Traverse
surveying
GROUP 2:
AGUINALDO, GILBERT
JAVONILLO, AIRA DIOSA
PENA, JULY ANNE
PISCO, VICENTE, JR.
What is traverse surveying?
A traverse consists of a series of
straight lines connecting successive
points. The points defining the ends of
the traverse lines are called traverse
stations or traverse points.
What is traverse surveying?
Distance along the line between successive
traverse points is determined either by direct
measurement using a tape or electronic
distance measuring (EDM) equipment, or
by indirect measurement using tachometric
methods. At each point where the traverse
changes direction, an angular measurement
is taken using a theodolite.
Types of traverse Surveying
Closed traverse: When the lines
form a circuit which ends at the
starting point, it is known as a closed
traverse.
Open traverse: When the lines
form a circuit ends elsewhere except
starting point, it is said to be an open
traverse.
• Traverse party: it usually consists of an instrument operator, a head tape
man and rare tape man.
• Equipments for the traverse party:the equipments for the traverse
party are the theodolite, tapes, hand level, leveling staff, ranging pole &
plumb bobs, EDM & reflector, stakes & hubs, tacks, marking crayon,
points, walkie talkies, & hammer etc.
Procedures in conducting traverse surveying
• First, we need to use chain and tape throughout the project. There is no angle measuring tool
utilized and the line directions are totally determined by linear measurements. The angle between
traverse lines is measured indirectly by using chain angle concept (constructing the third side
utilizing tie stations to find the angle between two adjoining sides)
• Next in this approach, the fore and rear bearings (a bearing is the clockwise or counterclockwise
angle between north or south) of the traverse legs are calculated with a prismatic compass, and
linear measurement (distances) is done by using chain or tape. The noted bearings are then double-
checked, and any necessary modifications for nearby attractions are made. A closure error may
occur in this procedure. Using ‘Bowditch’s rule,’ this error is graphically adjusted.
Procedures in conducting traverse surveying
• With the help of theodolites directions can be measured in the form of the bearings, Deflection angle, Angle to
the right, interior angles or azimuths and distance with a tape, electric distance measuring equipment (EDM) or a
tachometer in theodolite traversing. Compass and theodolite can be used to measure bearing using either the lose
needle method or the fast needle method. Traverse is called deflection angle traverse if angles measured by
deflection angle method. It is especially employed in urban areas where triangulation is not practicable.
• Next is, you need to use the plane table to trace topographic details by drawing survey lines amid stations that
have been formerly places by other survey procedures. The plane table is placed in a specific location e.g. A.
Sight toward B is taken from there, and the distance AB is calculated. The plane table is repositioned at station B
and aimed towards A.(this is called back sighting). BA was assessed in terms of distance. On the drawing paper,
the average distance between AB and BA is plotted to a suitable scale. The distance was determined after spotting
point C from B. This procedure is carried out for each station. Perform some checks at regular intervals.
INSTRUMENTS
• TAPE MEASURE
• A tape measure or measuring tape
is a flexible ruler used to measure
size or distance. It consists of a
ribbon of cloth, plastic, fiber glass,
or metal strip with linear-
measurement markings. It is a
common measuring tool to
measure distances, heights, and
widths.
INSTRUMENTS
• THEODOLITE
• It is the most precise instrument for
the measurement of the angle between
two pre-decided visible points in either
horizontal or vertical plane.. There
are two types of theodolite– transit
and non–transit.
INSTRUMENTS
• RANGING POLES
• Ranging rods are 2-3
meters in length and
are painted with alternate bands of two
colors like white and black, red and w
hite in succession. Each band is kept at
a length of 20 centimeters. They are
used to range an intermediate point on
a survey line.
INSTRUMENTS
• PLANIMETER
• A planimeter is a table-top instrument
for measuring areas, usually the areas of
irregular regions on a map or
photograph. They were once common,
but have now largely been replaced by
digital tools.
