Correction Applied in Distance Measurement
Temperature Correction (Add or Subtract)
Ct = αL∆T
α = 11.6x106 ; ∆T = Tf − To
Correction Due to Pull (Add or Subtract)
∆PL (PActual − Po )L
CP = =
AE AE
Correction Due to Sag (To be Subtracted Only)
ω2 L3
Cs =
24(PActual )2
W
ω = Weight per tape length =
L
Correction Due To Slope (To Be Subtracted only)
h2
CSlope =
2S
H = S − CSlope
Normal Tension – the pull used to compensate the
correction due to sag
Csag = Cpull
0.204W√AE
PN =
√PN − Po
Sea Level Correction
′
h
L = L (1 − )
R
MD
CTotal = (Ct )
L
TD = MD ± CTotal
MD
No. of Sag =
L
CTotal = Cs1 + Cs2
Probability
Probable Error Of Single Observation
∑ V2
PEs = ±0.6745√
n−1
Probable Error Of The Mean
∑ V2 PEs
PEm = ±0.675 √ =
(
n n−1 ) √n
Standard Deviation
∑ V2
SD = √
n−1
Standard Error
SD
SE =
√n
Where:
n = no. of obsevation
∑ V 2 = Sum of the square of the residuals
Weighted Observation
The weights are directly proportional to the number of
observations.
w= n
The weights are inversely proportional to the square of
the corresponding probable errors.
1
w= 2
e
The errors are directly proportional to the square roots
of the distances.
e = √L
The errors are inversely proportional to the number of
set-ups. Degree / Angle.
1
e=
n
The weights are inversely proportional to the distances.
1
w=
L
Weighted Observation
wo = Elevation x Weights
∑ wo
MPv =
WT
1
Cal. Tech for w = [MODE 3 | 4 | Shift | MODE | ↓ | 4 |AC | x = Shift 1 | 4 | 2 | =]
e2
Leveling
Elev1 + BS1 = Elev2 + FS2
Two – Peg Test
∆ + elev1 = elev2 + e ∆ + elev1 = elev2 + e
Cal. Tech.
MODE | 5 |1 | ∆ + e = elev2 − elev1 | ∆ − e = elev2 − elev1 | = | ∆= x | e = y |
∆ + elev1 − e = elev2 − e ∆ + elev1 − e1 = elev2 − e2
Level line of Sight LS = elev − e
Error Due to Settlement of the Rod eT = e(TP)
L
No. of Set up NST =
BS+FS
No. of Turning Point NTP = NST − 1
Bubble sensitivity
b−a S π
tan n θ = θrad = rad =
L R 180
Effect of Earth’s Curvature & Reflection
2 hcr
hcr = 0.067k k=√ k = k1 + k 2
0.067
Where: hcr = meters ; k = kilometers
Compass Surveying
Magnet Declination
True Bearing (TB) – Bearing with reference to the true direction
Magnetic Bearing (MB)
Traverse Surveying
Latitude – Projection of North and South Line
Departure – Projection of East and West Line.
Lat = Dcos θ Dep = D sin θ D = √Lat 2 + Dep2
Error of Closure – for a closed traverse, the sum of the latitudes and departures
should be equal to zero.
Linear Error of Closure Relative Error
LEC
LEC = √∑ Lat 2 + ∑ Dep2 RE =
∑P
Area Computation (DMD, DPD, Coordinate method)
DMD DPD
DMD1 = Dep1 DPD1 = DMD1 (Lat1 )
DMD2 = DMD1 + Dep1 + Dep2 DPDn = DMDn (Lat n )
DMDn = DMDn + Depn + Depn 2A = ∑ DPD
(x1 y2 − y1 x2 ) + (x2 y3 − y2 x3 ) + ⋯ + (xn y1 − yn x1 )
A=
2
Balancing Survey
Compass Rule – Total Correction
CLat/Dep L
=
CTotal Lat/Dep ∑ Lat or ∑ Dep
Transit Rule – Arithmetical Sum
CLat/Dep Lat or Dep
=
CTotal Lat/Dep ∑ Lat or ∑ Dep
Tachymetry Survey
D = C + Ks
f
D = c + f + (s)
( )
i
D = (c + f) + x
f x f
=s ; x = i (s)
i
f x′
=
i s′
f x′
′ f
= x = i (Scosθ)
i Scos θ
D = (c + f) + x ′
f
D = c + f + (Scosθ)
( )
i
D = C + K(Scosθ)
Where:
C = (c + f) = Stadia constant H = Dcosθ
f
K = = Stadia factor V = Dsinθ
i
For Continuous Rod
S = Upper Reading − Lower Reading
f ∑K
K=i ;K =
n
The Subtense Bar Method
𝜃 1
tan ( ) =
2 𝐻
1
𝐻=
𝜃
tan ( )
2
Topographic Surveys
𝐷𝑖𝑠𝑡. 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑝 𝐷𝑚𝑎𝑝 𝐴𝑚𝑎𝑝
𝑆𝑐𝑎𝑙𝑒 =
𝐷𝑖𝑠𝑡. 𝑜𝑛 𝑎𝑐𝑡𝑢𝑎𝑙
=
𝐷𝑎𝑐𝑡
(𝑆𝑐𝑎𝑙𝑒 = )2
𝐴𝑎𝑐𝑡
1 −1 (
𝑥
𝑆𝑐𝑎𝑙𝑒 = 𝜃 = tan )
𝑥 𝐷𝑎𝑐𝑡
𝑥 = 𝐶𝑜𝑛𝑡𝑜𝑢𝑟 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 400 𝑔𝑟𝑎𝑑 360°
𝜃= ; 𝜃 = 6400 𝑚𝑖𝑙𝑠
360°
Photographic Surveys
𝑋1 𝑓
=
𝑥2 𝐻 − ℎ
𝑓
𝑆𝑐𝑎𝑙𝑒 =
𝐻−ℎ
𝑥2 = 𝐴𝑐𝑡𝑢𝑎𝑙 𝑠𝑖𝑧𝑒
ℎ𝑚𝑖𝑛 + ℎ𝑚𝑎𝑥
ℎ=
2
Mine Surveying
𝑥 𝑧 𝑧
𝑠𝑖𝑛𝛼 = 𝑥= 𝑦=
𝑦 tan 𝜃𝑑𝑖𝑝 𝑔%
𝑔%
sin 𝛼 =
tan 𝜃𝑑𝑖𝑝
