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Given that for a triangulation survey
D = distance in km
h = the visible horizon from a station of known elevation above the datum (in metres) if there is no obstruction due to intervening ground, then h is equal to
  • a)
    0.6735 D2
  • b)
    6.735 D2
  • c)
    0.06735 D2
  • d)
    0.006735 D2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Given that for a triangulation surveyD = distance in kmh = the visible...
Understanding the Visible Horizon in Surveying
In triangulation surveys, determining the visible horizon is crucial for understanding how far one can see from a station of known elevation. The formula that relates the visible horizon (h) to the distance (D) is derived from geometric principles.
Formula Explanation
The visible horizon can be approximately calculated using the following relationship:
- h = k * D²
Here, 'k' is a constant that depends on the units used. For the specific case of kilometers and meters, this constant equates to 0.06735.
Breakdown of the Options
Analyzing the answer choices:
- Option A: 0.6735 D² - This is too large and not applicable for the given units.
- Option B: 6.735 D² - This value is again excessively large and not valid.
- Option C: 0.06735 D² - This aligns perfectly with the derived formula where h is in meters and D is in kilometers.
- Option D: 0.006735 D² - This is incorrectly scaled down and does not represent the relationship accurately.
Conclusion
Therefore, the correct answer is indeed option 'C', h = 0.06735 D². This formula captures the relationship between the distance to the horizon and the height of the observer, allowing surveyors to calculate visibility accurately in triangulation surveys. Understanding this relationship is essential for effective land surveying, ensuring precise measurements and calculations.
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Given that for a triangulation surveyD = distance in kmh = the visible horizon from a station of known elevation above the datum (in metres) if there is no obstruction due to intervening ground, then h is equal toa)0.6735 D2b)6.735 D2c)0.06735 D2d)0.006735 D2Correct answer is option 'C'. Can you explain this answer?
Question Description
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