In levelling by the Height of Instrument (HI) method, the Height of Instrument is calculated as:
Correct Answer: A. RL of BM + BS reading
📚 Detailed Explanation: HI = RL of BM + Back Sight Reading
Why A (HI = RL of BM + BS) is correct: The Height of Instrument (HI) is the elevation of the line of sight above the datum. It is calculated by adding the back sight staff reading (taken at a benchmark of known RL) to that benchmark's Reduced Level.
Formula: HI = RL of BM + BS reading
Example:
RL of BM = 100.000 m
BS reading on BM = 1.855 m
HI = 100.000 + 1.855 = 101.855 m
Then for any staff reading S from this setup:
RL of point = HI – S = 101.855 – S
HI Method: Complete Logic
| Item | Symbol | Definition | Relationship |
|---|---|---|---|
| Benchmark RL | RLBM | Known elevation above datum | Given (measured previously) |
| Back Sight | BS | Staff reading on BM (first reading at a new setup) | Measured in field |
| Height of Instrument | HI | Elevation of line of sight above datum | HI = RLBM + BS |
| Any staff reading | S | Reading on a point whose RL is needed | Measured in field |
| RL of that point | RL | Elevation above datum | RL = HI − S |
- HI = RL of BM + BS: the instrument's line of sight is BS metres above the BM, and the BM is RL metres above datum.
- HI is the elevation of the line of sight, not the height of the instrument above the ground.
- One HI is valid for all readings taken from that instrument position (before it is moved).