Lecture 3-4(part 2).pdf

Bearing and Distance of a Survey Line

Latitude and departure
 Both terms are introduced with plotting the traverse.
latitude and departure both are required for plotting
the position of different point w.r.t y-axis and x- axis. y
axis and x axis are known as reference line and are also
known as the co-ordinates.
N
S
E
W
Reference axis- x axis
Reference axis- y axis Departure
Easting =
+
Latitude
northing=+
Latitude
Southing= -ve
Departure
Westing= -ve
Ø

Latitude and departure
 Latitude of line =l cos Ø
 Departure of line = l sin Ø
 If N 30 º S is the bearing of a any given line N show
that its latitude and S shows departure of the line.

Offsets:
These are the lateral measurements from the base line to
fix the positions of the different objects of the work with
respect to base line. These are generally set at right angle
offsets. It can also be drawn with the help of a tape.
There are two kinds of offsets:
1) Perpendicular offsets, and
2) Oblique offsets.
The measurements are taken at right angle to the survey
line called perpendicular or right angled offsets.
The measurements which are not made at right angles to
the survey line are called oblique offsets or tie line offsets.

Conversions
a) Convert the following angles taken as whole degrees and
decimals, into whole Degrees, Minutes and Seconds
(round Seconds to whole number).
50.672777
45.50833
80.34028
16.35251
b)Convert the following angles taken as whole Degrees
Minutes and Seconds ,into whole Degrees and decimals
(to 5 decimal places)
910 15’ 30”
1110 14’ 45”
880 00’ 20”
1140 26’ 40”

Calculation of Latitude ,Departure and
Coordinates
Lin
e
Length(
m)
Bearing Latitude
(LcosӨ)
Departur
e(LsinӨ)
Stat
ions
Co-ods N Co-ods
E
A 1000.00 1000.00
AB 160.00 351°30̕
B
BC 280.00 102°36̕
C
CD 120.00 144°04̕
D
DA 320.00 270°00̕
A

Calculation of Latitude and Departure.
Line Length(m) WCB Latitude Departur
e
Station
s
Co-ods N Co-ods
E
AB 316.0 20°31̕ 30”
BC 650.5 357°16̕ 00”
CD 189.0 120°04 ̕00”
DE 442.0 188°27̕ 30”
EA 334.5 213°31̕ 00”

Calculate coordinates of points B,C,D taking
coordinates of initial points as 1000,1000 .
Line Length(m) WCB Latitude Departur
e
Statio
ns
Co-ods N Co-ods
E
A 1000.00 1000.00
AB 751 358°50̕ 750.84 -15.59
B
BC 392 63°04̕ 177.56 349.48
C
CD 561 169°10̕ -551.00 105.44
D
DA 579.4 239°22̕ -295.33 -498.54
A

Coordinates
Lin
e
Length(
m)
Azimath Latitude
(LcosӨ)
Departur
e(LsinӨ)
Stat
ions
Co-ods N Co-ods
E
A 1000.00 1000.00
AB 160.00 351,30 158.24 _23.65
B 1158.24 976.35
BC 280.00 102,36 _61.08 273.25
C 1097.16 1249.6
CD 120.00 144,04 _97.16 70.42
D 1000.00 1320.0
DA 320.00 270,00 0.0 _320.0
0.0 A 1000.0 1000.0

Calculation of Latitude and
Departure
Line Length
(m)
Whole
Circle
Bearing
Quadrant
Bearing
Latitude Departure Remark
s
AB 232 N32.12E
BC 148 S41.24E
CD 417 S22.24W
DE 372 N68.OW
EA ? ?

The details of a part of a theodolite traverse survey are as under.
Calculate the distance between a point P on AB 60m from A and
a point Q on CD 250m from C and also determine the bearing of
line PQ.
Line Length Bearing
AB 200 300°20̕
BC 500 25°30̕
CD 300 145°30̕

ABCD is a closed traverse in which the bearing of AD has not been
observed and the length of BC has been missed to be recorded .The
rest of the field record is as follows. Calculate the bearing of AD and
the length of BC.
Line Bearing Length
AB 181°18̕ 335
BC 90°00̕ ?
CD 357°36̕ 408
DA ? 828

The lengths and bearings of a traverse ABCD are as
follows .Calculate the length and bearing of line DA.
Line Length Bearing
AB 250.5 30°15̕
BC 310.4 145°30̕
CD 190.2 222°15̕
DA ? ?

