During a levelling survey from a single instrument position, the backsight at A was greater than the foresight at B. Which of the following is correct?
Correct Answer: B. Elevation of B is more than that of A
📚 Detailed Explanation: BS at A > FS at B (Single Setup) → Elevation of B Is Greater
Why B (elevation of B is more than that of A) is correct: From a single instrument position, HI = RL(A) + BS. RL(B) = HI − FS = RL(A) + BS − FS. If BS > FS, then RL(B) > RL(A) — B is higher than A.
Mathematical proof:
HI = RL(A) + BS_A … (instrument height above A)
RL(B) = HI – FS_B = RL(A) + BS_A – FS_B
HI = RL(A) + BS_A … (instrument height above A)
RL(B) = HI – FS_B = RL(A) + BS_A – FS_B
If BS_A > FS_B:
BS_A – FS_B = positive value
RL(B) = RL(A) + (positive value)
RL(B) > RL(A) → B is HIGHER than A
Example:
RL(A) = 100 m, BS = 2.50 m, FS = 1.20 m
HI = 100 + 2.50 = 102.50 m
RL(B) = 102.50 – 1.20 = 101.30 m → B is higher by 1.30 m
Intuitive Understanding
| Condition | Ground Relationship | Result |
|---|---|---|
| BS at A is large | A is low; the horizontal line of sight is far above A | Staff at A reads a large value |
| FS at B is small | B is high; the horizontal line of sight barely clears B | Staff at B reads a small value |
| BS > FS | B is closer to the line of sight from above → B has higher elevation | RL(B) > RL(A) |
- From a single setup: RL(B) = RL(A) + BS − FS.
- BS > FS → (BS − FS) is positive → B is higher than A.
- Cannot determine from HI alone which is higher — you need both BS and FS.