1. Traversing 1

2. Required readings: 9-1,9-2.1,9-2.2, 9-3 to 9-8 &9-10
10-1 to &10-8, 10-10, 10-11, 10-15, and 10-17
Required solved examples: 10-1 to 10-4
Required figures: 10-1, tables 10-1 to 10-5

3. Traversing
Definition: A traverse is a series of consecutive lines whose lengths and directions have been measured.
Traversing: The act of establishing traverse stations and making the necessary measurements.
Why?
Closed (polygon or link) and opened traverses 2

4. Procedure
Grass
N (mag) A C D E B
Assume that you wanted to map “calculate coordinates of the building, trees, and the fence in the drawing, you are given points A and B only, cannot measure angle and distance to corner F or the trees!! F
You need to construct new control points “points of known precise coordinates” such as C, D, and E to measure from.
You do that with a traverse

6. Traverse Notations
We will only discuss closed Traverse with interior angles measured.
The polygon corners will be numbered or lettered in anti-clockwise direction.
All angles are measured in a clockwise direction, and the average of direct and reverse readings is computed at all the angles.
Angles are designated with three letters, the backsight station will be given first, the occupied station second, and the forsight station third. 3

8. Traverse Stations Successive stations should be inter visible.
Stations are chosen in a safe, easy to access places.
Lines should be as long as possible, and as equal as possible, Why?
Stations must be referenced to retrieve them if lost 5

10. Traversing by Interior Angles
A polygon is established around the site
All internal angles and all horizontal distances are measured
Each angle is measured in direct and reverse, the average is a single observation of the angle, how many readings?
Each angle is observed at least three times, how many readings?
A line of known direction should either be given or assumed, what is a line with known direction?
If the line of known direction is not a member of the traverse, the angle to a traverse member should be measured. Why? (SITES 1 AND 2 PROJECT 1) 2

11. The concept of Angle Misclosure
Here is how the measured traverse will look:
Line AB was correct A B c D
Line BC was correct, but angle B was wrong
The rest of the lines and angles are correct A’

12. Angle Misclosure
The sum of internal angles of a polygon of (n) points =
(n - 2) * 180o
Angle misclosure = difference between the sum of the measured angles and the geometrically correct total for the polygon.
The misclosure is divided equally among the readings keeping in mind the measuring accuracy, and should be done at the beginning of the adjustment.
Accuracy Standards: c = k * n where (n) is the number of points.
K: a constant defined according to which standards used, example: The Federal Geodetic Control Subcommittee: 1.7, 3, 4.5, 10, and 12” for first-order, second-order class I, second-order class II, third-order class I, third-order class II. 3

13. The concept of Linear Closing ErrorB c D
Assume that the traverse in reallity was a perfect square.
Assume that there was an error in measuring the length AB only, all other lengths and angles were correct A’
ΔE
ΔN
- A will close at A’,
- AA’ is the linear closing error

14. If the traverse is closed, then ΔX = 0 and ΔY = 0
XDA
XCD N
- ve
- ve D
ΔY C
XBC
ΔX
If the traverse is closed, then
ΔX = and
ΔY = 0 A’ A
XAB ? B E ?
If the traverse is not closed,
+ ve
+ ve
Then ΔX = Xw and ΔN = Ycw

15. Computations of Linear Closing Error
If he closing error is (W) then
Xw = ΔX and
Yw = ΔY,
W = length of closing error =  Xw2 + Yw2
Fractional Closing error = traverse precision = W /  L

16. Traverse Adjustment Two kinds of misclosures.
Compute and adjust the angle misclosure
Compute the linear misclosure:
Compute the azimuth of a traverse side
Compute the azimuth of all the sides
Compute the departure and latitude of all the sides
Compute the Misclosure in X direction = sum of the departures.
Compute the Misclosure in Y direction = sum of the latitudes.
Compute the linear misclosure
Use the Compass (Bowditch) rule to adjust:
-(total dep or lat misclosure)
Correction in dep or lat for AB =
x AB length
traverse perimeter 4

17. - Use Bowdich (Compass) rule to compute the adjustments for
- Use Bowdich (Compass) rule to compute the adjustments for departures and latitudes of all sides,
for a line such as AB:
-(total departure misclosure)
Correction in departure for AB =
x length AB
traverse perimeter
And,
-(total latitude misclosure)
Correction in latitude for AB =
x length AB
traverse perimeter
Add the corrections to the departure or the latitude of each line. Get the adjusted departure latitude
Compute the adjusted point coordinates using the corrected
departure/latitude:
Xi = X i-1 + D X
Yi = X i-1 + D Y
Check that the misclosure is zero.

18. To solve a problem, it is easier to use a table such as table 10-4
Review equations in section
Three checks:
Compare adjustments to errors
After corrections are added, check that the sum of longitudes is zero, same for longitudes
Compare coordinates of last and first points after adjustment
It is important to practice how to compute length and azimuth from departure and latitude, or from coordinates:
tan(azimuth) = departure
latitude
departure
latitude
length = =
sin (azimuth)
cos (azimuth)
departure = D X = d (sin azimuth)
latitude = D Y= d (cos azimuth) 5

19. 0.00 -0.54 +0.72 D sin (Az) D cos (Az) Correction Balanced Station
Length (ft) L
Azimuth AZ
Departure
Latitude
-(Wx/P)* L
-(Wy/P)* L X Y A
10,000
285.10 ’
125.72
255.88
-0.06
+0.08 B
10,125.66
10,255.96
610.45 ’
590.77
-0.13
+0.18 C
10,716.3
10,102.4
720.48 ’
-0.15
+0.21 D
10,523.58
203.00 ’
-5.99
202.91
-0.05
+0.06
-6.04 E
10,517.54
747.02
388.5
-0.14
+0.19
Sum P=
Wx =+0.54
Wy =-0.72
-0.54
+0.72
0.00

20. Linear Misclosure = ft
Relative precision = 0.90 / 2466 = 1: 2700

21. Traverse Area C D B E A Traverse area = 1 S { Xi (Yi+1 - Yi-1)} 2
Multiply the X coordinate of each point by the difference
in Y between the following and the preceding points, half the sum
is the area
Formula page 27-4 will work for traverses lettered in a clockwise direction, but it will give a correct area with a negative sign.
The formula should work if you switch the X and the Y. 6