The roof of a room was taken as BM with RL = 100 m. Inverted staff reading on the BM = 3.500 m. Staff reading at ground point P = 1.200 m. Find the RL of point P.
Correct Answer: B. 95.3 m
📚 Detailed Explanation: Inverted Staff Calculation — RL of Point P = 95.3 m
Why B (95.3 m) is correct: The roof is the Bench Mark (RL = 100 m). An inverted staff is held on the roof, so the BS is negative. This gives a HI below the roof level. The ground point P has a normal (upright) staff reading.
Given:
RL of BM (roof) = 100 m
Inverted BS on roof = 3.500 m → treated as NEGATIVE: BS = -3.500 m
FS at Point P (ground) = 1.200 m (upright staff, normal +ve)
RL of BM (roof) = 100 m
Inverted BS on roof = 3.500 m → treated as NEGATIVE: BS = -3.500 m
FS at Point P (ground) = 1.200 m (upright staff, normal +ve)
Calculation:
HI = RL of BM + BS = 100 + (-3.500) = 96.50 m
RL of P = HI – FS = 96.50 – 1.200 = 95.3 m
Why P Is Below the Roof
| Item | Value | Meaning |
|---|---|---|
| RL of roof | 100 m | Known BM |
| HI | 96.50 m | Instrument line of sight is 3.5 m below the roof |
| FS at P | 1.200 m | Staff at P reads 1.200 m above ground; ground is 1.2 m below HI |
| RL of P | 95.30 m | P is 4.7 m below the roof |
Quick check:
Drop from roof to instrument line of sight: 3.500 m (inverted BS)
Drop from line of sight to P: 1.200 m (FS)
Total drop from roof to P: 3.500 + 1.200 = 4.700 m
RL of P = 100 – 4.700 = 95.3 m ✓
Drop from roof to instrument line of sight: 3.500 m (inverted BS)
Drop from line of sight to P: 1.200 m (FS)
Total drop from roof to P: 3.500 + 1.200 = 4.700 m
RL of P = 100 – 4.700 = 95.3 m ✓
- BM on roof (overhead) + inverted BS → HI = RL − |BS| = 100 − 3.5 = 96.50 m.
- RL(P) = 96.50 − 1.200 = 95.3 m.
- Point P is 4.7 m below the roof benchmark.