The combined correction for curvature of Earth and refraction in levelling for a distance of 6 km would be __________ m (rounded off to two decimal places). Assume the radius of earth is 6370 km.
Levelling Correction: Curvature and Refraction
This section calculates the combined correction required in leveling due to Earth's curvature and atmospheric refraction over a specific distance.
Combined Correction Formula
For surveying calculations, the combined correction ($C$) in meters is typically estimated using the distance ($d$) in kilometers and the Earth's radius ($R$) in kilometers with the formula:
$ C = \frac{7}{8} \times \frac{d^2}{2R} \times 1000 $
Levelling Parameters
- Distance ($d$): 6 km
- Earth Radius ($R$): 6370 km
Step-by-Step Calculation
Substitute the known values into the formula:
$ C = \frac{7}{8} \times \frac{(6)^2}{2 \times 6370} \times 1000 $
Calculate the square of the distance:
$ 6^2 = 36 $
Calculate the denominator term:
$ 2 \times 6370 = 12740 $
Now, compute the correction value:
$ C = \frac{7}{8} \times \frac{36}{12740} \times 1000 $
$ C = \frac{252}{101920} \times 1000 $
$ C = \frac{252000}{101920} $
$ C \approx 2.4725 $
Calculated Correction Value
Rounded to two decimal places, the combined correction is 2.47 m.
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
