TRAVERSE

Table 1.7: The calculation the area use the D

Stn Bearing Distance Latitude De
NS E

1

2 16 38 12 252.230 241.725 72.262

3 73 19 12 284.210 81.636 272.305

4 195 17 30 384.730 371.028

1 281 04 36 247.840 47.668
Start

Area = ½ [DKLi x Dipati + DKLi + 1 x Dipati + 1……
= ½ [ (337.061 x 72.262) + (660.422 x 272.305)
+ (371.030 x –101.392) + (47.668 x –243.176)]
= ½ [(24356.702) + (179836.213) – (37619.474)
- (11591.714)]
= ½ (204192.915) – (49211.188)
= ½ (154981.727)
= 77490.864 m2
= 7.749 ha

DMD method– Double Meridian Distance

eparture Final Final Coordinate
N/S E / W
W Latitude Departures

Start

337.061 72.262

660.422 416.829

101.392 371.030 587.742

243.176 47.668 243.174

calculation

47.668 72.262
+ 47.668 + 72.262
95.336 144.524
+ 241.725 + 272.305
337.061 416.829
+ 241.725 + 272.305
578.786 689.134
+ 81.636 - 101.392
660.422 587.742
+ 81.636 - 101.392
742.058 486.350
- 371.028 - 243.176
371.030 243.174

43

Coordinate method
Another method to determine the area is to use Coordinate Geometry, o�en called
the COGOComoerdtihnoatde.mTehtihsomd ethod can use when the traverse sta�on have the coordi-
nate valuAen. oTthheer XmaetnhdodYtcoodoertdeirnmaitneesthfoeraereaachis ptooiunsteoCnootrhdeintartaevGeerosemeatrrey,doe�teenrmcailnleeddthe COGO
using a remfeertheondc.eTphoisinmteathnoddacdadniunsgetwhheelna�thteudtreavsearsnedsdtae�poanrhtuavreesthteoctohoerdnineaxttepvoaliunet.aTshe X and
you go arYocuonodrdtihnaetetrsafvoer resaech. pOonincteoenatchhe tproavinerts’se caoreodredtienramteinsedaruesidngetaerremfeirneendce, tphoeinat raenad adding
can be catlhceullaa�tetudd.es and departures to the next point as you go around the traverse. Once each point’s
Calcula�ocnoomrdeintahtoeds ,are determined, the area can be calculated.

Calcula�on method,

Figure 1.28 : Area computa�on using coordinate method

Figure 1.28 : Area computation using coordinate method

For example the traverse have 5 sta�ons are 1, 2, 3, 4 and 5.

For example the traverse have 5 sta�ons are 1, 2, 3, 4 and 5.
AREA = AREA A23B + AREA B34D + AREA D45E – l AREA A21C – AREA C15E
2 AREA = (T2 + T3)(U2 – U3) + (T3 + T4)(U3 – U4) + (T4 + T5)(U4 – U5) – (T2 + T1)(U2 –

U1) – (T1 + T5)(U1 – U5)
EVALUATE;
2 AREA = (U1T2 + U2T3 + U3T4 + U4T5 + U5T1) – (U2T1 + U3T2 + U4T3 + U5T4 + U1T5)

44 44

Calcula�on applica�on in prac�cal: EAST
a) Arrange the coordinate: T1
T2
NORTH T3
U1 T4
U2 T5
U3 T1
U4
U5
U1

b) Then, cross mul�plica�on the NORTH and East value (le� side) and add the
total. Repeat the same process for right side.

c) The area value must get posi�ve. Ignore the nega�ve value.
d) Following is the calcula�on using this method: (Refer Table 7.4)

Area = ½ [ 1000 1241.725 1323.361 952.333 1000.001]
[1000 1072.262 1344.567 1243.175 999.999]

= ½ (5339345.817) – (5184365.237)
= ½ (154980.580)
= 77490.290 m2
= 7.749 ha

45

EXERCISE

1. A 2nd class traverse survey fieldwork has been forma�ed at FIVE (5) sta�on. The
observa�on data from the theodolite are recorded in table below. Calculate the bear-
ing adjustment and determine the final bearing for each line of the traverse.

Stn Bearing Min From Stn Final Bearing To Stn
Bearing 2 1200 30’ 00’’ 1
Face Left Face Right 2 3
3 4
Datum from PC 1200 30’ 00’’ 4 5
5 1
1 1200 30’ 00’’ 3000 30’ 00’’ 1 2

2
3 3230 52’ 27’’ 1430 53’ 08’’

2

3
4 360 44’ 58’’ 2160 44’ 56’’

3

4
5 1320 03’ 49’’ 3120 05’ 22’’

4

5

1 2250 21’ 21’’ 450 20’ 00’’

5

1
2 3000 30’ 40’’ 1200 30’ 60’’

2. Table below shows data for theodolite booking at site. Based on this
informa�on, solve:
i. La�tude and departure for each line
ii. Calculate the Arithme�cal sum of departure and la�tude
iii. Calculate the closing error

Line Bearing Length(M)
AB 343° 54’ 00’’ 235.00
BC 87° 52’ 00’’ 317.50
CD 172° 42’ 00’’ 215.00
DE 265° 14’ 00’’ 281.50

ANSWERS

46

REFERENCE

Main reference suppor�ng the course
Jerry Nathanson (2011), Surveying Fundamentals and Prac�ces. New Jersey: Pearson
Educa�on Inc.

Addi�onal references suppor�ng the course
Ab. Hamid Mohamed (2000), Asas Ukur Kejuruteraan. Skudai Malaysia: UTM.
Arthur Bannister (1998), Surveying. England: Addison Wesley Longman Ltd.
Barry F. Kavanagh, S.J. Glenn Bird (2008), Surveying: Principles and Applica�ons.
New Jersey: Pren�ce Hall.
Barry F. Kavanagh, Dianne K. Sla�ery (2015) Surveying with Construc�on
Applica�ons. England. Pearson educa�on inc.
Charles D. Ghilani, Paul R. Wolf (2012), Elementary Surveying: An Introduc�on to
Geoma�cs. New Jersey: Pearson Educa�on Inc.
Jasmee Jaafar, Redzwan Misran, Adli Redzuan Shaary, Roslina Idris,
Mohd Nasri Md Rani (2016), Asas Ukur Kejuruteraan. Shah Alam Malaysia: UiTM.

47

NAFISAH BINTI HARUN
The Writer is a lecturer in the Department of Civil Engineering,
Sultan Azlan Shah Polytechnic, Behrang Sta�on, Tanjong Malim,
Perak Darul Ridzuan since 2006 and Tuanku Sultanah Bahiyah
Polytechnic for two (2) years, 2004-2005. With 16 years of
teaching experience in Civil Engineering Department,
she specializes in Engineering Survey Course.

NORAYAHATI BINTI NGAGIMAN
The Writer is a lecturer in the Department of Civil Engineering,
Sultan Azlan Shah Polytechnic, Behrang Sta�on, Tanjong Malim,
Perak Darul Ridzuan since 2004. With 16 years of teaching
experience in Civil Engineering Department, she specializes in
Engineering Survey Course.

CHE NORHAYATI BINTI MOHD SALLEH
The Writer is a lecturer in the Department of Civil Engineering,
Sultan Azlan Shah Polytechnic, Behrang Sta�on, Tanjong Malim,
Perak Darul Ridzuan since 2013. With 10 years of teaching
experience in Civil Engineering Department, she specializes
in Engineering Survey Course.

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