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CivilAdvanced Survey
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The multiplying constant for the tacheometer is, generally, kept a

A
B

100

C

20

D

50

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleCivilAdvanced Survey
Option B

100

Quick Summary:

In tacheometry, the multiplying constant (kkk or KKK) is a ratio of the focal length of the objective lens (fff) to the distance between the top and bottom stadia hairs (iii). It converts the staff intercept (sss) into horizontal distance. For standard tacheometers, this value is intentionally fixed and kept at 100100100 to simplify distance calculations.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

In tacheometry, the multiplying constant (kkk or KKK) is a ratio of the focal length of the objective lens (fff) to the distance between the top and bottom stadia hairs (iii). It converts the staff intercept (sss) into horizontal distance. For standard tacheometers, this value is intentionally fixed and kept at 100100100 to simplify distance calculations.

ЁЯФв Key Formulas

K=fiK = \frac{f}{i}K=ifтАЛ тАФ Multiplying constant

C=f+dC = f + dC=f+d тАФ Additive constant

D=Ks+CD = Ks + CD=Ks+C тАФ Horizontal distance formula for horizontal line of sight

тЪЩя╕П Working Principle

Tacheometry is an optical method of distance measurement based on the principle of isosceles triangles, where the ratio of the distance from the vertex to the base and the base length remains constant. By designing the telescope optics such that K=fi=100K = \frac{f}{i} = 100K=ifтАЛ=100, the horizontal distance equation D=Ks+CD = Ks + CD=Ks+C simplifies directly to D=100s+CD = 100s + CD=100s+C.

ЁЯУМ Key Points
  • тЦ╕

    The multiplying constant (KKK) is generally kept at 100100100.

  • тЦ╕

    The additive constant (C=f+dC = f + dC=f+d) is usually kept at 000 by providing an anallatic lens in modern tacheometers.

  • тЦ╕

    Using an anallatic lens makes the distance directly proportional to the staff intercept (D=100sD = 100sD=100s).

тЬЕ Advantages
  • тЦ╕

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

  • тЦ╕

    Provides rapid survey measurements for topographic mapping.

  • тЦ╕

    Significantly simplifies field office calculations when K=100K = 100K=100 and C=0C = 0C=0.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Precision is lower compared to precise electronic distance measurement (EDM) or invar tape chaining.

  • тЦ╕

    Accuracy decreases at longer sight distances due to reading errors on the staff.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Contouring and topographic surveying in hilly or rugged terrain.

  • тЦ╕

    Location surveys for roads, railways, and reservoirs.

ЁЯУД Additional Information
  • тЦ╕

    The additive constant C=f+dC = f + dC=f+d ranges from 30┬аcm30\text{ cm}30┬аcm to 45┬аcm45\text{ cm}45┬аcm for external focusing telescopes and 8┬аcm8\text{ cm}8┬аcm to 20┬аcm20\text{ cm}20┬аcm for internal focusing telescopes.

  • тЦ╕

    Anallatic lens (invented by Porro) reduces the additive constant CCC to strictly zero.

ЁЯУК Diagram / Illustration
Multiplying Constant FormulaMultiplying Constant (K) =Focal Length of Lens (f)Stadia Interval (i)Standard Value K = 100
тЬЕ

B is correct тАФ The multiplying constant of a tacheometer is fixed at 100 to simplify the calculation of horizontal distances.

Core Concepts Used
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Tacheometry Constants Stadia Hair Interval Anallatic Lens
ЁЯТб EXAM TIP

Remember that for an ideal tacheometer fitted with an anallatic lens, K=100K = 100K=100 and C=0C = 0C=0, reducing the distance equation to D=100sD = 100sD=100s.

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