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SURVEYING
( LECTURE 1 )
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SURVEYING
SURVEYING IS THE ART OF DETERMINING THEPOSITIONS OF POINTS ON OR NEAR THE EARTHS
SURFACE BY MEANS OF MEASUREMENTS IN THE 3ELEMENTS OF SPACE ; NAMELY, DISTANCE ,DIRECTION , AND ELEVATION.RAYNER AND SCHMIDT
SURVEYING IS THE ART OF MEASURING HORIZONTALAND VERTICAL DISTANCES BETWEEN OBJECTS , OFMEASURING ANGLES BETWEEN LINES , OFDETERMINING THE DIRECTION OF LINES , AND OF
ESTABLISHING POINTS BY PREDETERMINED ANGULARAND LINEAR MEASUREMENTS.
DAVIS , FOOTE , ANDERSON , AND MIKHAIL
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SURVEYING
SURVEYING IS THE ART OF MAKING SUCHMEASUREMENTS OF THE RELATIVE POSITIONS OFPOINTS ON THE SURFACE OF THE EARTH THAT , ONDRAWING THEM TO SCALE , NATURAL AND ARTIFICIALFEATURES MAY BE EXHIBITED IN THEIR CORRECTHORIZONTAL OR VERTICAL RELATIONSHIPS.CLARKE
SURVEYING IS THAT BRANCH OF APPLIEDMATHEMATICS WHICH TEACHES THE ART OFDETERMINING THE AREA OF ANY PORTION OF THEEARTHS SURFACE , THE LENGTH AND DIRECTIONS OF
THE BOUNDARY LINES , THE CONTOUR OF THESURFACE , AND OF ACCURATELY DELINEATING THEWHOLE IN PAPER.
WEBSTER
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SURVEYING
SURVEYING IS THE SCIENCE OR ART OF MAKING SUCHMEASUREMENTS AS ARE NECESSARY TO DETERMINETHE RELATIVE POSITION OF POINTS ABOVE , ON , ORBENEATH THE SURFACE OF THE EARTH , OR TOESTABLISH SUCH POINTS.BREED , HOSMER AND BONE
SURVEYING IS THE SCIENCE AND ART OFDETERMINING RELATIVE POSITIONS OF POINTSABOVE , ON OR BENEATH THE SURFACE OF THE EARTH, OR ESTABLISHING SUCH POINTS.
BRINKER AND WOLF
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SURVEYING
SURVEYING IS THE ART AND SCIENCE OFDETERMINING ANGULAR AND LINEARMEASUREMENTS TO ESTABLISH THE FORM , EXTENT ,AND RELATIVE POSITION OF POINTS , LINES ANDAREAS ON OR NEAR THE SURFACE OF THE EARTH ORON OTHER EXTRATERRESTIAL BODIES THROUGHAPPLIED MATHEMATICS AND THE USE OF SPECIALIZEDEQUIPMENT AND TECHNIQUES.JUNY PILAPIL LA PUTT
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Two Main Categories
Equatorial plane
Polar axis
Ellipsoid
Geoid
b
a
Geodetic line /
Plumb line
Geocentric line
Geodetic Surveying Considers curvature of the earth
Provide an accurate framework for a largesurvey
Plane Surveying Surface of the earth: as an infinite horizontal
plane
Direction of gravity:
Constant over the entire site.
Defines vertical lines( plumb lines),
Plane normal to a plumb line horizontalplane.
Hence, rectangular coordinate system:most suitable for plane surveying
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Types of Surveying
Cadastral surveys Determine lawful boundaries & areas of properties rather
than detail features of the landscape Used in legal disputes, taxation, etc.
Also calledpropertysurveys / boundary surveys
City surveys Surveys of areas in and near city
For planning expansions or improvements , locatingproperty lines , fixing reference monuments , determiningphysical features and configuration of the land , andpreparing maps.
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Types of Surveying
Construction surveys Surveys undertaken at construction site For providing data regarding grades , reference lines ,
dimensions , ground configuration , and location and
elevation of structures which are of concern toengineers, architects, and builders.
Forestry surveys Surveys executed in connection with forest management
and mensuration, and the production and conservation offorest lands.
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Types of Surveying
Hydrographic surveys Surveying streams , lakes , reservoirs , harbors, oceans , and
other bodies of water. Made to map shore lines , chart the shape of areas
underlying water surfaces, and measure the flow of streams. Of general importance in connection with navigation,
development of water supply and resources , flood control ,irrigation , production of hydro electric power, subaqueousconstructions, and recreation.
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Types of Surveying
Industrial surveys Sometimes known as optical tooling. Refers to use of surveying techniques in shipbuilding ,
construction and assembly of aircraft , layout and installation
of heavy and complex machinery, and in other industries wherevery accurate dimensional lay outs are required.
Mine surveys Performed to determine the position of all underground
excavations and surface mine structure , to fix surfaceboundaries of mining claims, determine geological formations,to calculate excavated volumes, and establish lines and gradesfor other related mining work.
