia method?
   A. Fixed hair method
   B. Movable hair method
   C. Tangential method
   D. Anallatic lens method
   Answer: C. Tangential and subtense bar methods do not use stadia hairs. (Key point: Classification)

2. For both angles of depression (β2 to lower vane, β2 > β1), D equals:
   A. s/(tanβ2 - tanβ1)
   B. s/(tanβ2 + tanβ1)
   C. s(tanβ2 - tanβ1)
   D. s/(tanβ1 - tanβ2)
   Answer: A. The depth difference between vanes is s. (Key point: Depression case)

3. If one angle is elevation α to the upper vane and one depression β to the lower vane:
   A. D = s/(tanα - tanβ)
   B. D = s/(tanα + tanβ)
   C. D = s(tanα + tanβ)
   D. D = s tanα tanβ
   Answer: B. The vanes lie on opposite sides of the horizontal, so the two heights add: s = D tanα + D tanβ. (Key point: Elevation and depression)

4. The tangential method compared with stadia is:
   A. More accurate because it uses more hairs
   B. Less accurate since angular errors affect D directly
   C. Equally accurate
   D. Not possible with theodolite
   Answer: B. Small errors in angles directly affect D. (Key point: Accuracy)

## Related in Surveying II

- [Optical distance principle, tangential horizontal distance](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-principle-tangential-horizontal-distance) — Surveying II, chapter 2
- [Tangential tacheometry, total station procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atangential-tacheometry-total-station-field-procedure) — Surveying II, chapter 2
- [Tangential method distance and elevation](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atangential-method-distance-measurement) — Surveying II, chapter 2
- [Tacheometry, methods, tangential formula](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atacheometry-methods-tangential-derivation) — Surveying II, chapter 2
- [Tangential tacheometry, both angles depression](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atangential-system-depression-expressions) — Surveying II, chapter 2
- [Stadia principle, tangential method depression](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Astadia-principle-tangential-depression) — Surveying II, chapter 2

## Related in other subjects

- [Distance measurement on sloping ground](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adistance-on-sloping-ground) — Surveying I, chapter 2
- [Correct horizontal distance 630 m, tape 8.9 N](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-630m-8-9n-30-005) — Surveying I, chapter 2
- [Correct horizontal distance, 28.00 m measured](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-fully-support-28-00m) — Surveying I, chapter 2
- [True horizontal distance from slope distances](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aslope-distances-tape-2cm-long) — Surveying I, chapter 2