SME
Surveying · Problem type
Compass-rule correction of one course
Use this for “Σlat = −0.045 m and Σdep = +0.060 m round 1250 m. Correct the 156.82 m course (lat −95.8275, dep 124.1354) by the compass rule.”
Diagram
e
=
√
Σlat² + Σdep²
=
√
−
0.045
2
+
0.06
2
=
0.075
m;
precision
one
part
in
P
e
=
16,700.
The gap is drawn 892 times the traverse’s scale.
Compass
rule:
the
lit
course
takes
L
P
=
157
1,250
of
the
gap,
the
other
way:
c
=
−Σ
×
L
P
.
This is an example. Type your own values to start a new problem.
cₗₐₜ (m)
=
−
(
Σlat (m)
)
×
L (m)
÷
P (m)
cdep (m)
=
−
Σdep (m)
×
L (m)
÷
P (m)
lat
Course latitude
example · m
dep
Course departure
example · m
lat′
Corrected latitude
calculated · m
dep′
Corrected departure
calculated · m
Formulas
cₗₐₜ
=
−Σlat
×
L
P
0.005646
=
−(−0.045)
×
156.82
1,250
cdep
=
−Σdep
×
L
P
−0.007527
=
−0.06
×
156.82
1,250
lat′ = lat + cₗₐₜ
−95.8219 = −95.8275 + 0.005646
dep′ = dep + cdep
124.1279 = 124.1354 + (−0.007527)
Assumptions
•
The compass (Bowditch) rule shares the misclosure in proportion to course length.
•
Each correction has the opposite sign to its sum.
•
Corrected this way, all the courses together close exactly.
Step-by-step
WE KNOW
Σlat = −0.045 m, Σdep = 0.06 m, L = 156.82 m, P = 1,250 m, lat = −95.8275 m, dep = 124.1354 m
FIND
latitude correction (cₗₐₜ), departure correction (cdep), corrected latitude (lat′), corrected departure (dep′)
Step 1 · Find latitude correction (cₗₐₜ)
Use cₗₐₜ = −Σlat × L ÷ P
The
course’s
share
L
P
of
the
north
gap,
the
other
way.
cₗₐₜ
=
−(−0.045)
×
156.82
1,250
cₗₐₜ
=
0.045
×
156.82
1,250
cₗₐₜ
=
7.0569
1,250
cₗₐₜ = 0.005646 m
Step 2 · Find departure correction (cdep)
Use cdep = −Σdep × L ÷ P
The
course’s
share
L
P
of
the
east
gap,
the
other
way.
cdep
=
−0.06
×
156.82
1,250
cdep
=
−
9.4092
1,250
cdep = −0.007527 m
Step 3 · Find corrected latitude (lat′)
Use lat′ = lat + cₗₐₜ
Add the correction to the latitude.
lat′ = −95.8275 + 0.005646
lat′ = −95.8219 m
Step 4 · Find corrected departure (dep′)
Use dep′ = dep + cdep
Add the correction to the departure.
dep′ = 124.1354 + (−0.007527)
dep′ = 124.1279 m
Check
Put the numbers back in. Both sides should match.
0.005646
=
−(−0.045)
×
156.82
1,250
✓
−0.007527
=
−0.06
×
156.82
1,250
✓
−95.8219 = −95.8275 + 0.005646 ✓
124.1279 = 124.1354 + (−0.007527) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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