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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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Difference between upper and lower stadia reading gives __________

A

A) stadia slope

B

B) stadia coordinate

C

C) stadia intercept

D

D) staff intercept

Correct Answer

⚙️ TE • Technical Concept & PrincipleCivilAdvanced Survey
Option C

stadia intercept

Quick Summary:

In tacheometry, the difference between the upper stadia hair reading and the lower stadia hair reading observed on a vertical leveling staff is known as the stadia intercept (or staff intercept). It is denoted by the variable SSS, calculated as S=Upper Reading−Lower ReadingS = \text{Upper Reading} - \text{Lower Reading}S=Upper Reading−Lower Reading. This value is directly proportional to the distance between the instrument station and the staff.

⚙️TETechnical SolutionConcept & Principle
💡 Explanation

In tacheometry, the difference between the upper stadia hair reading and the lower stadia hair reading observed on a vertical leveling staff is known as the stadia intercept (or staff intercept). It is denoted by the variable SSS, calculated as S=Upper Reading−Lower ReadingS = \text{Upper Reading} - \text{Lower Reading}S=Upper Reading−Lower Reading. This value is directly proportional to the distance between the instrument station and the staff.

🔢 Key Formulas

S=Readingupper−ReadinglowerS = \text{Reading}_{\text{upper}} - \text{Reading}_{\text{lower}}S=Readingupper​−Readinglower​ — Stadia Intercept equation

D=K⋅S+CD = K \cdot S + CD=K⋅S+C — Tacheometric Distance formula for horizontal sight

⚙️ Working Principle

Tacheometry relies on the principle of similar triangles. When sighting through a telescope equipped with a stadia diaphragm, the fixed vertical spacing between the outer horizontal hairs subtends a proportional height on a distant staff. As the staff is moved farther away, the intercepts observed between the upper and lower stadia lines increase linearly with horizontal distance.

📌 Key Points
  • ▸

    The diaphragm of a tacheometer contains three horizontal cross-hairs: top, central (axial), and bottom.

  • ▸

    Multiplying constant K=fiK = \frac{f}{i}K=if​ is typically 100 for standard instruments.

  • ▸

    Additive constant C=(f+c)C = (f + c)C=(f+c) is typically 0 for modern or anallatic lens systems.

✅ Advantages
  • ▸

    Eliminates the need for physical chaining or taping over rough terrain.

  • ▸

    Allows rapid determination of both horizontal distances and vertical elevations.

❌ Disadvantages / Limitations
  • ▸

    Sight distances are limited by staff visibility and optical magnification.

  • ▸

    Reading errors on the staff scale directly impact calculated horizontal distances.

🛠️ Applications / Uses
  • ▸

    Topographical surveys in hilly, steep, or broken ground where chaining is difficult.

  • ▸

    Contour mapping and location surveys for roads, railways, and reservoirs.

📄 Additional Information
  • ▸

    The central axial reading gives the height of the line of sight on the staff.

  • ▸

    Option A (stadia slope) refers to the angle of inclination of the telescope line of sight.

  • ▸

    Option B (stadia coordinate) is not a standard surveying parameter term.

  • ▸

    Option D (staff intercept) is sometimes used synonymously, but 'stadia intercept' precisely describes the distance measured between stadia hair readings on the reticule.

📊 Diagram / Illustration
Stadia Intercept (S)S = Upper Hair Reading - Lower Hair ReadingUpper Reading (Staff Top Sight)Lower Reading (Staff Bottom Sight)Distance Equation: D = K × S + C
✅

C is correct — The difference between upper and lower stadia hair readings on a leveling staff defines the stadia intercept.

Core Concepts Used
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Tacheometry Principles Stadia Diaphragm Multiplying and Additive Constants
💡 EXAM TIP

For horizontal line of sight, D=KS+CD = KS + CD=KS+C; if an anallatic lens is used, C=0C = 0C=0, simplifying the relation to D=100SD = 100SD=100S.

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