FORMULAS TO BE USED IN GETTING THE
AREA OF A TRAVERSE
1. By using COORDINATES
2. By using DOUBLE MERIDEAN DISTANCE(DMD)
FIND THE AREA USING THE COORDINATE’ METHOD
1. LIST X AND Y COORDINATES IN TWO COLUMNS
2. REPEAT COORDINATES OF STARTING POINT AT THE END
3. SUM THE PRODUCTS DESIGNATED BY THE ARROWS
STAT X Y
1 30 30
2 40 70
3 90 100
4 100 20
1 30 30
FIND THE AREA USING THE COORDINATE’ METHOD
1. LIST X AND Y COORDINATES IN TWO COLUMNS
2. REPEAT COORDINATES OF STARTING POINT AT THE END
3. SUM THE PRODUCTS DESIGNATED BY THE ARROWS
STAT X Y
1 30 30
2 40 70
3 90 100
4 100 20
1 30 30
COMPUTATION
A=
A=
=
=
=
=
=
FIND THE AREA USING DOUBLE MERDIAN
DISTANCE’S METHOD
• DMD METHOD STEPS
• Step 1. Tabulate the latitudes and departure.
• Step 2. Perform the DMD Method.
• Step 3. Calculate DA (Product of the latitude and DMD).
• Step 4. Calculate the area which is half of the sum of DA. Ignore the sign if the result
is negative.
A closed traverse has the following data:
Course Bearing Distance (m)
1- 2 N 9.27° E 58.70
2–3 S 88.43° E 27.30
3–4 N 86.787° E 35.20
4–5 S 5.30° E 35.00
5-1 S 72.07° W 78.96
Determine the AREA of the closed traverse
LATTUDE DEPARTURE DMD DA=LAT × DMD AREA
+ 57.933 +09.456 +09.456 +547.814
-00.748 +27.290 +46.202 -34.559
+01.973 +35.147 +108.639 +214.345 3.111.075m²
-34.850 +03.233 +147.019 -5123.612
-24.308 -75.125 +75.127 -1826.139
∑ DA= -6222.15
COMPUTATION
LAT A= (58.70)cos 9.27 DEP A= (58.70)cos 9.27
FORMULA: = +57.933 = +57.933
LAT= (Distance)cos Bearing
LAT B= (27.30)cos 88.43 DEP B= (27.30)cos 88.43
DEP= (Distance)sin Bearing = -00.748 = -00.748
LAT C= (35.20)cos 86.787 DEP C= (35.20)cos 86.787
= +01.973 = +01.973
LAT D= (35.00)cos 5.30 DEP D= (35.00)cos 5.30
= -34.850 = -34.850
LAT E= (79.96)cos 72.07 DEP E= (79.96)cos 72.07
= -24.308 = -24.308
North and East are positive.
NOTE: South and West are negative.
COMPUTATION
DMD AB= 09.456 DMD METHOD RULE
Rule 1. The DMD of the first course is equal to the
DMD BC= 09.456+09.456+27.290 departure of the course.
= 46.202 Rule 2. The DMD of any other courses is equal to the
DMD of the preceding course, plus the departure of
DMD CD= 46.202+27.290+35.147 the preceding course, plus the departure of the course
= 108.639 itself.
Rule 3. The DMD of the last course is numerically
DMD DE= 108.639+35.147+03.233 equal to the departure of that course, but with the
=147.019 opposite sign.
DMD EA= 147.019+03.233-75.125
= 75.127
COMPUTATION
AREA=
DA= LAT x DMD
=
DA A= 57.933 x 09.456 DA D= -34.850 x 147.019
= 547.814 = -5123.612 = 3.111.075m²
DA B= -00.748 x 46.202 DA E= -24.308 x 75.127
= -34.559 = -1826.139
DA C= 01.973 x 108.639
= 214.345
Determining area of field
with irregular curved
boundary
WHAT IS AN IRREGULAR BOUNDARY?
An Irregular boundary is defined as the
region in two dimensional heat
conduction in which the total volume of
an element cannot be replaced by using a
simple volume of rectangular elements
and plane wall strips.
3 WAYS TO SOLVE A FIELD WITH
IRREGULAR BOUNDARIES
A. TRAPEZOIDAL RULE
B. SIMPSON’S RULE
A. TRAPEZOIDAL RULE
• In trapezoidal rule, boundaries between the ends of ordinates are assumed to be straight.
The areas enclosed between the base line are considered as trapezoids.
B. SIMPSON’S RULE
• The boundaries between the ends of ordinates are assumed to form an arc of parabola. As
a result, the Simpson’s Rule is sometimes called parabolic rule.
• It states that, sum of first and last ordinates has to be done. Add twice the sum of
remaining odd ordinates and four times the sum of remaining even ordinates. Multiply to
this total sum by 1/3rd of the common distance between the ordinates which gives the
required area.
Sample problems
Sample problems
