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Which is the following correction applied when the points are having small distance between them?
A) Correction for curvature
B) Correction for refraction
C) Combined correction
D) None of the above
None of the above
In trigonometrical levelling, corrections for curvature and refraction are negligible and usually neglected when the distance between points is small (typically up to about 200 m to 500 m). Since these corrections depend directly on the square of the distance, their values for short distances are exceedingly small and practically zero.
In trigonometrical levelling, corrections for curvature and refraction are negligible and usually neglected when the distance between points is small (typically up to about 200 m to 500 m). Since these corrections depend directly on the square of the distance, their values for short distances are exceedingly small and practically zero.
Cc=2RD2=0.0785D2 meters — Correction for Earth's curvature (D in km)
Cr=712RD2=0.0112D2 meters — Correction for refraction (D in km)
CC=Cc−Cr=0.0673D2 meters — Combined correction for curvature and refraction
Curvature correction accounts for the Earth's surface bending away from a level line, scaling as Cc=0.0785D2. Refraction correction accounts for light bending through air layers, scaling as Cr=0.0112D2. When distance D is small, D2 becomes insignificantly small, rendering neither individual nor combined corrections necessary.
Curvature correction is always subtractive from the staff reading.
Refraction correction is always additive to the staff reading.
Combined correction is subtractive because curvature dominates refraction (Cc>Cr).
For distances up to 200 m, the combined correction is less than 3 mm, which is within common observational tolerance.
Determining height differences in short-distance sights without needing complex atmospheric/earth corrections.
Trigonometrical levelling over small survey control nets.
Option A (Correction for curvature) is required for long distances to compensate for the Earth's surface dropping below the horizontal sight line.
Option B (Correction for refraction) is required for long distances to compensate for rays bending downward through atmospheric density gradients.
Option C (Combined correction) applies both curvature and refraction corrections for longer sights (CC=0.0673D2).
D is correct — For small distances between points, corrections for curvature and refraction are negligible and thus no correction is applied.
Remember that curvature and refraction corrections depend on D2, where D is in kilometers. When checking whether to apply corrections in competitive exam numericals, calculate 0.0673D2 first to see if it exceeds reading precision.