BM reduced level = 100 m, BS on BM = 1.34 m. Staff reading at point A (2 km from instrument) = 2.56 m. Find the true RL of point A after correcting for refraction and curvature.
Correct Answer: C. 99.05 m
📚 Detailed Explanation: True RL of Point A Corrected for Curvature and Refraction = 99.05 m
Why C (99.05 m) is correct: The staff reading at A is taken from 2 km away. At this distance, the combined curvature and refraction correction of 0.2692 m is significant and must be subtracted from the observed staff reading before computing the true RL.
Given:
RL of BM = 100 m, BS on BM = 1.34 m
Staff reading at A (observed) = 2.56 m
Distance from instrument to A = 2 km
RL of BM = 100 m, BS on BM = 1.34 m
Staff reading at A (observed) = 2.56 m
Distance from instrument to A = 2 km
Step 1: Height of Instrument
HI = RL of BM + BS = 100 + 1.34 = 101.34 m
Step 2: Combined curvature and refraction correction at 2 km
C_combined = 0.0673 × D² = 0.0673 × (2)² = 0.0673 × 4 = 0.2692 m
This correction is NEGATIVE (readings appear too large due to curvature)
It must be SUBTRACTED from the observed reading
Step 3: Corrected staff reading at A
Corrected reading = Observed – C_combined = 2.56 – 0.2692 = 2.2908 m
Step 4: True RL of A
True RL(A) = HI – Corrected reading = 101.34 – 2.2908 = 99.049 m ≈ 99.05 m
- Combined correction at 2 km: 0.0673 × 4 = 0.2692 m (subtract from observed reading).
- Corrected reading = 2.56 − 0.2692 = 2.2908 m.
- True RL(A) = 101.34 − 2.2908 = 99.05 m.