Levelling Calculation: Elevation Comparison
In surveying, levelling determines the elevation difference between points using instrument readings.
Let:
- HI = Height of the Instrument above datum
- BS = Backsight reading taken on point P
- FS = Foresight reading taken on point Q
- Elevation(P) = Elevation of point P
- Elevation(Q) = Elevation of point Q
With a fixed instrument location:
The height of the instrument (HI) can be calculated using the backsight reading:
$ \text{HI} = \text{Elevation}(\text{P}) + \text{BS} $
The elevation of the next point (Q) can be calculated using the foresight reading:
$ \text{HI} = \text{Elevation}(\text{Q}) + \text{FS} $
Equating the two expressions for HI:
$ \text{Elevation}(\text{P}) + \text{BS} = \text{Elevation}(\text{Q}) + \text{FS} $
Rearranging to find the elevation difference between P and Q:
$ \text{Elevation}(\text{P}) - \text{Elevation}(\text{Q}) = \text{FS} - \text{BS} $
The question states that the backsight reading at P is more than the foresight reading at Q:
$ \text{BS} > \text{FS} $
This implies that the difference (FS - BS) is negative:
$ \text{FS} - \text{BS} < 0 $
Therefore:
$ \text{Elevation}(\text{P}) - \text{Elevation}(\text{Q}) < 0 $
Which means:
$ \text{Elevation}(\text{P}) < \text{Elevation}(\text{Q}) $
Conclusion:
Point P has a lower elevation than point Q.
Important Questions from Levelling Methods
- Which one of the following is the purpose of taking a backsight observation in levelling?
- The observations of a reciprocal levelling operation carried out from two stations A and B are given in table. It is known that the instrument has collimation error. The correct staff reading over station B when the instrument is set very near to station A is ________ m (Rounded off to three decimal places).
Assume all other errors are negligible.Staff readings at station Instrument set very near to station A (m) B (m) A 1.275 2.005 B 1.040 1.660 - 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).
- In levelling between two points P and Q on opposite banks of a river, the level was set up near P, and the staff reading on P and Q were 2.165 m and 3.810 m, respectively. The level was then moved and set up near Q and the respective staff readings on P and Q were 0.910 m and 2.355 m. The true difference of level between P and Q is __________ m (rounded off to 3 decimal places).
- Change Point (CP) in levelling refers to a location where
