1. Horizontal Control
Horizontal control is required for initial survey work (detail surveys) and for setting out.
The simplest form is a TRAVERSE - used to find out the co-ordinates of
CONTROL or TRAVERSE STATIONS.

2. Grass
N (mag) A C D E B

3. Horizontal Control
Horizontal control is required for initial survey work (detail surveys) and for setting out.
The simplest form is a TRAVERSE - used to find out the co-ordinates of
CONTROL or TRAVERSE STATIONS.

4. Horizontal Control A B C D E F B C D E F A G
Horizontal control is required for initial survey work (detail surveys) and for setting out.
The simplest form is a TRAVERSE - used to find out the co-ordinates of
CONTROL or TRAVERSE STATIONS.
Horizontal Control
a) POLYGON or LOOP TRAVERSE
There are two types : -
b) LINK TRAVERSE A B C D E F B C D E F A G

5. A B C D E F G X Y Both types are closed. a) is obviously closed
b) must start and finish at points whose co-ordinates are known,
and must also start and finish with angle observations to other known points.
Working in the direction A to B to C etc is the FORWARD DIRECTION
This gives two possible angles at each station.
LEFT HAND ANGLES
RIGHT HAND ANGLES

6. Using a theodolite we can measure all the internal angles.B C D E F
Consider the POLYGON traverse
The L.H.Angles are also the
INTERNAL ANGLES
Using a theodolite we can measure all the internal angles.
Σ (Internal Angles) =
( 2 N ) * 900
The difference between
Σ Measured Angles and Σ Internal Angles
is the Angular Misclosure
(or 3)
Maximum Angular Misclosure =
Theodolite *  (No. of Angles)
2 * Accuracy of
(Rule of thumb)

7. A F B C Standing at A looking towards F - looking BACK ΘAB ΘAF
Hence ΘAF is known as a BACK BEARING A B C F
ΘBA
ΘBC
LH angle ABC
Angle FAB
(LH angle)
Standing at A looking towards B - looking FORWARD
Hence ΘAB is known as a FORWARD BEARING
BACK BEARING (ΘAF ) L.H.ANGLE (<FAB)
= NEXT FORWARD BEARING (ΘAB)
Reminder: every line has two bearings
ΘBA =
ΘAB
1800
FORWARD BEARING ( )
BACK BEARING (

8. Observed Clockwise Horizontal Angle
Traverse Example
12” / 4 = 3”
Observations, using a Zeiss O15B, 6” Theodolite, were taken in the field for an
anti - clockwise polygon traverse, A, B, C, D.
Traverse Station
Observed Clockwise Horizontal Angle
‘ “ C N B A
- 3” A B C D D
Σ (Internal Angles) =
Line
Horizontal
Distance
Σ (Internal Angles) should be
(2N-4)*90 =
Allowable = 3 * 6” * N= 36” AB
638.57
OK - Therefore distribute error BC
The bearing of line AB is to be
assumed to be 00 and the
co-ordinates of station A are
( mE ; mN) CD DA

9. LINE
BACK BEARING
STATION
ADJUSTED LEFT
HAND ANGLE
FORWARD
BEARING
WHOLE
CIRCLE q
HORIZONTAL
DISTANCE D + = + =
Use Distance and Bearing to go from
POLAR to RECTANGULAR to get
Delta E and Delta N values.
Check 1 AD A
+or-
1800
638.57 AB BA B C D
+or-
1800 BC CB CD DC DA
+or-
1800 AD

10. WHOLE
CO-ORDINATE DIFFERENCES
HORIZONTAL
CIRCLE
DISTANCE
CALCULATED
BEARING q D D E D N
638.57
0.000 G
-0.094
-0.654

11. =+931.227m =+638.570m =-3677.764m =+2107.313m D EBC D NCD D NBC D ECD
NAB
= m
= m A D
NDA D
EDA
= m D

12. e is the LINEAR MISCLOSURE
e =  (eE2 + eN2 ) B eE A eN e A’ D

13. Fractional Linear Misclosure (FLM) = 1 in G D / e
WHOLE
CO-ORDINATE DIFFERENCES
HORIZONTAL
CIRCLE
DISTANCE
CALCULATED
BEARING q D D E D N
638.57
0.000 G G
-0.094
-0.654 eE eN
e =  (eE2 + eN2) =  ( ) = 0.661m
Fractional Linear Misclosure (FLM) = 1 in G D / e
= 1 in ( / 0.661) = 1 in 13500
[To the nearest 500 lower value]

14. Acceptable FLM values :-
1 in for most engineering surveys
1 in for control for large projects
1 in for major works and monitoring for
structural deformation etc.

15. Fractional Linear Misclosure (FLM) = 1 in G D / e
WHOLE
CO-ORDINATE DIFFERENCES
HORIZONTAL
CIRCLE
DISTANCE
CALCULATED
BEARING q D D E D N
638.57
0.000 G G
-0.094
-0.654 eE eN
e =  (eE2 + eN2) =  ( ) = 0.661m
Fractional Linear Misclosure (FLM) = 1 in G D / e
= 1 in ( / 0.661) = 1 in 13500
Check 2
If not acceptable ie 1 in 3500 then we have an error in fieldwork

16. If the misclosure is acceptable then distribute it by: -
a) Bowditch Method - proportional to line distances
b) Transit Method - proportional to D
N values E
and
c) Numerous other methods including Least Squares
Adjustments

17. Bowditch and transit methods to be covered next