TRIGONOMETRIC LEVELING TRAVERSE (CALTECH)
hcr correction due to curvature and refraction INPUT MODE [2] (CMPLX) RESULTS
k horizontal distance TRAVERSE
A fr. N w/ sign a + b SHIFT [2][3] r
R radius of earths curvature
L; NE L L
Derived Formula L; NW L(360 ) L
For R = 6400 km Lat + Dep LA fr. N
L; SE L(180 ) (L )
m hcr = 0.067k2 km L; SW L(180 + ) (L)
L:Length of Course Azimuth from North: Bearing STORE Every Traverse in Every Letter (A-F)
For R = 6350 km :Bearing clockwise from North (+)clockwise
m hcr = 0.0675k2 km ()counter cw NOTE: Abs(LA fr. N) = L
All
arg(LA fr. N) = A fr. N
General Formula (+)from North
()from South
6 k2
km hcr = ( ) km
7 2R
Latitude, Departure, Linear Error of Closure
LA fr. N (using the table) = ( Lat) + ( Dep)
Principles khor
klevel hcr ( Lat) + ( Dep) SHIFT [2][3] r LECLEC
1) khorizontal = klevel
2) k y1 and k y2 R Corrected Latitude and Departure
R
Elevation Compass Rule
A L
el. A = el. ins. +hcr + y1 LA fr. N course
L
[( Lat) + ( Dep)] = Corr. Lat + Corr. Dep
y1
y1 = k tan k Transit Rule
|Latcourse |
hcr LA fr. N |Lat| [( Lat) + ( Dep)] = Corr. Lat + b
el. B = el. ins. +hcr y2 y2 |Depcourse |
LA fr. N [( Lat) + ( Dep)] = a + Corr. Dep
y2 = k tan B |Dep|
Corrected Length, Bearing/Azimuth from North
Corr. Lat + Corr. Dep SHIFT [2][3] r Corr. LCorr. A
TRAVERSE (Angular Measurement) (+)clockwise
SHIFT [2][1] arg[Corr. LCorr. A] = Corr. A Corr. fr. N ()counter cw
Interior Angle (Closed Traverse) Corr. fr. S = 180 Corr. fr. N
= 180(n 2) Omitted Measurement (One Traverse Unknown)
Exterior Angle (Closed Traverse) L = LA fr. N
(+)clockwise
= 180(n + 2) SHIFT [2][1] arg[LA fr. N] = A fr. N fr. N ()counter cw
fr. S = 180 fr. N
Angle To The Right
Clockwise
Angle To The Left
Counter Clockwise AREA BY DOUBLE MERIDIAN DISTANCE
Deflection Angle AND DOUBLE PARALLEL DISTANCE
= 360 (Closed Traverse) BY DMD
+
+, R, Right: Clockwise DMDfirst = Depfirst Lat Dep DMD 2A
, L, Left: Counter Clockwise DMDnext = DMDfirst + Depfirst + Depnext Lat1 Dep1DMD1 2A1
Bearing DMDlast = Deplast Lat2 Dep2 DMD2 2A2
MODE [3][2]
NE, NW, SE, SW 2Acourse = DMD Lat x for DMD
Due North, Due East, Due West, Due South 1 y for Lat Lat n DepnDMDn 2An
Atotal = | 2Acourse | SHIFT [1][3][5]
If AB : NE then AB : SW 2 1
A total = 2 | xy|
AB = BA NW
Azimuth BY DPD
Dep Lat DPD 2A
Clockwise from N (Land) DPDfirst = Lat first
Dep1 Lat1DPD1 2A1
Clockwise from S (Navigation) DPDnext = DPDfirst + Lat first + Lat next
A fr. N Dep2 Lat 2 DPD2 2A2
A 180 = A A fr. S DPDlast = Lat last MODE [3][2]
2Acourse = DPD Dep x for DPD
1 y for Dep Depn Lat nDPDn 2An
Atotal = | 2Acourse | SHIFT [1][3][5]
TRAVERSE (Linear Measurement) 2 1
A total = 2 | xy|
Lat
OMITTED MEASUREMENTS
Dep SIMPLE CURVES
Latitude Departure Radius of Curvature
Lat = L cos Dep = L sin Arc Basis (20m arc) 20 m LC
1145.916 20 RI
180
Rec(L, ) = Lat, Dep R= D
D
= I R D
R I
Traverse Length Bearing Chord Basis (20m chord)
20 m 10 m
Dep 10 20/2 D
L = Lat 2 + Dep 2 tan = | | R= D = sin ( 2 ) D
sin( ) R R R
Lat 2
D 2
Pol(Lat, Dep) = L, Length of Curve
RI PI I
Sign Convention (After Using Formula) LC = RIrad = 180
T T
Lat: N + S Tangent Distance LC E
I
Dep: E + W T = R tan 2 PC M PT
Long Chord Distance C
I
CLOSED TRAVERSE C = 2R sin 2
R R
Lat = 0 Dep = 0 Middle Ordinate I
I
M = R (1 cos 2)
Disclosure PI: point of intersection
Lat 0 Latitude Disclosure External Distance PC: point of curvature
I
Dep 0 Departure Disclosure E = R (sec 2 1) PT: point of tangency
Linear Error of Closure Deflection Angle of a Point on the Curve
a
=2
LEC = ( Lat)2 + ( Dep)2
a
tan = b
Relative Precision b R
LEC Ra
RP = cos = R
Perimeter PC Ra
Station
BALANCING THE TRAVERSE Sta. PC = Sta. PI T
Sta. PT = Sta. PC LC
Adjustment (with sign convention)
Corr. Lat = Prelim. Lat CLat COMPOUND CURVES
Corr. Dep = Prelim. Dep CDep REVERSE CURVES
Compass Rule
L
course
CLat = Lat Perimeter
Lcourse
CDep = Dep Perimeter
Transit Rule
|Lat|course
CLat = Lat |Lat|
|Dep| course
CDep = Dep |Dep|
