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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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CivilAdvanced Survey
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Which of the instrument used for tacheometry survey

A

Stadia road

B

Tacheometer

C

Chain

D

Both A and B

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey
Option D

Both A and B

Quick Summary:

Tacheometry is a branch of angular surveying in which the horizontal and vertical distances of points are determined by optical measurements, eliminating the need for direct chain or tape measurements. A tacheometer (a transit theodolite fitted with a stadia diaphragm) and a stadia rod (or leveling staff) are the primary instruments used together to perform tacheometric surveying.

⚙️TETechnical SolutionConcept & Principle
💡 Explanation

Tacheometry is a branch of angular surveying in which the horizontal and vertical distances of points are determined by optical measurements, eliminating the need for direct chain or tape measurements. A tacheometer (a transit theodolite fitted with a stadia diaphragm) and a stadia rod (or leveling staff) are the primary instruments used together to perform tacheometric surveying.

🔢 Key Formulas

D=K⋅s+CD = K \cdot s + CD=K⋅s+C — Horizontal distance for horizontal line of sight

D=K⋅s⋅cos⁡2(θ)+C⋅cos⁡(θ)D = K \cdot s \cdot \cos^2(\theta) + C \cdot \cos(\theta)D=K⋅s⋅cos2(θ)+C⋅cos(θ) — Horizontal distance for inclined line of sight

V=12K⋅s⋅sin⁡(2θ)+C⋅sin⁡(θ)V = \frac{1}{2} K \cdot s \cdot \sin(2\theta) + C \cdot \sin(\theta)V=21​K⋅s⋅sin(2θ)+C⋅sin(θ) — Vertical distance component

⚙️ Working Principle

Tacheometry works on the principle of isosceles triangles, where the ratio of the distance of the base from the apex to the length of the base is constant. The vertical angle and the staff intercept (difference between upper and lower stadia hair readings on the stadia rod) are measured to compute horizontal and vertical distances using optical constants.

📌 Key Points
  • ▸

    A tacheometer is a transit theodolite equipped with a stadia diaphragm containing two extra horizontal cross-hairs.

  • ▸

    A stadia rod (or stadia staff) is specially graduated to allow clear reading of staff intercepts over long sight distances.

  • ▸

    The multiplying constant K=fiK = \frac{f}{i}K=if​ is typically manufactured to be 100.

  • ▸

    The additive constant C=f+dC = f + dC=f+d is usually kept as 0 by incorporating an anallatic lens inside the telescope.

✅ Advantages
  • ▸

    Rapid surveying in rough, broken, or steep terrain where chaining is difficult or impossible.

  • ▸

    Measures both horizontal distance and vertical elevation simultaneously without direct physical measurements.

❌ Disadvantages / Limitations
  • ▸

    Lower precision compared to precise chaining or Electronic Distance Measurement (EDM) over long distances.

  • ▸

    Sight lines can be obscured by vegetative cover or atmospheric refraction errors.

🛠️ Applications / Uses
  • ▸

    Preparation of contour maps and topographic surveys in hilly or undulating areas.

  • ▸

    Location survey work for railways, highways, and reservoir site selection.

📄 Additional Information
  • ▸

    Chain (Option C) is used for direct linear measurements in basic linear surveying, not in optical tacheometric surveying.

  • ▸

    Option A (Stadia rod) and Option B (Tacheometer) work as a pair; hence both instruments are required for a complete tacheometric setup.

📊 Diagram / Illustration
Tacheometric Distance Formula CardHorizontal Distance (Line of Sight Horizontal): D = K · s +CWhere: K = Multiplying Constant (f / i ≈ 100)C = Additive Constant (f + d ≈ 0 for anallatic lens)s = Staff Intercept (Top Hair Reading − Bottom Hair Reading)
✅

D is correct — Both the tacheometer (transit theodolite with stadia diaphragm) and the stadia rod (leveling staff) are essential instruments used together in tacheometry.

Core Concepts Used
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Stadia Tacheometry Multiplying Constant and Additive Constant Optical Distance Measurement
💡 EXAM TIP

Always remember for exam questions: if an anallatic lens is fitted in the telescope of a tacheometer, the additive constant CCC becomes zero (000) and the multiplying constant KKK is held fixed at 100100100.

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