Brief History of Surveying:
6. 20th Century and Beyond: As technology advanced,
population increased, and land value caused
development of licensure for surveyors in all states.
 Educational requirements for licensure began in the early
1990’s
 Capable of electronic distance measurement, positioning
using global positioning systems, construction machine
control, and lidar (scanning) mapping
 Involvement in rebuilding of the infrastructure and
geographic information systems (GIS)
 Shortage of licensed professionals is projected well into the
21st century

Sources of Errors
 Instrumental Errors:Error may arise due to
imperfection or faulty adjustment.
 Personal:Error may also arise due to want of perfection
of human sight in observing and touch in
manipulating instruments.
 Natural: Error may arise due to variation of
temperature,humadity,gravity,refraction

Errors
 Types of errors
1. Random
2. Systematic
3. Natural
4. Personal
Random
 Not predictable
 Tend to be small and will usually
cancel themselves.
 Best controlled by repeating
measurements.
Systematic
 Usually caused by damaged
equipment.
 Error tends to multiply (occur
for each measurement)
 Best control is calibration of
equipment.
Natural
 Factors in the environment that
can cause error.
 Curvature
 Refraction
 Must use correction values
Personal
– Commonly called blunders
– Best controlled by following
established procedures.

Taping Error:
1. Instrumental Error – a tape may have different length due to
defect in manufacture or repair or as.
2. Natural Error – length of tape varies from normal due to
temperature, wind and weight of tape (sag)
3. Personal Error – tape person may be careless in setting pins,
reading the tape, or manipulating the equipment
►Instrumental and natural error can be corrected
mathematically, but personal error can only be corrected by
remeasure.
►When a tape is obtained, it should either be standardized or
checked against a standard.
►Standardized at 68 degrees F and 12 lbs. tension fully
supported.


Errors in taping further
 Erroneous length in tape
 Bad ranging
 Careless holding and marking
 Bad straightening
 Non –Horizontality
 Sag in chain or tape
 Variation in temperature
 Variation in pull
 Personal errors

Tape Error Correction:
Measuring between two existing points:
If a tape is long, the distance will be short, thus any correction
must be added
If tape is short, the distance will be long, thus any correction
must be subtracted
If you are setting or establishing a point, the above rule is
reversed.
Generally can correct for tape length, temperature, tension,
and sag, but tension and sag are negated by increasing
tension to approximately 25 – 30 lbs.

Error in Taping:
 Tape Length: Correction per foot = Error in 100’/100’
 If tape was assumed to be 100.00’ but when standardized was
found to be 100.02’ after distance measured at 565.75’
 then: Correction =(100.02-100.00)/100.00 = 0.0002’ error/ft
 565.75’ X .0002’ = 0.11’ correction and based upon rule, must be
added, thus true distance = 565.86’
 If tape had been 99.98’ then correction would be subtracted
and true distance would be 565.64’

Error in Taping:
 Temperature – Tapes in U.S. are standardized at 68F;
the temperature difference above or below that will
change the length of the tape
 Tapes have a relatively constant coefficient of expansion of
0.0000065 per unit length per F
 CT = 0.0000065(Temp (F)-68) Length
 Example: Assume a distance was measured when
temperature was 30°F using a 100’ tape was 872.54’ (68
– 30) X 0.00000645 X 872.54’ = 0.21’ error tape is
short, thus distance is long, error must be subtracted and
thus 872.54’ – 0.21’ = 872.33’
(note: temperature difference is absolute difference)

Corrections for tape
measurements
1 Correction due to incorrect tape length
2 Correction due to slope
3 Correction due to temperature
4 Correction due to tension
5 Correction due to sag
6.Correction for alignment

Manufacturers of measuring tapes do not usually guarantee the exact length of
tapes, and standardization is a process where a standard temperature and tension
are determined at which the tape is the exact length. The nominal length of tapes
can be affected by physical imperfections, stretching or wear.
The correction due to tape length is given by:
Where:
CL is the corrected length of the line to be measured or laid out;
ML is the measured length or length to be laid out;
NL is the nominal length of the tape as specified by its mark.
Note that incorrect tape length introduces a systematic error that must be
calibrated periodically.
Correction due to incorrect tape length

Correction due to temperature
When measuring or laying out distances, there is always a change in temperature especially when the
taping operation requires time to do so. Usually, to avoid circumstances where there is an introduced
error due to temperature, tapes were standardized as a response to such factor, and a standard
temperature for the tape determined.
The correction of the tape length due to change in temperature is given by:
Where:
is the correction to be applied to the tape due to temperature;
T is the observed temperature or average observed temperature at the time of measurement;
is the standard temperature, the temperature at which the tape was standardized;
C is the coefficient of thermal expansion of the tape;
L is the length of the tape or length of the line measured.
The correction is added to to obtain the corrected distance:
Usually, for common tape measurements, the tape used is a steel
tape with coefficient of thermal expansion C equal to 0.0000116 units
per unit length per degree Celsius change. This means that the tape
changes length by 1.16 mm per 10 m tape per 10°C change from the
standard temperature of the tape.

