2.Position on the Earth

POSITION ON THE EARTH

Do you really know where you are?

ANGULAR MEASUREMENT SYSTEM

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ANGULAR MEASUREMENT SYSTEM

•Circle = 360º•1º = 60’•1’ = 60’’

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PROPERTIES:

Sexagesimal system:

Directions always refered to a datum (North, Prime Meridian or Equator)

Cartesian System (x,y)

ANGULAR MEASUREMENT SYSTEM

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PROPERTIES:

Always mesured in clockwise direction from the reference datum

Recap trigonometry!

LATITUDE

DEFINITION: Angle of the arc along the meridian joining the Eq. and the point.

Also, the angle of the arc along a meridian between the Eq. and the paralel where the point is.

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LATITUDE

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LATITUDEPROPERTIES:

• From 0º up to 90º (North/South)• 2 digits needed • Standard expressions:

• 6015N or N6015 (Accuracy 0.5’ of arc or 0.5nm)

• 601508N or N601508 (Accuracy 0.5’’ of arc or 15.4m)

• 6015.13N or N6015.13 (Accuracy 0.5’’ of arc or 15.4m)

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LONGITUDE

DEFINITION: Shortest angular distance between the Prime Meridian and the meridian passing through that point

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LONGITUDE

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LONGITUDEPROPERTIES:

• From 0º to 180º (East/West) (Up to Greenwich Anti- Meridian)

• 3 Digits• Standard expressions:

• 05530E or E05530 (Accuracy of 0.5’ of arc)

• 0553020E or E0553020 (Accuracy of 0.5’’ of arc)

• 05530.30E or E05530.30 (Accuracy the same)

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DIFFERENCE & CHANGE IN LATITUDEDEFINITION: Shortest angular distance along a

meridian between two parallels of latitude.

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D LAT: MinutesCH LAT: Degrees and minutes

*Exercises!

DIFFERENCE & CHANGE IN LONGITUDE

DEFINITION: Shortest angular distance along a parallel between two meridians

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D LONG: MinutesCH LONG: Degrees and minutes

*Exercises!

MEAN LATITUDE

DEFINITION: Algebraic middle value of latitude for two positions.

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MEAN LONGITUDE

DEFINITION: Algebraic middle value of longitude for two positions.

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THE GRATICULE

DEFINITION: Net drawn on the surface of the Earth formed by the Prime Meridian and the rest of meridians in one sense, and the Equator plus the parallels of latitude.

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Basis for Position Reference System

Creates a Cartesian System

THE GRATICULE

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DEPARTURE

DEFINITION: Longitudinal distance along a parallel of latitude between two predetermined meridians

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DEPARTURE

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D = (2 π R/360) β

d = (2 π r / 360) βd

DR

r

000º

NP

β = CHLong

DEPARTURE

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r

α = LAT

Rr = R Cos α = R Cos LAT

DEPARTURE

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d = (2 π r / 360) β r = R Cos LATβ = CHLong

d = (2 π /360) R CosLAT CHLong

Departure (d) = 60 CHLong CosLAT

DEPARTURE

For every GC: 1nm = 1’ -> 60nm = 1º

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D = 60(nm/º) CHLong Cos(Lat)

EARTH CONVERGENCY

DEFINITION: Tilt angle of meridians towards one another.

Angular change of direction of a GC course as it passes from one meridian to the other

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EARTH CONVERGENCY

PROPERTIES:

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• All meridians meet at the poles with an angle equal to the CHLong between them

• All meridians are parallel as they cross the Equator

• Increases with an increasing latitude• Increases with and increasing change in

longitude• Angular difference between the initial and final

course along a GC passing through two definite points

EARTH CONVERGENCY

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EARTH CONVERGENCY

CALCULATION:

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CONVERGENCY : CHLong x Sin (LAT)

CONVERGENCY: GCTTin - GCTTfin

¡ Convergency between two positions on different latitudes might be calculated using the mean latitude !

EARTH CONVERGENCY

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EARTH CONVERSION ANGLE

DEFINITION: Difference in direction between the GC track and the RL track running through two positions, observed at any of the points

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C.A. = ½ CONVERGENCY

C.A. = 0.5 CHLong Sin MLat

EARTH CONVERSION ANGLE

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EARTH CONVERSION ANGLE

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EARTH CONVERSION ANGLE

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EARTH CONVERSION ANGLE

The GC track will always be closer to the nearest pole than a RL

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EARTH CONVERSION ANGLE

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QUESTIONS TO THINK ABOUTWhat is the difference in nm and km from position A

(41º25’N) to position B(79º30’N). Both on the same meridian?

An aircraft is to fly from position 72ºN 002º30’E to position 72ºN 177º30’W on the shortest possible route

a) Give the initial True track direction.

b) Will the track direction remain the same for the whole flight?

c) Give a reason for the answer given in b above

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