SME
Surveying · Problem type
Curvature and refraction over a long sight
Use this for “A level sight runs 2 km to a rod. How much too high does the rod read from curvature and refraction?”
Diagram
h = 0.0675K² = 0.0675 × 2² = 0.27 m: the earth falls away from the level line; refraction bends the sight back a little.
The curve and h are drawn far bigger than life.
This is an example. Type your own values to start a new problem.
h (m)
=
0.0675
m/km²
×
(
K (km)
)
2
Formulas
h
=
0.0675
×
K
2
0.27
=
0.0675
×
2
2
Assumptions
•
h = 0.0675 m/km² × K², K in km: the earth’s curve (0.0785K²) less a seventh for refraction.
•
The level line is horizontal at the instrument; the earth’s surface falls away from it.
•
The rod reads high by h, so subtract h from the reading.
Step-by-step
WE KNOW
K = 2 km
FIND
combined correction (h)
Step 1 · Find combined correction (h)
Use h = 0.0675 × K²
The drop grows with the square of the distance.
h
=
0.0675
×
2
2
h
=
0.0675
×
4
h
=
0.27
m
Check
Put the numbers back in. Both sides should match.
0.27
=
0.0675
×
2
2
✓
Topic check
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