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Types of Surveying
Topographic surveys Made for determining the shape of the ground, and the
location and elevation of natural and artificial features upon it.
The features shown include such natural objects as hills ,mountains , rivers , lakes , relief of the ground surface, andworks of man , such as roads , buildings , ports , towns ,municipalities, and bridges.
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Compass
For measuring angles anddirections
Observe bearings
Used in reconnaissance and hastywork
Compass
CommonSurveying Instruments
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For measuring lengths:
Measuring tape
Direct linearmeasurements
Cheap & robust
For small details
Fiberglass
measuringtape
Steeltape
Tapes
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Alidade and Plane Table Survey
The alidade is an instrument
designed mainly for
moderately accurate surveys
and geological mapping
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Leveling Instrument
AutomaticLevel
For measuringheight differences:
Level: has a telescope thatcan be rotated about thevertical axis whilemaintaining a horizontal lineof sight
Staff: long rod, when heldvertically over the point ofinterest, provides height
readings to be read by thelevel
A pair of readingsdetermines the change in
height
StaffReadings
on
a staff
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EngineersTransit
For measuring angles,directions & distance
A telescopic sight pivoted
both horizontally & vertically
Built-in graduated circles for
measuring horizontal & vertical
angles
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Theodolite
Optical TheodoliteElectronic theodolite withEDM mounted on top
For measuring angles, directions &distance
A telescopic sight pivoted both
horizontally & vertically
Built-in graduated circles for
measuring horizontal & vertical
angles
Theodolites used on construction
sites: 20, 6, 5 or 3 of arc
Geodetic theodolites: 1 or even 0.1
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Electronic Distance Measurement
ED
M
EDM & rechargeable
battery
Laser equipment for very accurate
distance measurement
Can typically measure thousands of
meters with only a few mms error
Used in all serious control work, &
often in detail surveys as well
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Total Station
More advanced instrument:
Theodolite, EDM, dataprocessor & display unitcombined into one; providesinstant data conversion intothree-dimensionalcoordinates & interface withcomputers
Total station withmemory cards
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Global Positioning System (GPS)
Satellites-based systemsgiving accurate three-dimensional coordinates ofany point on earth occupied bya GPS receiver. Also used fornavigation purposes
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ERRORS
Defined as the difference between the true valueand the measured value of a quantity and is oftenbeyond the control of the one performing theoperation.
MISTAKES
Are inaccuracies in measurements which occurbecause some aspect of a surveying operation is
performed by the surveyor with carelessness,inattention, poor judgment , and improperexecution. Also caused by a misunderstanding ofa problem , inexperience, or indifference of thesurveyor.
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TYPES OF ERRORS
SYSTEMATIC ERRORSThis type of error is one which will always have the same signand magnitude as long as field conditions remains constantand unchanged.
Will repeat itself in other measurements still maintaining thesame sign, and thus will accumulate.
Can be computed and their effects be eliminated by applyingcorrections , employing proper techniques in the use ofinstruments or by adopting a field procedure which will
automatically eliminate it.
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TYPES OF ERRORS
ACCIDENTAL ERRORSThis type of error is purely accidental in character.
Caused by factors beyond the control of the surveyor and arepresent in all surveying measurements.
Usually of minor importance in surveying operations sincethey are variable in sign and are of a compensating nature.
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SOURCES OF ERRORS
INSTRUMENTAL ERRORSDue to imperfections of the instrument used , either fromfaults in their construction or from improper adjustmentsbetween the different parts prior to use.
a. Measuring with a tape of incorrect lengthb. Using a leveling rod with painted graduations not perfectlyspaced
NATURAL ERRORS
Caused by variations in the phenomena of nature such aschanges in magnetic declination , temperature , humidity ,wind , refraction , gravity and curvature of the earth.
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SOURCES OF ERRORS
PERSONAL ERRORSArise principally from limitations of the senses of sight , touchand hearing of the human observer which are likely to beinaccurate.
ex. error in determining a reading on a rod which is out ofplumb
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ACCURACY AND PRECISION
ACCURACYIndicates how close a given a given measurement is to theabsolute or true value of the quantity measured.
PRECISION
The degree of refinement and consistency with which anyphysical measurement is made.
Portrayed by the closeness of one another of a set of repeatedmeasurements of quantities.
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MOST PROBABLE VALUE ( MPV or X )
ARITHMETIC MEAN OR THE AVERAGE.
REFERS TO A QUANTITY WHICH, BASED ON AVAILABLEDATA , HAS MORE CHANCES OF BEING CORRECT THANHAS ANY OTHER.
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SAMPLE PROBLEMS
1. A SURVEYING INSTRUCTOR SENT OUT SIX GROUP OF
STUDENTS TO MEASURE A DISTANCE BETWEEN TWO
POINTS MARKED ON THE GROUND. THE STUDENTS CAME
UP WITH THE FOLLOWING SIX DIFFERENT VALUES :
250.25, 250.15, 249.90, 251.04, 250.50, AND 251.22 METERS.
