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    KEJ. GEOMATIK

    ECV 3501

    Assoc. Prof. Dr. Ahmad Rodzi Mahmud

    [email protected]

    [email protected]

    Credit to Dr. Helmi Zulhaidi Mohd Shafri

    4. Angle Measurement

    Outcomes:-

    Understand and apply the concept measurement, traversing,

    equipment used, plotting and accuracy

    mailto:[email protected]:[email protected]:[email protected]:[email protected]
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    Outline

    Introduction

    Units of angle measurement

    Kinds of horizontal angles Bearing & Azimuths

    Computation

    Applications

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    Introduction

    Angles measured in surveying horizontal and vertical depending onwhich plane they are measured.

    Useful for locating points anddetermining directions of lines.

    Horizontal angles* to determine

    bearings and azimuth. Bearings & Azimuth = Directions

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    Introduction

    Can be measured directly using compass, theodolite, total station andsextant.

    Measured indirectly using tape method& geometric formulae.

    3 basic requirements to determine anangle:

    Reference / Starting line

    Direction of turning

    Angular distance (value of the angle)

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    Basic requirements todetermine an angle

    Angular

    measurement

    Direction of turning (+)

    Target

    North /Reference Line

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    Units of angle measurement

    Sexagesimal System: Degrees, Min,Sec

    Centesimal System: Grad

    European Radians rad = 180 degrees

    1 rad = 360/2 = 57.30

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    Types of horizontal angles

    Clockwise angles

    Deflection angles

    Bearings / Azimuths

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    Direction of a line

    In surveying, the direction of a line isdescribed by the horizontal angle thatit makes with a reference line.

    This reference line is called aMERIDIAN or North Point.

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    Meridian or North Point

    Three types of meridians

    Astronomic (or true) N-S reference

    line through the Earths geographic

    poles.

    Magnetic direction taken by a magneticneedle at observers position.

    Assumed arbitrary direction taken forconvenience.

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    The North Pole

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    True North Vs Magnetic North

    1000 miles

    4035

    Magnetic Decl ineation

    Grid

    North

    TRUE

    (Astronomic)

    North

    Magnetic North

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    Magnetic Declineation

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    Azimuth Declineation in topomaps

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    True North Vs Magnetic North

    Today, the magnetic northpoleis located approximately

    1000 miles south of the astronomic NorthPolein the

    Canadian artic near Bathurst Island.

    The compass needle lines up with magnetic north. In

    most places this means that the needles points slightlyeast or west of astronomic north, depending on the

    locality.

    The angle between astronomic north and magnetic north

    is referred to as the magnetic declination, which is 40

    minutedeflected.

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    Magnetic North - Shifted

    The shifting is caused by liquidiron at the Earths core, whichis perpetually in motion. Thatmotion creates electric currents

    in the core, which in turn,creates magnetic fields. Themotion of the Earths corechanges over time andtherefore, the planets magnetic

    fields change as well.

    Blue lines show Earth'snorthern magnetic field andthe magnetic north pole.

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    Bearings

    Two types:

    Quadrant bearing (QB)

    Whole-circle bearing (WCB) or Azimuth

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    Quadrant Bearings

    A method of describing the direction of aline.

    The QB of a line is defined as the smallest

    angle which that line makes with thereference meridian.

    A QB cannot be greater than 90.

    - QB are measured in relation to the north

    or south end of the meridian NE, NW,SE or SW.

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    Quadrant Bearing

    N

    E

    S

    W

    NW

    SW

    NE

    SE

    Y

    X

    Notes:

    ie// xy : N 48 0000 E

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    Quadrant Bearings (QB)

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    Quadrant Bearings

    The reference meridian may be astronomic,magnetic or assumed.

    Its convenient to say: N90E is due East

    S90W is due West

    Until the last few decades Americansurveyors favoured the use of QB.

    With the advent of computers and

    calculators, surveyors and engineersgenerally use WCB / azimuth instead of QB.

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    WCB Bearing / Azimuths

    0

    90

    180

    270

    Y

    X

    Notes:

    ie// xy : 48 0000

    CLOCK WISE ROTATION ! !

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    Forward and Reverse WCB / Azimuth

    Forward bearing XY = 480000

    Reverse bearing XY or bearing

    YX = 48 0000 + 180

    Every line consists two direction.

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    WCB / Azimuths

    Orientation is synonymous withbearing from the surveyors point ofview.

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    EquipmentCompass

    Compass is always

    showing the magnetic

    poles. It is a wonderful

    direction finder. The

    earths magnetic field

    and the use of thecompass have been

    known to navigators

    and surveyors for many

    centuries

    The compass was the

    only means by which

    the surveyor could

    measure angles and

    directions.

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    Magnetic compass

    For surveyors, however, the magneticcompass is not a true workmate.

    It is not accurate enough, and is exposed

    to disturbing effects. E.g. under theinfluence of iron objects

    It may point to a direction which deviatesfrom the north to a high extent.

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    Equipment- Transit / Theodolite - Total

    Station

    http://www.leica-geosystems.com/metrology/en/products/theodolites/lgs_788.htm
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    Advanced equipment -Gyrotheodolite

    - Theodolite +

    gyroscope

    - Determine the true

    bearing

    -Typically used in

    mining surveyingand engineering

    underground.

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    Applications

    Details maps or plans to describe aparticular site or area.

    Setting-out of infrastructure.

    Navigation.

    Positioning of points or targets.

    Many other important applications in

    civil engineering and land surveying.

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    House

    Shed

    Path

    Tree

    Trees

    Angle-angle intersectionExample application - mapping

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    Example Application - Settingout

    e.g. determining the location of a new construction on a site

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    Application - Mapping

    House

    Shed

    Path

    Tree

    Trees

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    Orientation /

    Direction?

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    Establishing orientation

    Approximate orientationcan beestablished using a magneticcompass

    A Certificate of Title showing thebearings of site boundaries could alsobe used

    A professional surveyor could beengaged to undertake a cadastral(title) survey

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    Certificate of Title

    Government Road

    900000

    100.045 m

    100.045 m

    2700000

    1800

    0

    00

    00

    0

    00

    67.2

    53m

    67.2

    53m

    30.257 m

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    Producing a plan

    Choose a standard scale

    Establish orientation

    North up the page

    Arbitrary Plot detail using protractor, compass,

    scale ruler

    Sharp, clean lines; neat, regular lettering

    Or use a CAD or drawing package

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    Exercise

    Compute Q.Bearings given the Azimuth

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    End of lecture