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EXAMPLE 2

polygon traverse

angular misclosure

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 2

Source: Uren and Price (2007)

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EXAMPLE 3

polygon traverse A1234A starts at Control Point A (at

642.515 mE, 483.980 mN) and is orientated to ControlPoint B (at 548.005 mE, 594.279 mN) i.e. AB = North

calculate adjusted coordinates of 14 and the fractional

linear misclosure

Source: Uren and Price (2007)

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LINK

TR VERSE

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The co-ordinates of Xare 1000.000Eand 1000.000N

and those ofYare 897.274Eand 1126.231Nas

determined using the main traverse. The direction XAisdue North.

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

measure all angles of a link traverse

on the same side(i.e. right orleft in

the forward direction)

usually a known Control Point before

Xan initial back bearing

and a further known Control Point after

Ya final forward bearing

to calculate the angular misclosure:sum of angles (including atX and Y) = (final forward bearinginitial back bearing) + (m 180)

Note: this example uses only coordinates to determine survey errorsLine

Length (m)

WCB (o' ") WCB

(decimal)

Easting

difference

(m)

Northing

difference

(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings

(m)

Corrected

Northings

(m)

dE (m) dN (m)

XA 138.163

AB 115.311

BC

186.967

CD

97.772

DY 160.221

f

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Line

Length (m)

WCB (o' ") WCB

(decimal)

Easting

difference

(m)

Northing

difference

(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings

(m)

Corrected

Northings

(m)

dE (m) dN (m)

XA 138.163

AB 115.311

BC

186.967

CD

97.772

DY 160.221

The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

to calculate Whole Circle

Bearing:Forward bearing = Back bearing + left-hand angle

Th di t f X 1000 000E d 1000 000N d

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Line

Length (m)

WCB (o' ") WCB

(decimal)

Easting

difference

(m)

Northing

difference

(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings

(m)

Corrected

Northings

(m)

dE (m) dN (m)

XA 138.163 000 00 00 0.000

AB 115.311 305 26 45 305.446

BC

186.967

265 39 03

265.651

CD

97.772

167 54 29

167.908

DY 160.221 078 50 24 78.840

The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

to calculate Eastingdifference:

E = D sin(WCB)

to calculate Northingdifference:

N = D cos(WCB)

where D is the measured length

Th di t f X 1000 000E d 1000 000N d

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Line

Length (m)

WCB (o' ") WCB

(decimal)

Easting

difference

(m)

Northing

difference

(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings

(m)

Corrected

Northings

(m)

dE (m)

dN (m)

X

XA 138.163

000 00 00

0.000

0.000

138.163

A

AB 115.311 305 26 45 305.446 -93.940 66.873 B

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

CD 97.772 167 54 29 167.908 20.481 -95.603 D

DY 160.221 078 50 24 78.840 157.191 31.011 Y

The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

Easting coordinate= E coord.

of previous point + E

Northing coordinate= N coord.

of previous point + N

Th di t f X 1000 000E d 1000 000N d

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

MISCLOSURE (error)in a link traverse, coordinates of

start and finish points are bothknown

in this case, E-error =

N-error =

Line Length (m) WCB (o' ") WCB

(Decimal)

Easting

difference(m)

Northing

difference(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings(m)

Corrected

Northings(m)

dE (m) dN (m)

X 1000.000 1000.000

XA 138.163

000 00 00

0.000

0.000

138.163

A

1000.000

1138.163

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

719.632

1190.857

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265

Y (actual)

897.274

1126.231

Th di t f X 1000 000E d 1000 000N d

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

MISCLOSURE (error)in a link traverse, coordinates of

start and finish points are bothknown

in this case, E-error =

897.304

897.274 = 0.030 m

N-error =

1126.2651126.231 = 0.034 m

Line Length (m) WCB (o' ") WCB

(Decimal)

Easting

difference(m)

Northing

difference(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings(m)

Corrected

Northings(m)

dE (m) dN (m)

X 1000.000 1000.000

XA 138.163

000 00 00

0.000

0.000

138.163

A

1000.000

1138.163

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

719.632

1190.857

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265

Y (actual)

897.274

1126.231

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The co ordinates of X are 1000 000E and 1000 000N and

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

MISCLOSURE (error)to calculate linear misclosure

e = (E-error2+ N-error2)

= 0.046 m

total surveyed length = 698.434 m

fractional linear misclosure=

1 intotal length

= 1 in 15,299.03

eLine Length (m) WCB (o' ") WCB

(Decimal)

Easting

difference(m)

Northing

difference(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings(m)

Corrected

Northings(m)

dE (m) dN (m)

X 1000.000 1000.000

XA 138.163

000 00 00

0.000

0.000

138.163

A

1000.000

1138.163

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

719.632

1190.857

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265

Y (actual)

897.274

1126.231

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if fractional linear misclosure is within specification for the

survey then the errors in the E and N coordinates can be

distributed proportionately throughout the survey

use the Bowditch Methodcreates a geometricallycorrect plan

this does not

correct the

actual errors

in the survey

Source: Uren and Price (2007)

