---
title: "Three-wire stadia field procedure for topo map"
subject: "Surveying II"
chapter: 2
key: "semester_4/surveying_ii:three-wire-stadia-field-procedure"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/three-wire-stadia-field-procedure
site: BCT Engineering
---

# Three-wire stadia field procedure for topo map

Surveying II · Chapter 2: Tacheometry

- Asked in: 2078 Poush, 4 marks
- Video: [SURVEYING: What is the Top, Middle and Bottom Hairs STAFF Readings?](https://www.youtube.com/watch?v=X1ioLGp5KO0) — Kelvin Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/three-wire-stadia-field-procedure
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2

## Question

Explain about the field procedure and method of taking field parameters in three wires stadia tacheometry for the preparation of topographic map.

## Short answer

Set up, centre, level, measure HI, orient, and back-sight a benchmark. At each detail point read horizontal circle, vertical angle, and top, middle, bottom hairs; check middle equals mean of top and bottom. Compute s = top minus bottom, D = Ks cos^2 θ, V = 1/2 Ks sin2θ, RL = RL axis ± V − h, and plot by bearing and distance.

## Answer

In three-wire stadia tacheometry, the top, middle (axial) and bottom hairs are read on a vertical staff. The method gives the distance from the intercept and a check on the readings (middle reading $\approx$ mean of top and bottom).

#### Field procedure
1. **Reconnaissance and control:** establish control stations (traverse) over the area; know the RL of a benchmark or station.
2. **Set up the tacheometer** on a station, centre and level it. Measure the height of the instrument (HI) with a tape.
3. **Orient:** with the horizontal circle at zero (or a known bearing) sight a known reference station or magnetic north.
4. **Back-sight** to a benchmark or known point with the staff to find the RL of the instrument axis.
5. **Detail points:** the staff-man holds the staff vertical at each ground feature (corners, break lines, spot heights). For each point:
   - bisect the staff and read the **horizontal circle** (bearing),
   - read the **top, middle and bottom hair** (staff readings),
   - read the **vertical angle**, with the middle hair at the same height as the HI where possible (this simplifies the calculation) or at any convenient reading,
   - book the readings with a point description.
6. **Check** that the mean of top and bottom hair equals the middle reading (within 0.005 m), and close on a known point at the end of the day.
7. **Computation:** $s=$ top $-$ bottom, $D=Ks\cos^2\theta$, $V=\frac{1}{2}Ks\sin2\theta$, RL $=$ RL of axis $\pm V-h$.
8. **Plotting:** each point is plotted by its bearing and horizontal distance (protractor and scale) or by coordinates, with its RL, and contours are interpolated for the topographic map.

#### Field book (typical)
| Inst. stn | HI | Staff stn | Bearing | V. angle | Top | Mid | Bottom | Remarks |
|---|---|---|---|---|---|---|---|---|
| A | 1.45 | 1 | 45°30' | +3°10' | 1.855 | 1.405 | 0.955 | Corner of house |
| | | 2 | 78°15' | -2°20' | 2.340 | 1.800 | 1.260 | Road edge |

## Check yourself

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

1. What is read at each detail point in three-wire stadia tacheometry?
   A. Only the middle hair
   B. Horizontal circle bearing, top, middle and bottom hair readings and the vertical angle
   C. Only the vertical angle
   D. Top and bottom hair readings without the angle
   Answer: B. Each point needs bearing, three hair readings and the vertical angle. (Key point: Readings at each point)

2. What check applies to the three hair readings?
   A. Top + bottom = 2 x HI
   B. Middle reading is about the mean of top and bottom (within 0.005 m)
   C. Top - middle = 1 m
   D. Middle = bottom + 0.3
   Answer: B. If the hairs are read correctly the middle reading equals the mean of top and bottom. (Key point: Check on readings)

3. How is the RL of the instrument axis found in the field?
   A. Back-sight with the staff on a benchmark or known point
   B. Measure HI only
   C. Assume a zero level
   D. Use the bearing to the known station
   Answer: A. A back-sight to a benchmark gives the RL of the axis. (Key point: RL of instrument axis)

4. Which formulas compute each point?
   A. s = top - bottom, D = Ks cos^2(theta), V = (1/2) Ks sin 2theta, RL = axis ± V - h
   B. D = s only, RL = HI
   C. D = Ks sin(theta), V = Ks cos(theta)
   D. D = Ks + C, RL = axis + h
   Answer: A. Intercept s is top minus bottom; D and V follow the inclined-sight formulas; RL = axis ± V - h. (Key point: Computation)

## Related in Surveying II

- [Stadia principle and field procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Astadia-principle-field-procedure-topo) — Surveying II, chapter 2
- [Tacheometry without staff, procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Astaffless-tacheometry-procedure) — 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
- [ODM principle, tacheometric field procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aodm-principle-field-procedure-theodolite) — Surveying II, chapter 2
- [Tacheometry principle, stadia distance and RL](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atacheometry-principle-stadia-formula) — 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

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