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INTRODUCTION
ADJUSTMENT COMPUTATIONS
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A distance PQ is measured using a steel tape of nominal length
20m and found to be 65.32m long. After calibrated against astandard, the tape was found to be 0.050m too long.
Compute the correct length PQ.
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Correct length PQ = measured length PQ + correction
Correction = (actual tape lengthnominal tape length) x
number or nominal tape length in line PQ
= (20.0520.0) x 65.32/20.0
= +0.16
Hence correct length PQ = 65.32 + 0.16
= 65.48m
Question: Name what other corrections commonly
applied in a steel tape distance measurement.
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The internal angles of a triangle ABC were measured as follows;
A = 590
B = 610
C = 630
Assuming that the measurements are free from gross and
systematic errors, compute the correct angles A, B and C.
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Sum of angles = 1830
Condition for sum of angles = (n-2)x1800 = 1800 as n=3
Difference or misclosure = + 30
(indicates the presence of random errors and observations need
adjustment)
Adjustment of the observed angles are carried out by distributing
the errors equally to the observed values by a certain amount of
correction.
Correction = - (30
/3 angles) = - 10
per angle
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DEFINITION OF TERMS
IN SURVEY MEASUREMENTS ANDADJUSTMENT COMPUTATIONS
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Adjustment is a process of making measured
values of a quantity more accurate before theyare used in the computations for the
determination of points position that are
associated with the measurements.
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m sur
to find the size, length, or amount of
something (unknown quantity), using standard units
such asinches, metres etc:
observation
the process of watching something or someonecarefully for a period of time
ob
serve
to see and notice something:
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com
pute
to calculate a result, answer, sum etc:
com
pu
ta
tion
the process of calculating or the result of calculating:
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adjustment
a small change made to a machine, system, or
calculation
adjustto change (something) to make it more correct; so that it
fits, corresponds or conforms to desired conditions
adjustmentis a process of distributing errors (random) in
measurements or observations so that they conform to
certain geometrical conditions (such as misclosure) .
adjust
to change or move something slightly to improve it or
make it more suitable for a particular purpose:
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PURPOSE OF SURVEYING
To determine the relative positions of points above, on, orbelow the earth surface by the measurements of distances and
directions.
Making measurements or observations and then
computations and analyses using the measurements are themain tasks of surveyors.
No measurement is exact and can be free of error. Thus thetrue value of the quantity being measured is never known.
It is important for surveyors to recognize errors, eliminate as
many errors as possible, and apply adjustments for errors thatcannot be eliminated.
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RELATIVE POSITIONING
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LINEAR SURVEYING
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COMPASS SURVEYING
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TOTAL STATION TRAVERSING
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LEVELLING
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TRIGONOMETRIC LEVELLING
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TRIANGULATION
Positioning of points in a network of triangles whose
internal horizontal angles were measured at the points aswell the length of one side of the triangle
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TRILATERATION
Positioning of points in a network of triangles whose
lengths of all sides of the triangle were measured
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INTERSECTIONS
Positioning of an unknown pointP from two or more known points
A and B using horizontal angles
(1,2) measured at the known
points.
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RESECTIONS
Positioning of an unknown point P from three or more
known points A, B and C using horizontal angles (,)measured at the unknown point.
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Global Positioning Satellite (GPS) Surveying
Baseline vectors = Coordinate differences (dX, dY, dZ)
between points
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SURVEY MEASUREMENTS OR
OBSERVATIONS
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WHAT ARE THEY DOING??
Observed what?
What errors exist?
What geometricalconditions/ misclosure?
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UNDERSTANDING ERRORSIN
SURVEY MEASUREMENTS OROBSERVATIONS
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Understand ......... ERRORS
Error (E) = The difference between a computed or measured value (O)
and a true or theoretically correct value (T).
E = 0 - T
Errors occur in survey observations/ measurements/ data;
Steel tape - length
Prismatic compass - bearing
Total StationHorizontal and vertical angles/ EDM distance
LevelsDifference in elevations
GPSBaseline vectors
In order to determine the most probable value (MPV) for the measured
quantity and its accuracy/precision, adjustment of the observation errors
is required
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Sources of errors
Natural errorscaused by winds, temperature, humidity, atmospheric pressure.
Instrumental errorscaused by maladjustments of instruments
Personal errorscaused by limitation of human sense of sight and touch
Types of errors
Gross error/mistakescaused by observer carelessness or poor judgments.
These errors can be eliminated.
Systematic errors/ biasescaused by the condition of measuring system that
obey physical law can be modeled mathematically. These errors can be
computed and corrected.
Random errors- caused by factors beyond the control of observer and theseerrors obey the law of probability. These errors cannot be eliminated and remain
in observations after gross and systematic errors have been eliminated. They
can be adjusted.Adjustment of observations deals with random errors
only.
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RANDOM ERRORS
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MISCLOSURES IN SURVEY
OBSERVATIONS
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WHY MISCLOSURES EXIST IN SURVEY
OBSERVATIONS?
Observations contain errors?
Good observations are dependent on the
human skill, instruments and
environmental factors.
