--- title: "ODM principle, tacheometric field procedure" subject: "Surveying II" chapter: 2 key: "semester_4/surveying_ii:odm-principle-field-procedure-theodolite" source: https://www.bctengineer.com/q/semester_4/surveying_ii/odm-principle-field-procedure-theodolite site: BCT Engineering --- # ODM principle, tacheometric field procedure Surveying II · Chapter 2: Tacheometry - Asked in: 2076 Baisakh, 4 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/odm-principle-field-procedure-theodolite - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-2 ## Question Describe the principle of optical distance measurement (ODM). Explain the field procedure of tacheometric survey by theodolite for preparing topographic map. ## Short answer ODM determines distance from angle subtended by known length: stadia method uses fixed stadia hairs (D=Ks+C), subtense method uses horizontal bar (D=(b/2)cot(θ/2)). Field procedure: establish control traverse, set up theodolite, orient, observe detail points reading three stadia hairs, horizontal and vertical angles, compute horizontal distance, vertical component, RL, plot by bearing and distance. ## Answer #### Principle of optical distance measurement (ODM) Optical distance measurement finds the horizontal distance to a point from the angle subtended at the instrument by a known length (a staff intercept or a bar), using only angles and the geometry of similar triangles. No tape is used. Two types are common. - **Stadia (tacheometric) method:** The diaphragm of the theodolite carries two extra horizontal hairs (stadia hairs) at a fixed spacing $i$. The rays through these hairs make a fixed angle at the instrument, so the staff intercept $s$ (top reading minus bottom reading) is proportional to the distance: $$ D = \frac{f}{i}\,s + (f + d) $$ For an anallactic lens the additive constant is zero, so $D = k\,s$ with multiplying constant $k = f/i = 100$ and $c = 0$. - **Subtense method:** a bar of known length $b$ is set perpendicular to the line of sight and the small angle $\theta$ it subtends is measured: $D = \frac{b}{2}\cot\frac{\theta}{2}$. For a vertical staff and a line of sight inclined at angle $\theta$: $H = k s\cos^2\theta$ and $V = \frac{ks}{2}\sin 2\theta$. #### Field procedure of tacheometric survey for a topographic map 1. **Reconnaissance and control:** Fix a traverse around the area with theodolite stations, and find their coordinates and RL (traverse computation plus levelling or trigonometric levelling from a BM). 2. **Setting up:** Set up the theodolite over a control station, level it and measure the height of the instrument (HI) with a tape. 3. **Orientation:** Sight a back station, set the horizontal circle to its known bearing. 4. **Detail observation:** Hold the staff vertically at each detail point (corners of buildings, road edges, streams, spot heights, break points of slope). For each point read: - the three hair readings (top, middle, bottom), - the horizontal circle (bearing or angle from the reference line), - the vertical circle (vertical or zenith angle) with the middle hair on the staff. 5. **Booking:** Enter the readings in the field book with a sketch of the detail and the point number. 6. **Computation:** Find $H$, $V$ and the RL of each point: $RL = RL_{station} + HI + V - r$ ($r$ = middle hair reading). 7. **Plotting:** Plot the control stations by coordinates, then plot each detail point by its bearing and horizontal distance to scale. Write the RL beside the point and interpolate contours between points. Points are spaced closer where the ground changes slope suddenly. Check readings by taking a few points from two stations. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Optical distance measurement finds distance from: A. An angle subtended by a known length, using similar triangles B. A tape pulled under tension C. Time of flight D. Differential levelling Answer: A. No tape is used; only angles and geometry of similar triangles. (Key point: Principle of ODM) 2. For a vertical staff and inclined sight, H and V are: A. H = ks cos^2θ, V = (ks/2) sin2θ B. H = ks, V = ks sinθ C. H = ks sin2θ, V = ks cos^2θ D. H = ks cosθ, V = ks sinθ Answer: A. These apply for the staff held vertical. (Key point: Inclined sight formulas) 3. The first step of the field procedure is: A. Plot contours B. Fix a traverse and find coordinates and RLs of control stations C. Read detail points D. Compute RLs Answer: B. Control stations with known coordinates and RL are needed before detail observation. (Key point: Control first) 4. At each detail point the observer reads: A. Only the middle hair B. Three hair readings, horizontal circle and vertical circle with middle hair on staff C. Only the bearing D. Only the vertical angle Answer: B. These give s, the bearing, and the vertical angle. (Key point: Readings at each detail) ## Related in Surveying II - [Principle of optical distance measurement](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aoptical-distance-measurement-principle) — Surveying II, chapter 2 - [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 - [Three-wire stadia field procedure for topo map](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Athree-wire-stadia-field-procedure) — Surveying II, chapter 2 - [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 - [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 - [Tacheometry without staff, procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Astaffless-tacheometry-procedure) — Surveying II, chapter 2 ## Related in other subjects - [Theodolite construction principle; micrometer](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-construction-principle-micrometer) — Surveying I, chapter 7, asked 2× - [Face observation errors; optical theodolite](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aface-observation-errors-optical-theodolite) — Surveying I, chapter 7, asked 2× - [Chain survey principle and operations](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Achain-principle-and-field-procedure) — Surveying I, chapter 3, asked 2× - [Field sketch and mapping by linear measurement](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Achain-field-sketch-mapping) — Surveying I, chapter 3