SME
Surveying
Leveling
Use this for “From BM at 100.000 m: BS 1.245, FS 2.110 on TP1; BS 0.876, FS 1.532 on B. Find B’s elevation and check it.”
Diagram
HI = elevation + BS; elevation = HI − FS: TP1 = 101 − 2.11 = 99.1 m, B = 100 − 1.53 = 98.5 m.
Check: ΣBS − ΣFS = 2.12 − 3.64 = −1.52 m = B − BM.
This is an example. Type your own values to start a new problem.
TP1 (m)
=
BM (m)
+
BS₁ (m)
−
FS₁ (m)
B (m)
=
TP1 (m)
+
BS₂ (m)
−
FS₂ (m)
HI₁
Height of instrument, setup 1
calculated · m
HI₂
Height of instrument, setup 2
calculated · m
ΔE
Rise from BM to B
worked out (not typed) · m
Formulas
HI₁ = BM + BS₁
101.245 = 100 + 1.245
TP1 = HI₁ − FS₁
99.135 = 101.245 − 2.110
HI₂ = TP1 + BS₂
100.011 = 99.135 + 0.876
B
=
HI₂
−
FS₂
98.479 = 100.011 − 1.532
ΔE = (BS₁ + BS₂) − (FS₁ + FS₂)
−1.521 = (1.245 + 0.876) − (2.110 + 1.532)
Assumptions
•
Backsight and foresight distances are balanced, so curvature, refraction and collimation errors cancel.
•
A backsight (BS) is read on a point of known elevation; a foresight (FS) on the next point.
•
The height of instrument (HI) is the elevation of the level’s line of sight.
Step-by-step
WE KNOW
BM = 100 m, BS₁ = 1.245 m, FS₁ = 2.110 m, BS₂ = 0.876 m, FS₂ = 1.532 m
FIND
height of instrument, setup 1 (HI₁), turning point elevation (TP1), height of instrument, setup 2 (HI₂), elevation of B (B), rise from BM to B (ΔE)
Step 1 · Find height of instrument, setup 1 (HI₁)
Use HI₁ = BM + BS₁
The line of sight stands BS₁ above the benchmark.
HI₁ = 100 + 1.245
HI₁ = 101.245 m
Step 2 · Find turning point elevation (TP1)
Use TP1 = HI₁ − FS₁
The turning point is FS₁ below the line of sight.
TP1 = 101.245 − 2.110
TP1 = 99.135 m
Step 3 · Find height of instrument, setup 2 (HI₂)
Use HI₂ = TP1 + BS₂
Move the level; its line of sight stands BS₂ above TP1.
HI₂ = 99.135 + 0.876
HI₂ = 100.011 m
Step 4 · Find elevation of B (B)
Use B = HI₂ − FS₂
B
is
FS₂
below
the
second
line
of
sight.
B
=
100.011
−
1.532
B
=
98.479
m
Step 5 · Find rise from BM to B (ΔE)
Use ΔE = (BS₁ + BS₂) − (FS₁ + FS₂)
The
arithmetic
check:
the
backsights
less
the
foresights
must
equal
B
−
BM.
ΔE = (1.245 + 0.876) − (2.110 + 1.532)
ΔE = 2.121 − 3.642
B
−
BM
=
98.479
−
100.000
=
−1.521
✓
ΔE = −1.521 m
Check
Put the numbers back in. Both sides should match.
101.245 = 100 + 1.245 ✓
99.135 = 101.245 − 2.110 ✓
100.011 = 99.135 + 0.876 ✓
98.479 = 100.011 − 1.532 ✓
−1.521 = (1.245 + 0.876) − (2.110 + 1.532) ✓
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Interior angle misclosure of a closed traverse
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Curvature and refraction over a long sight
Topic check
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