Surveying Errors and Adjustment
A short Training Course
Prepared By:Prepared By:
Dr. Maher A. El-HallaqLecturer of SurveyingFaculty of Engineering
The Islamic University of Gaza
April, 2011
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Part One:
Surveying Errors (sources and types)
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Sources of Errors در ا;���ء� �
Measure a distance several times and compare
the obtained measurements????
They are not equal and the reason:They are not equal and the reason:
The imperfections of the instruments
The fallibility of the human operator
The uncontrollable nature of the environment
Errors always exist in measurements, where:
The error (The error (eeii)) = the measured value (x= the measured value (xii) ) –– the true value (x)the true value (x)
But since the true value can never be determined, we But since the true value can never be determined, we
can use instead the most probable value (xm). Thus:
eeii = x= xi i –– xxmm
Where,
Types of Errors ا;���ء > ? @
Blunders (Mistakes) أ���ء $� ��
Random Errors �B5اA � أ���ء
Systematic Errors �?���1 أ���ء
Blunder Errors (Mistakes) أ���ء $� ��
caused by human carelessness, fatigue and haste
can be positive or negative, large or small and theiroccurrence is unpredictable
recording 43.18 instead of 34.18 and sighting a wrongtarget when measuring an observation
Blunders are disastrous if left in the surveyingmeasurements
must be eliminated by careful work and by using fieldprocedures that provide checks for blunders
Random Errors � Aا�B5 أ���ء
caused by imperfections of the measuring instruments,the surveyor to make an exact measurement, and thevariations in the environment
can be minimized by using better instruments andcan be minimized by using better instruments andproperly designed field procedures and by makingrepeated measurements
have small magnitudes
Positive and negative errors of the same magnitude occur with the same frequency. Cancel each other
Consider the mean value
Systematic Errors ���1 � أ���ء
behave according to a particular system or physical lawof nature, which may or may not be known
When the law of occurrence is known, systematic errorscan be calculated and eliminatedcan be calculated and eliminated
always occurs with the same sign and magnitude and istherefore often referred to as a constant error
Examples: assuming occupy point coordinates, earth curvature and temperature or pressure corrections
Correction doesn’t require field re-measurements
Example:
Given 12 measurements of a certain distance, as follows:
58.78، 58.83، 58.80، 58.85، 58.18، 58.77، 58.79، 58.80
58.81 & 58.82، 58.79 ،58.82
First iteration (n = 12)
= 58.75 m
= ± 0.18 m
Second iteration (n = 11):
xm = 58.81 m σx = ± 0.02 m max. error= ± 0.06 m
Precision and Accuracy
Precision and Accuracy
In general, to obtain high precision and high accuracy in surveying, the following strategies must be followed:
Follow techniques that will help detect andFollow techniques that will help detect andeliminate all the blunders.
Eliminate or correct all systematic errors byfrequent calibration and adjustment of theinstruments
Minimize the random errors by using goodinstruments and field procedures.
Part Two:
Control points Selection
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Control points
Control points may be:
Benchmark points (z)Benchmark points (z)
Horizontal coordinate points (x, y)
Combined (x, y, z)
Benchmark points \ (�?� [��@ ط���
The following conditions should be considered:
Its elevation should be accurately measured
Evenly distributed to enable surveyors to use themto determine elevations every where in the region
Well marked and fixed in the ground
Have precise description to locate them easily
Benchmark points \ (�?� [��@ ط���
Positioning before GPS
Surveys took on the form of networks of triangles. The vertices of the triangles often became horizontal control points. Initial positions were points. Initial positions were determined using astronomical observations.
Horizontal coordinates (latitude and longitudes) were determined separately form vertical coordinates (elevation)
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The following conditions should be considered:
Suitable location (away from multistory buildings,electric wires, traffic, changeable area, etc)
Enough distributed points, see at least two otherpoints (backsight and foresight)
Well marked and fixed in a firm ground
Have precise description to locate them easily, welldocumentation
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GPS points 9��3( 3( أس � ���ط @��] ا�&ا/ �ت أ*� Increasing the accuracy of GPS coordinate calculation:
Point location
The specification of the used receiver
Number of used receivers
Surveyor and GPS operator
� Before measuring
� During measuring
� After measuring
Property surveys to establish boundaries -Traverse
Opentraverse
Closedtraverse
Property surveys to establish boundaries -Traverse
The following conditions should be considered:
Minimum number of stations, as needed
lines should be as close as possible to the details to be surveyedlines should be as close as possible to the details to be surveyed
Distances between traverse stations should be approximatelyequal
Stations should be chosen on firm ground, or monumented in away to make sure that they are not easily lost or damaged
easy to see the backsight and foresight stations from onestation
Part Three:
Adjustment of Surveying Networks
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Leveling Networks
Ordinary levelingK=30 mm
Precise levelingK=5 mm
D= Distance in Kmmm
Coordinate Networks (Traversing)
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Coordinate Networks (Traversing)
Adjustment process includes:
Angle correction
Distance correction
1. Angles Adjustment
True sum of internal angles = (n – 2)×180˚
Determine the measured sum
Angle error = measured sum – true sumAngle error = measured sum – true sum
If angle error ≤ (60 – 90)˝ , accept the error, else, reject.
Correct each angle by adding to it
Compute the corrected azimuth for each traverse side using:
2. Position Adjustment
Starting from the known point, calculate thecoordinate of all points ending to the start point
Error in the easting direction(εx) = xmeasured – xtrue
Error in the northing direction(εy) = ymeasured – ytrue
Accept or reject errors according to specifications
Correct positions according to compass rule
Allowable errors in traverse surveying
Example:
Angle correction step
Position correction step
∆x= ∆y= yx
Position correction step
Thank You !!!!Thank You !!!!