TUS REFRESHER COURSE
TRAVERSING
Presented by
Daw Than Mar Swe
Associate Professor
Department of Civil Engineering
Mandalay Technological University (MTU)
21.4.2022
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Outlines
• Introduction
• Methods of Traversing
• Plotting Traverse Survey
• Checks
• Closing Error
• Balancing a Traverse
• Computation of Area of A Closed Traverse by Coordinates
• Omitted Measurements
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Introduction
The word traverse literally means ‘passing across’.
In surveying it means ‘determining the lengths and directions of
consecutive lines’.
The linear measurements are made with a chain or tape and
the relative directions of the lines are measured with a chain,
compass or theodolite.
(a) Chain (b) Tape (c) Compass (d) Theodolite
Figure 1. Instruments for Surverying
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(Continued)
Traversing consists of reconnaissance (selecting, marking
and referencing stations), picking up details, and booking the
field notes.
Traverse are classified as either closed or open.
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Closed Traverse
A traverse is said to be a closed one if it returns to the starting
point, thereby forming a closed polygon.
In addition, a traverse which begins and ends at the points
whose positions on the plan is known are also referred to as a
closed traverse.
A closed traverse is employed for locating the boundaries of
lakes and woods across which tie lines cannot be measured,
for area determination, control for mapping, and for surveying
moderately large areas.
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(Continued)
Figure 2. Closed Traverse
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Open Traverse
An open traverse is one that does not return to the starting
point.
It consists of a series of lines expanding in the same direction.
An open traverse cannot be checked and adjusted accurately.
It is employed for surveying long narrow strips of country, e.g.
the path of a highway, railway, canal, pipelines, coastline,
transmission line, etc.
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(Continued)
Figure 3. Open Traverse
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Methods of Traversing
The precision usually specified for traversing requires the use
of a steel tape and the theodolite.
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Plotting Traverse Survey
The traverse can be plotted by any of the following methods
depending on the data collected or reduced.
1) By Parallel Meridians Through Each Station
2) By Included Angles
3) By Tangents
4) By Chords
5) By Rectangular Coordinates
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1) By Parallel Meridians Through Each Station
Figure 4. Plotting Traverse by Parallel Meridians
Meridian: the fixed direction in which the bearings of survey lines are
expressed. (north-south reference line)
Magnetic Meridian: is employed as a line of reference on rough
surveys.
Bearing: the horizontal angle between the reference meridian and the
survey line measured in clockwise or anticlockwise direction.
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2) By Included Angles
Figure 5. Plotting Traverse by Included Angles
The included angle = F.B. of the forward line – B.B. of the previous line
= a negative value + 360 ိ (exterior included angle)
= a positive value (interior included angle)
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3) By Tangents
Figure 6. Plotting Traverse by Tangents
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4) By Chords
Figure 7. Plotting Traverse by Chords
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5) By Rectangular Coordinates
Figure 8. Plotting Traverse by rectangular coordinates
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(Continued)
The latitude of a line is its
projection onto the reference
meridian (northsouth line). The
distance measured towards the
north is called northing, whereas
that measured towards the south is
called southing.
The departure of a line is its
projection onto a line at right angles
of the reference meridian. Any
distance measured towards the east
is called easting, whereas that
measured towards the west is called Figure 9. Representing Latitude
westing. and Departure
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(Continued)
The latitudes and departures of the traverse lines can be
calculated if the reduced bearings and lengths of the lines are
known.
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(Continued)
The coordinates of any point, i.e., the latitude and the
departure, when measured with respect to the origin are
called independent coordinates, whereas if measured with
respect to the previous point are called consecutive
coordinates.
The method of plotting by independent coordinates is
better than by consecutive coordinates.
In the former case, the error is localised.
In the latter case, error accumulates.
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Checks
1) Closed Traverse
Check on Linear Measurements
i) Every line of the traverse is measured twice. The two
measurements are done with the same precision, on different
days and in opposite direction.
ii) Sum of northings should be equal to sum of southings. Sum of
eastings should be equal to sum of westings.
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(Continued)
Check on Angular Measurements
i) Traversing by included angles: The sum of interior included
angles should be = (2n – 4) right angles, and the sum of exterior
included angles should be = (2n + 4) right angles, where n is the
number of sides of the traverse.
ii) Traversing by deflection angles: The algebraic sum of the
deflection angles should be = 360° (the right-hand deflection
angles are taken as positive and the left-hand deflection angles
are taken as negative).
iii) Traversing by direct observation of bearings: The fore bearing
of the last line is compared with the back bearing of the line at
the initial station. The two values should have a difference of
180°.
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(Continued)
2) Open Traverse
Though the linear errors cannot be determined, the angular
errors may be found by some of the methods discussed as
follows.
i) Cut-off lines
ii) Well-defined point
iii) Astronomical observations
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Closing Error
• In a closed traverse if the work is correct, the algebraic sum of
the latitudes (L) should be equal to zero, i.e., ∑L = 0, and the
algebraic sum of the departures (D) should also be equal to
zero, i.e., ∑D = 0.
Figure 10. Closing Error
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Balancing a Traverse
A traverse is balanced by applying correction to latitudes and
departures.
Following are the rules/methods of balancing a traverse.
1) Bowditch rule
2) Transit rule
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1) Bowditch rule
It is also called compass rule. It is used to balance a traverse
when the linear and angular measurements are equally
precise.
Correction to latitude (or departure of any side)
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2) Transit rule
It is employed when the angular measurements are more
precise as compared to the linear measurements (theodolite
traversing).
Correction to latitude (or departure of any side)
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(Continued)
If the corrections are to be applied separately, then the following
rules may be used:
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Graphical Adjustment of Closing Error
In case where the closing error needs to be adjusted, a
graphical adjustment is made.
This method of adjustment, known to be proportionate method, is
based on Bowditch rule and is used when traversing with compass.
Figure 11. Proportionate Method
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Gale’s Traverse Table
Traverse computations are usually done in a tabular form.
The following steps are involved in theodolite traversing.
1) In the case of theodolite traversing, the included angles are
adjusted to satisfy the geometrical conditions.
2) From the observed bearing of a line, the whole circle bearings
of all other lines are calculated and then these bearings are
reduced to those in the quadrantal system.
3) From the lengths and computed reduced bearings of the lines,
the consecutive coordinates, i.e., latitudes and departures are
worked out.
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(Continued)
4) Check ∑L = 0 and ∑D = 0. If not, a correction is applied using
the transit rule. In the case of a compass traverse, the correction
is applied by Bowditch rule.
5) The origin is so selected that the entire traverse lies in the
north-east quadrant.
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Table 1. Gale’s Traverse Table
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Computation of Area of a Closed Traverse
by Coordinates
If the coordinates of the traverse stations are known.
Arrange the coordinates for N = 4
Figure 12. Area of Coordinates
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Omitted Measurements
Often it becomes impossible to measure all the lengths and
bearings of a closed traverse.
The values of the missing quantities can be determined,
provided they do not exceed two in number.
The algebraic sum of the all the latitudes and that of all the
departures are each zero, i.e. ∑L = 0 and ∑D = 0
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(Continued)
If the missing data be the bearings of any two adjacent lines of
a closed traverse.
Let ABCDEFA be a closed traverse and let the bearings of two
adjacent lines CD and DE be missing.
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(Continued)
Sometimes the bearings of two lines, which are not adjacent,
are missing.
let the bearings of lines CD and FA are missing.
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Solution
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Let the length and the bearing of line DA be l and θ.
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From ∆ADE,
DE EA DA
= =
sin EAD sin ADE sin AED
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Thank You Very Much
For Your Attention!
