--- title: "Stadia principle and field procedure" subject: "Surveying II" chapter: 2 key: "semester_4/surveying_ii:stadia-principle-field-procedure-topo" source: https://www.bctengineer.com/q/semester_4/surveying_ii/stadia-principle-field-procedure-topo site: BCT Engineering --- # Stadia principle and field procedure Surveying II · Chapter 2: Tacheometry - Asked in: 2071 Bhadra, 8 marks - Video: [Tacheometric Surveying: Introduction, Field Procedure, Principle and Distance Measurement](https://www.youtube.com/watch?v=HuJMSS3T070) — CIVIL Solved - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/stadia-principle-field-procedure-topo - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2 ## Question State the principle of stadia tacheometry and describe the field procedure of tacheometry survey for preparing topographic map. ## Short answer Principle: fixed stadia hairs give intercept s proportional to distance, D = Ks + C. Procedure: establish control, set up tacheometer, orient, backsight to BM, then for each detail point read bearing, staff hairs, vertical angle; compute horizontal distance and RL; plot and contour. ## Answer **Principle of stadia tacheometry:** the telescope has two extra horizontal hairs (stadia hairs), one above and one below the central cross-hair. The rays through these hairs make a fixed small angle at the focus, so the staff intercept $s$ between them is proportional to the distance of the staff from the instrument. ```text Diaphragm Objective Staff a | | \ A top | i | \ ... | ---+-----------+-------F--------------+---- axis | | / | b | | / B bottom |<-- f --->|<--- D1 ---->| ``` #### Horizontal sight, staff vertical From the similar triangles formed at the external focus $F$ (stadia hair interval $i$, focal length $f$, intercept $s$): $$ \frac{D_1}{f}=\frac{s}{i}\ \Rightarrow\ D_1=\frac{f}{i}\,s $$ Adding the distance of the focus from the instrument axis, $(f+d)$, where $d$ is the distance from the objective to the vertical axis: $$ D=\frac{f}{i}\,s+(f+d)=Ks+C $$ $K=f/i$ is the **multiplying constant** (usually 100) and $C=f+d$ is the **additive constant** (about 0.3 m for an external focusing telescope, and zero for an internal focusing or anallatic telescope). A horizontal sight gives $D=Ks+C$. For an inclined sight with a vertical staff, $D=Ks\cos^2\theta+C\cos\theta$ and $V=\tfrac12Ks\sin2\theta+C\sin\theta$. #### Field procedure of a tacheometric survey for a topographic map 1. **Reconnaissance and control:** establish control stations (a traverse) over the area, and find the RL of a benchmark or station. 2. **Set up the tacheometer** on a station, then centre and level it. Measure the height of the instrument (HI) with a tape. 3. **Orient:** with the horizontal circle at zero (or at 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 hairs** (staff readings), - read the **vertical angle**, setting the middle hair at the same reading as the HI where possible (this simplifies the calculation) or at any convenient reading, - book the readings with a description of the point. 6. **Check** that the mean of the top and bottom hair readings 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:** plot each point by its bearing and horizontal distance (protractor and scale) or by coordinates, write its RL beside it, and interpolate contours 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 the principle of stadia tacheometry? A. The staff intercept between fixed stadia hairs is proportional to distance from the instrument B. The intercept is inversely proportional to distance C. The distance equals the vertical angle D. The intercept is independent of distance Answer: A. Rays through the hairs make a fixed small angle, so by similar triangles D = (f/i)s + (f + d). (Key point: Stadia principle) 2. In D = Ks + C, what are K and C? A. K = i/f; C = f - d B. K = f/i multiplying constant (usually 100); C = f + d additive constant C. K = 0.3; C = 100 D. K = f + d; C = f/i Answer: B. K is the ratio of focal length to hair interval; C is focal length plus distance of objective from the vertical axis. (Key point: Meaning of K and C) 3. With a vertical staff and inclined sight, what are D and V (C = 0)? A. D = Ks cosθ, V = Ks sinθ B. D = Ks sin^2θ, V = Ks cos2θ C. D = Ks cos^2θ, V = (1/2)Ks sin2θ D. D = Ks, V = Ks tanθ Answer: C. The vertical intercept s projects to s cosθ normal to the sight. (Key point: Formulae for inclined sight) 4. What check is applied to the staff readings at each point? A. Top hair must equal bottom hair B. Middle reading must equal HI C. Intercept must be exactly 1 m D. Mean of top and bottom hair should equal the middle reading (within 0.005 m) Answer: D. The check catches misreading of hairs. 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