Traverse
A traverse is a series of consecutive lines whose ends have been
marked in the field, and whose lengths and directions (angle,
bearing or azimuth) have been determined from measurements.
Closed Traverses
Geometrically and
mathematically closed
traverse
Geometrically open,
mathematically closed
traverse
Traverse
Open Traverse
Geometrically and
mathematically Open
Open traverses should be avoided because they offer no
means of checking for errors or mistakes
Closed Traverse
Step 1: Angle Misclosure
For a closed loop traverse with n
internal angles, the check that is
used is:
0
=
n
"
2
*180
# ( )
Check the error with the
Permissible misclosure (c)
!
c =K n
!
n is the number of angles
K is a constant depends on the level
of accuracy.
Closed Traverse
Example 10.1 (textbook)
Check Interior Angle Closure
Observed
A
B
C
D
E
= 1000 45’ 37”
= 2310 23’ 43”
= 170 12’ 59”
= 890 03’ 28”
= 1010 34’ 24”
Total = 540000’ 11”
Adjusted
1000 45’ 35”
2310 23’ 40”
170 12’ 56”
890 03’ 27”
1010 34’ 22”
= 5400 00’ 00”
Should = 5400 00’ 00” = (n-2)*180
Misclosure = 00’ 11” = 11”
Adjustment = 11/5 = -2.2” per angle
Closed Traverse
Step 2: Compute Azimuths/Bearings
Example 10-2 (textbook)
Azimuths are horizontal angles
measured clockwise from any
reference meridian (North).
The bearing is the actual horizontal
angles between a reference meridian
(North or South) and the line.
Closed Traverse
Step 2: Compute Azimuths/Bearings
Example 10-2 (textbook)
Adjusted Angles
A = 1000 45’ 35”
B = 2310 23’ 40”
C = 170 12’ 56”
D = 890 03’ 27”
E = 1010 34’ 22”
Azimuths of AW = 2340 17’ 18”
Measured angle WAE = 1510 52’ 24”
AB = 2340 17’ 18”+ 1510 52’ 24”+ 1000 45’
35”- 3600 = 126055’17”
BA = 126055’17” + 1800 = 306055’17”
BC = 306055’17”+ 2310 23’ 40”
= 538018’58” -3600 = 1780 18’58”
CB = 1780 18’58” + 180 = 358018’58”
etc …
Closed Traverse
Step 3: Compute Latitudes and Departures
Once all the azimuths are calculated, traverse closure is checked
by computing the departure, or easting (ΔX) and latitude, or
northing (ΔY) of each line.
"X = L sin #
"Y = L cos #
where L is the horizontal length
!
Example 10-3 (textbook)
Closed Traverse
Step 4: Linear Misclosure and Relative Precision
If all angles and distances were
measured perfectly, the algebraic sum
of the departures of all lines in the
traverse should equal zero. Likewise,
the algebraic sum of all latitudes should
equal zero.
Cx = "#X
Cy = "#Y
where:
Cx = total closure distance of X
Cy = total closure distance of Y
!
Example 10-3 (textbook).
Closed Traverse
Step 4: Linear Misclosure and Relative Precision
The error of linear closure (E) is
determined using Pythagorean’s
Theorem as:
E = Cx2 + Cy2
E
Relative Pr ecision =
P
P is the traverse perimeter or
total length
Example 10-3 (textbook).
Closed Traverse
Step 5: Traverse Adjustment (Compass Rule)
For any closed traverse the linear
misclosure must be adjusted (or
distributed) throughout the traverse to
“close” or “balance” the figure.
ABx _ Corr = Cx
ABy _ Corr = Cy
AB
P
AB
P
ABx_Corr is amount of adjustment
for length AB in the X direction,
! ABy_Corr is amount of adjustment
for length AB in the Y direction,
Example 10-4 (textbook)
Closed Traverse
Step 6: Calculate Final Coordinates
Using adjusted lats and deps and the
coordinates of your starting point (A),
compute coordinates of all traverse
points (B, C, D, E)
X = X coordinate of the previous point + ΔX
Y = Y coordinate of the previous point + ΔY
Example 10-4 (textbook)
Field Procedure
Objective
♦
♦
♦
♦
Learn the principles of running a closed
field traverse.
A
Learn how to compute a traverse (by hand
or using Excel) and properly adjust the
measured values of a closed traverse to
achieve mathematical closure.
Determine the error of closure and compute
the accuracy of the work.
Establish horizontal control points for the
Area A.
D
Area A
B
C
Field Procedure
Area A
♦
♦
♦
Azimuth of AB is given (232o42’40”).
Easting and Northing of A (X,Y)
♦ (324540.698 m, 5270414.258 m)
♦ Newfoundland-MTM Zone 1
N
CP1
Start your traverse on one corner of the
area you staked out.
♦
Measure the horizontal angle and distance
between the two adjacent points.
♦
Each horizontal angle should be measured B
using the telescope in direct and reverse CP2
position. Record the average of the angles.
♦
Compute the misclosure for the geometry
and check that the internal angles of your
parcel sum to (n-2) *180 (should be within ±
30’ of 360°).
A
D
Area A
C