The co ordinates of X are 1000 000E and 1000 000N and

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

BOWDITCH CORRECTIONto calculate Easting correction:

dE = E-error length of traverse segmenttotal length of traverse

dN = N-error length of traverse segment

total length of traverse

then apply these corrections to

the differences(columns 5 & 6)

then recalculate the coordinates

Line Length (m) WCB (o' ") WCB

(Decimal)

Easting

difference(m)

Northing

difference(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings(m)

Corrected

Northings(m)

dE (m) dN (m)

X 1000.000 1000.000

XA 138.163

000 00 00

0.000

0.000

138.163

A

1000.000

1138.163

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

719.632

1190.857

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265

Y (actual)

897.274

1126.231

The co ordinates of X are 1000 000E and 1000 000N and

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

BOWDITCH CORRECTIONto calculate Easting correction:

dE = E-error length of traverse segmenttotal length of traverse

dN = N-error length of traverse segment

total length of traverse

then apply these corrections to

the differences(columns 5 & 6)

then recalculate the coordinates

Line Length (m) WCB (o' ") WCB

(Decimal)

Easting

difference(m)

Northing

difference(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings(m)

Corrected

Northings(m)

dE (m) dN (m)

X 1000.000 1000.000

XA 138.163

000 00 00

0.000

0.000

138.163

A

1000.000

1138.163

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

719.632

1190.857

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265

Y (actual)

897.274

1126.231

The co-ordinates of X are 1000 000E and 1000 000N and

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Line

Length (m)

WCB (o' ") WCB

(decimal)

Easting

difference

(m)

Northing

difference

(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings

(m)

Corrected

Northings

(m)

dE (m) dN (m)

X 1000.000 1000.000 1000.000 1000.000

XA 138.163 000 00 00 0.000 0.000 138.163 A 1000.000 1138.163 -0.006 -0.007 -0.006 138.156 999.994 1138.156

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036 -0.005 -0.006 -93.945 66.867 906.049 1205.023

BC

186.967

265 39 03

265.651

-186.429

-14.179

C

719.632

1190.857

-0.008

-0.009

-186.437

-14.188

719.613

1190.836

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

-0.004

-0.005

20.477

-95.607

740.090

1095.228

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265 -0.007 -0.008 157.184 31.003 897.274 1126.231

The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

show the E-error, N-error and

the linear misclosure below the

main table

show the total survey (traverse)

length and the fractional linear

misclosure below the main table

The co-ordinates of X are 1000 000E and 1000 000N and

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The co-ordinates of Xare 1000.000Eand 1000.000N and

those ofYare 897.274Eand 1126.231Nas determined

using the main traverse. The direction XAis due North.

show the E-error, N-error and

the linear misclosure below the

main table

show the total survey (traverse)

length and the fractional linear

misclosure below the main table

Line Length (m) WCB (o' ") WCB

(Decimal)

Easting

difference(m)

Northing

difference(m)

co-

ordinates

Eastings

(m)

Northings

(m)

Adjustments Corrected E

diff (m)

Corrected

N diff (m)

Corrected

Eastings(m)

Corrected

Northings(m)

dE (m)

dN (m)

X 1000.000

1000.000

1000.000

1000.000

XA 138.163

000 00 00

0.000

0.000

138.163

A

1000.000

1138.163

-0.006

-0.007

-0.006

138.156

999.994

1138.156

AB 115.311 305 26 45 305.446 -93.940 66.873 B 906.060 1205.036 -0.005 -0.006 -93.945 66.867 906.049 1205.023

BC 186.967 265 39 03 265.651 -186.429 -14.179 C 719.632 1190.857 -0.008 -0.009 -186.437 -14.188 719.613 1190.836

CD

97.772

167 54 29

167.908

20.481

-95.603

D

740.113

1095.254

-0.004

-0.005

20.477

-95.607

740.090

1095.228

DY 160.221 078 50 24 78.840 157.191 31.011 Y 897.304 1126.265 -0.007 -0.008 157.184 31.003 897.274 1126.231

Perimeter 698.434 m Y (actual) 897.274 1126.231 -0.030 -0.034

Error (eastings) =

30.337

mm =

0.030

m

Error (northings) = 34.114mm = 0.034m

Overall error = 45.652mm = 0.046m

Total circumference =

698.434

m

Error = 1 in 698.434 / 0.046 = 15299.03(i.e. ~ 15200)

mE mN

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mE mN

A 375.369 543.008

EXAMPLE 2 B 264.507 604.938

coordinates of Control Points: X 601.624 404.041

Y 698.076 384.945calculate adjusted coordinates of 14 and the fractionallinear misclosure

Source: Uren and Price (2007)

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REFERENCES

Irvine W, Maclennan F (1995) Surveying for Construction(5th

Edition). McGraw-Hill Education, Maidenhead.

Schofield W, Breach M (2007) Engineering Surveying(6th Edition)

Butterworth-Heinemann, Oxford.

Uren J, Price WF (2006) Surveying for Engineers (4th Edition).

Palgrave Macmillan, Basingstoke.