![Page 1: Traversing. Required readings: 9-1,9-2.1,9-2.2, 9-3 to 9-8 &9-10 10-1 to 10-7.1 &10-8, 10-10, 10-11, 10-15, and 10-17 Required solved examples: 10-1 to](https://reader038.vdocuments.net/reader038/viewer/2022110116/55164fff550346b2068b587a/html5/thumbnails/1.jpg)
Traver
sin
g
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Required readings: 9-1,9-2.1,9-2.2, 9-3 to 9-8 &9-10
10-1 to 10-7.1 &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
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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
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Grass
N (mag)
A
C
D
E
B
Procedure
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
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!!
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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.
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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
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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)
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• Here is how the measured traverse will look:
The concept of Angle Misclosure
A
B c
D
Line AB was correct
Line BC was correct, but angle B was wrong
The rest of the lines and angles are correct
A’
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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.
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A
B c
D
ΔE
ΔN
The concept of Linear Closing Error
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’
- A will close at A’,
- AA’ is the linear closing error
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N
E
D
C
B
A
XAB XBC
XDA XCD
+ ve+ ve
- ve- ve
If the traverse is closed, then
ΔX = 0 and
ΔY = 0
A’
ΔY
ΔX
If the traverse is not closed,
Then ΔX = Xw and ΔN = Ycw
?
?
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Computations of Linear Closing Error
• If he closing error is (W) then
Xw = ΔX and
Yw = ΔY,
W = length of closing error = Xw2 + Yw
2
Fractional Closing error = traverse precision = W / L
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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:
Correction in dep or lat for AB = -(total dep or lat misclosure)traverse perimeter
x AB length
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Correction in departure for AB = -(total departure misclosure)traverse perimeter
x length AB
Correction in latitude for AB = -(total latitude misclosure)traverse perimeter
x length AB
- Use Bowdich (Compass) rule to compute the adjustments for departures and latitudes of all sides, for a line such as AB:
And,
• 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.
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• To solve a problem, it is easier to use a table such as table 10-4• Review equations in section 10-10.• 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
length =departure
sin (azimuth)latitude
= cos (azimuth)
departure = D X = d (sin azimuth)latitude = D Y= d (cos azimuth)
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D sin (Az) D cos (Az) Correction Balanced
Station Length (ft) L
Azimuth AZ
Departure Latitude Departure-(Wx/P)* L
Latitude-(Wy/P)* L
Departure Latitude X Y
A 10,000 10,000
285.10 26 10.0’ 125.72 255.88 -0.06 +0.08 +125.66 +255.96
B 10,125.66 10,255.96
610.45 104 35.2’ 590.77 -153.74 -0.13 +0.18 +590.64 -153.56
C 10,716.3 10,102.4
720.48 195 30.1’ -192.56 -694.27 -0.15 +0.21 -192.72 -694.04
D 10,523.58 9408.34
203.00 358 18.5’ -5.99 202.91 -0.05 +0.06 -6.04 +202.97
E 10,517.54 9611.31
747.02 306 54.1 -517.40 388.5 -0.14 +0.19 -517.54 +388.69
A 10,000 10,000
Sum P=2466.05
Wx =+0.54 Wy =-0.72 -0.54 +0.72 0.00 0.00
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Linear Misclosure = 0.90 ftRelative precision = 0.90 / 2466 = 1: 2700
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Traverse Area
A
B
CD
E
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.