Correction due to tension
Tension introduces error when the tape is pulled at a force that differs from the standard tension used
at standardization. It will stretch less than its standard length when an insufficient pull is applied
making the tape too short.
The tape stretches in an elastic manner (up until it reaches its elastic limit where it will deform
permanently, essentially ruining the tape).
The correction due to tension is given by:
Where:
is the total elongation in tape length due to pull; or the correction to be applied due to
incorrect pull applied on the tape; meters;
is the pull applied tothe tape during measurement; kilograms;
is the standard tension, it is the pull applied to the tape during standardization; kilograms;
A is the cross-sectional area of the tape; square centimeters;
E is the modulus of elasticity of the tape material; kilogram per square centimeter;
L is the measured or erroneous length of the line; meters
The correction is added to to obtain the corrected distance:
The value for A is given by:
Where:
W is the total weight of the tape; kilograms;
is the unit weight of the tape; kilogram per cubic centimeter.
For steel tapes, the value for is given
by .

Correction due to sag
A tape not supported along its length will sag and form a catenary between supports. The correction
due to sag must be calculated for each unsupported stretch separately and is given by:
Where:
is the correction applied to the tape due to sag; meters;
is the weight of the tape per unit length; kilogram per meters;
L is the length between two ends of the catenary; meters;
P is the tension or pull applied to the tape; kilogram.
The correction is subtracted from to obtain the corrected distance:
Note that the weight of the tape per unit length is equal to the weight of the
tape divided by the length of the tape:
so:
Therefore, we can rewrite the formula for correction due to sag by:

Chain Survey
44
Chain survey is the simplest method of surveying. In this
survey only measurements are taken in the field, and the
rest work, such as plotting calculation etc. are done in the
office. This is most suitable adapted to small plane areas
with very few details. The necessary requirements for field
work are chain, tape, ranging rod

Coordinates
Lin
e
Length(
m)
Azimath Latitude
(LcosӨ)
Departur
e(LsinӨ)
Stat
ions
Co-ods N Co-ods
E
A 1000.00 1000.00
AB 160.00 351,30
B
BC 280.00 102,36
C
CD 120.00 144,04
D
DA 320.00 270,00

Offsets
These are the lateral measurements from the base line to fix
the positions of the different objects of the work with respect
to base line. These are generally set at right angle offsets. It
can also be
drawn with the help of a tape. There are two kinds of offsets:
1) Perpendicular offsets, and
2) Oblique offsets.
The measurements are taken at right angle to the survey line
called perpendicular or right angled offsets.
The measurements which are not made at right angles to
the survey line are called oblique offsets or tie line offsets.
47

Example 2
Sketch the field represented by this field diagram.
A
D
27
47
79
94
29
35
39
E
B
C
A
B
C
D
E
27
20
32
15
29
35
39
You may also be asked to:
1. Make a scale drawing of the
field
2. Find lengths such as AB or
BC.

Step 5: Compute Linear Misclosure (continued)
Linear misclosure = [(departure misclosure)2 + (latitude misclosure)2]1/2

Traversing
 Definition:
 A traverse is a series of consecutive lines whose lengths and
directions have been measured.
 Why?
 The purpose of establishing a traverse is to extend the
horizontal control. A survey usually begins with one given
vertical control and two ( or one and direction) given in
horizontal
 You need more than two points to control the project, have
enough known points to map any point, and set-out any object
any where in a large project.

Closed and Open Traverses
 A closed traverse is the one that starts and ends at
known points and directions, whether the shape is
closed or not
 A closed traverse can be a polygon {closed shape} or
Link {closed geometry-open shape

Traverse Stations
 Successive stations should be inter visible.
 Stations are chosen in safe, easy to access places.
 Lines should be as long as possible
 To reduce the number of lines
 Short lines will produce less accurate angles, the traverse
gets distorted as shown below.
A
B
T1
T2
T3
T4

Step 5: Compute Linear Misclosure
Because of errors in the measured angles and distances there will be
a linear misclosure of the traverse. Another way of illustrating this is
that once you go around the traverse from point A back to point A’
you will notice that the summation of the departures and latitudes do
not equal to zero. Hence a linear misclosure is introduced.

Lecture 3-4(part 2).pdf

More Related Content

Similar to Lecture 3-4(part 2).pdf

Recently uploaded

Lecture 3-4(part 2).pdf