No observation is free from errors. Three
types of errors: Gross, Systematic and
Random
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DETERMINATION OF SURVEY
MISCLOSURES
Detection the presence of random errors
- comparison between observations and certain conditions that fit
to the geometry of the measurements
- Examples:
> total elevation difference in a closed loop is zero
> total internal angles of a triangle is 1800
> total angles around the horizon at a point is 3600
> total latitude and departure of a closed traverse is zero
> total interior angles of a closed polygon/traverse = (n2)1800
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ADJUSTMENT OF SURVEY
OBSERVATIONS
COMPASS SURVEY ADJUSTMENT
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A
B
C
A
b/d
b/d
b/d
Linear misclosure (AA)
A B C A
Error AError C
Error BB
C A
Adjusted traverse (ABCA)Observed traverse (ABCA)
COMPASS SURVEY ADJUSTMENT
B
C
TRAVERSE SURVEY ADJUSTMENT
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A
B
C
A
b/d
b/d
b/d
Linear misclosure (AA)
Adjusted traverse (ABCA)Observed traverse (ABCA)
TRAVERSE SURVEY ADJUSTMENT
B
C
Adjustment steps:
1. Compute angular misclosure and check angular
tolerance/precision
2. Adjust angles by C and M corrections
3. Compute linear misclosure and check linear
tolerance/precision
4. Adjust latitude and departure using Bowditch rule
5. Compute coordinates of traverse points
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Internal angles observations of a triangle assuming free from gross and systematic
errors.
What is the true values for angle A, B and C (i.e. perform an adjustment of the angles)
Angles
Observed
values (deg)
Corrections
(deg)
Adjusted
values
A 59 -1 58
B 61 -1 60
C 63 -1 62
Total 183 -3 180
Sum of angles = 183
Condition for sum of angles = 180
Difference or misclosure = + 3 (indicates the presence of random errors and observations need
adjustment)
Adjustment of the observed angles are carried out by distributing the errors equally to the
observed values by a certain amount of correction.Correction = - (3 deg/3 angles) = - 1 deg per angle
Keypoints:
Determination/ estimation of errors in the observed values
Geometrical condition and misclosure of figure
Distribution of errors for the observed values
Determination of true values/ most probable values/ adjusted values for the observations
Example: Adjustment of angles in a triangle
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Line Distance Bearing
AB 1435.67 000 00' 00
BC 856.94 2670 36' 14
CD 1125.66 2130
23' 41
DE 1054.54 1330 20' 43
EA 756.35 690 35' 09
Given the measured distances and bearings of a traverse ABCDEA as above;
Compute the actual linear misclosure of the traverse.
Adjust the traverse using Bowditch method.
Example: Adjustment of survey traverse observations
(equal precision observations)
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Line Distance Bearing
AB 1435.67 0.02 000 00' 00" 00"
BC 856.94 0.02 2670 36' 14" 3.1"
CD 1125.66 0.02 2130
23' 41" 4.8"
DE 1054.54 0.02 1330 20' 43" 5.7"
EA 756.35 0.02 690 35' 09" 6.9"
Given the measured distances and bearings of a traverse ABCDEA as above;
a) Compute the actual linear misclosure of the traverse.
b) Determine the expected linear misclosure at the 95% confidence level and
comment whether or not the traverse contains blunders.
Example: Adjustment of survey traverse observations
(Unequal precision observations)
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UNDERSTANDING THE QUALITY
OF SURVEY MEASUREMENTS OROBSERVATIONS
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Precision
Degree of closeness of observation values. The closer the values the higher the
precision of the observation
Accuracy
Degree of closeness between the mean of observations and the true values
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ERRORSIN SURVEY MEASUREMENTS
OR OBSERVATIONS
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HORIZONTAL ANGLE MEASUREMENTS
Reading errors
Pointing errors
Target-centering errors
Instrument centering errors
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ELECTRONIC DISTANCE MEASUREMENTS
Instrumental errors
Target-centering errors
Instrument centering errors
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DIFFERENTIAL LEVELING MEASUREMENTS
Rod reading errors
Instrument leveling errors
Instrument collimation errors
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TRIGONOMETRIC LEVELING MEASUREMENTS
VERTICAL/ ZENITH ANGLE
Reading errors
Pointing errors
Vertical circle compensator
ELECTRONIC SLOPE DISTANCE
Instrumental errors
Target-centering errors
Instrument centering errors
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GPS MEASUREMENTS
Orbital errors in the satellite
Signal transmission timing errors due to
atmospheric conditions
Receiver errors
Multipath errorsMiscentering errors of the receiver antennas
over the ground station and heighting measuring
errors above the station
Process Carrier phase observations to obtain Baseline vectors
Process network of stations based on baseline vectors
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NOTES
Aim of Surveying (geomatics)?
T d t i th l ti iti f i t b b th th th f
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To determine the relative positions of points above, on or beneath the earths surface
How to determine the values for points position
By performing measurements (observations) of desired quantities such as coordinates
(X,Y,Z), lengths/distances, angles, bearings, azimuths, elevation differences , using
surveying instruments and technologies, and computational techniques
What are the surveying instruments/ technologies?
Electronic Total Station
Global Positioning System (GPS)
Prismatic compass Steel tapes
Levels
Observations contain errors?
Good observations are dependent on the human skill, instruments and environmental
factors. No observation is free from errors. Three types of errors: Gross, Systematic andRandom
Values of quantity: True or Most Probable?
The value of a quantity can be known based on measurements or observations. As the
observations contain errors, hence the observed value that contains the least errors is
considered as closest to the true value
Finding the most probable values (mpv) of observations
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Finding the most probable values (mpv) of observations
Using a steel tape and measure one time the length of line AB. The value of length AB ?
Using a steel tape and measure 10 times the length of line AB. The value of length AB ?
Using a steel tape and measure the length AB in two sections A-H (10 times) and H-B
(20 times), each section was measured different number of times. The value of length
AB?
Using a total station and measure one time each angle in a triangle PQR. The values of
each of the three angles?
Using a total station and measure 10 times (angle P), 20 times (angle Q) and 30 times
(angle R) in a triangle PQR. The values for each of the three angles?
Finding the errors of observations
Gross
Systematic
Random
What is adjustment of observations?The method of estimating and distributing random errors in the observed values in order
to make it conform to certain geometrical conditions, hence the resulted/adjusted values
are known as the most probable values for the quantity involves.