adj comp lecture_1

7/24/2019 ADJ COMP lecture_1

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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 errorscaused 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




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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




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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.

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