When utilizing the stadia method of tacheometry for distance measurement, the stadia interval factor (k) plays a crucial role. Assuming the instrument constant (i) is zero, which of the following is true about the stadia interval factor in the context of horizontal distances?

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  1. The value of k is inversely proportional to the stadia interval (S), hence the formula D = 1/kS is used to calculate the horizontal distance.
  2. The horizontal distance (D) to the rod is directly proportional to the stadia interval (S) and can be calculated using the formula D = kS.
  3. The stadia interval factor (k) has a fixed value that depends on the make and model of the tacheometer being used.
  4. In the stadia method, k represents the vertical angle, and it is used to calculate the elevation difference between instrument and staff position.

Answer (Detailed Solution Below)

Option 2 : The horizontal distance (D) to the rod is directly proportional to the stadia interval (S) and can be calculated using the formula D = kS.
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Detailed Solution

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Concept:

The stadia method of tachometry is used to measure horizontal distances using the formula:

\( D = kS + i \)

  • \( D \) = Horizontal distance
  • \( k \) = Stadia interval factor (typically around 100)
  • \( S \) = Stadia interval (difference between upper and lower stadia readings)
  • \( i \) = Instrument constant (assumed 0 in modern instruments)

Since \( i = 0 \) for properly calibrated instruments, the equation simplifies to:

\( D = kS \)

The horizontal distance (D) to the rod is directly proportional to the stadia interval (S) and can be calculated using the formula \( D = kS \).

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