ASSUMING THESE VALUES ARE EQUALLY RELIABLE AND
THAT VARIATIONS RESULT FROM ACCIDENTAL ERRORS,
DETERMINE THE MOST PROBABLE VALUE OF THE
DISTANCE MEASURED.
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SAMPLE PROBLEMS
2. THE ANGLES ABOUT A POINT Q HAVE THE FOLLOWING
OBSERVED VALUES, 1301520 , 1423730 , AND 870740.
DETERMINE THE MOST PROBABLE VALUE OF EACH
ANGLE.
Q3 1
2
SAMPLE PROBLEMS
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SAMPLE PROBLEMS3. THE OBSERVED INTERIOR ANGLES OF A TRIANGLE ARE
A = 351437, B = 963009, AND C = 481505. DETERMINE
THE DISCRIPANCY FOR THE GIVEN OBSERVATION ANDTHE MOST PROBABLE VALUE OF EACH ANGLE
P
4. MEASUREMENT OF THREE HORIZONTAL ANGLES ( SEE
ACCOMPANYING FIGURE ) ABOUT A POINT P ARE:
APB= 123150, BPC= 372920,AND CPD= 473630. IF
THE MEASUREMENT OF THE SINGLE ANGLE APD=
973700,DETERMINE THE MOST PROBABLE VALUES OF
THE ANGLES.
A
B
CD
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RESIDUAL ( V )
SOMETIMES REFERRED TO AS DEVIATION.
DEFINED AS THE DIFFERENCE BETWEEN ANY MEASUREDVALUE OF A QUANTITY AND ITS MOST PROBABLE VALUE.
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PROBABLE ERROR ( PES )
A QUANTITY WHICH , WHEN ADDED TO AND SUBTRACTED
FROM THE MOST PROBABLE VALUE , DEFINES A RANGEWITHIN WHICH THERE IS A 50 PERCENT CHANCE THAT THETRUE VALUE OF THE MEASURED QUANTITY LIES INSIDE (OR OUTSIDE ) THE LIMITS THUS SET.
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RELATIVE ( ERROR ) PRECISION
EXPRESSED BY A FRACTION HAVING THE MAGNITUDE OF
THE ERROR IN THE NUMERATOR AND THE MAGNITUDE OFA MEASURED QUANTITY IN THE DENOMINATOR.
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SAMPLE PROBLEMS
1. PROBABLE ERROR. THE FOLLOWING VALUES WEREDETERMINED IN A SERIES OF TAPE MEASUREMENTS OF A
LINE : 1000.58, 1000.40, 1000.38, 1000.48, 1000.40, AND 1000.46
METERS. DETERMINE THE FOLLOWING:
A. MOST PROBABLE VALUE OF THE MEASURED LENGTHB. PROBABLE ERROR OF A SINGLE MEASUREMENT AND
PROBABLE ERROR OF THE MEAN.
C. FINAL EXPRESSION OF THE MOST PROBABLE LENGTH
D. RELATIVE PRECISION OF THE MEASUREMENT
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SAMPLE PROBLEMS
1. WEIGHTED MEASUREMENTS. FOUR MEASUREMENTS
OF A DISTANCE WERE RECORDED AS 284.18 , 284.19 , 284.22, AND 284.20 METERS AND GIVEN WEIGHTS OF 1 , 3 , 2 ,
AND 4 , RESPECTIVELY. DETERMINE THE WEIGHTED
MEAN.
2. WEIGHTED MEASUREMENTS. IT IS DESIRED TO
DETERMINE THE MOST PROBABLE VALUE OF AN ANGLE
WHICH HAS BEEN MEASURED AT DIFFERENT TIMES BY
DIFFERENT OBSERVERS WITH EQUAL CARE. THE VALUES
OBSERVED WERE AS FOLLOWS : 743945 ( IN 2MEASUREMENTS ) , 743927(IN 4 MEASUREMENTS) , AND
743935(IN 6 MEASUREMENTS)
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SAMPLE PROBLEMS
3. WEIGHTED MEASUREMENTS. LINES OF LEVELS TO
ESTABLISH THE ELEVATION OF A POINT ARE RUN OVER 4DIFFERENT ROUTES. THE OBSERVED ELEVATIONS OF THE
POINT WITH PROBABLE ERRORS ARE GIVEN BELOW
DETERMINE THE MOST PROBABLE VALUE OF THE
ELEVATION OF THE POINT.
LINE
OBSERVED
ELEVATION
(ELEV)
PROBABLE
ERROR
( E )
E2 W= 1 / E2 RELATIVE
WEIGHT
( RW )
P=ELEV(RW)
1 219.832 0.006 0.000036 27778
2 219.930 0.012 0.000144 6944
3 219.701 0.018 0.000324 3086
4 220.021 0.024 0.000576 1736 1
1.78
416 3517.312
879.720
391.608
220.021
22.78SUM 5008.121
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