Question

A level with the height of the instrument being 2.550 m has been placed at a station having a Reduced Level (RL) of 130.565 m. The instrument reads 3.665 m on a levelling staff held inverted at the bottom of a bridge deck. The RL of the bottom of the bridge deck is __________ m (rounded off to 3 decimal places).

Hint:

When the staff is held inverted (e.g., under a bridge), the reading is added to the height of the instrument to determine the elevation of the measured point.

Answer 1

Given:

Height of instrument = 2.550 m
RL of instrument setup point = 130.565 m
Inverted staff reading at the bottom of the bridge deck = 3.665 m

First, calculate the RL of the line of sight:
\[ \text{RL}_{\text{Instrument Axis}} = 130.565 + 2.550 = 133.115 \, \text{m} \]

Since the staff is held inverted, the point being measured is above the instrument axis by the staff reading:
\[ \text{RL}_{\text{Bridge Deck Bottom}} = 133.115 + 3.665 = 136.780 \, \text{m} \]

Final Answer: \(\boxed{136.780 \, \text{m}}\)