Post on 01-Nov-2014
description
POSITION ON THE EARTH
Do you really know where you are?
ANGULAR MEASUREMENT SYSTEM
8 Apr 2023
Alejandro Menéndez , MA 2
ANGULAR MEASUREMENT SYSTEM
•Circle = 360º•1º = 60’•1’ = 60’’
8 Apr 2023
Alejandro Menéndez , MA 3
PROPERTIES:
Sexagesimal system:
Directions always refered to a datum (North, Prime Meridian or Equator)
Cartesian System (x,y)
ANGULAR MEASUREMENT SYSTEM
8 Apr 2023
Alejandro Menéndez , MA 4
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.
8 Apr 2023
5Alejandro Menéndez , MA
LATITUDE
8 Apr 2023
6Alejandro Menéndez , MA
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)
8 Apr 2023
7Alejandro Menéndez , MA
LONGITUDE
DEFINITION: Shortest angular distance between the Prime Meridian and the meridian passing through that point
8 Apr 2023
Alejandro Menéndez , MA 8
LONGITUDE
8 Apr 2023
Alejandro Menéndez , MA 9
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)
8 Apr 2023
Alejandro Menéndez , MA 10
DIFFERENCE & CHANGE IN LATITUDEDEFINITION: Shortest angular distance along a
meridian between two parallels of latitude.
8 Apr 2023
Alejandro Menéndez , MA 11
D LAT: MinutesCH LAT: Degrees and minutes
*Exercises!
DIFFERENCE & CHANGE IN LONGITUDE
DEFINITION: Shortest angular distance along a parallel between two meridians
8 Apr 2023
Alejandro Menéndez , MA 12
D LONG: MinutesCH LONG: Degrees and minutes
*Exercises!
MEAN LATITUDE
DEFINITION: Algebraic middle value of latitude for two positions.
8 Apr 2023
Alejandro Menéndez , MA 13
MEAN LONGITUDE
DEFINITION: Algebraic middle value of longitude for two positions.
8 Apr 2023
Alejandro Menéndez , MA 14
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.
8 Apr 2023
Alejandro Menéndez , MA 15
Basis for Position Reference System
Creates a Cartesian System
THE GRATICULE
8 Apr 2023
Alejandro Menéndez , MA 16
DEPARTURE
DEFINITION: Longitudinal distance along a parallel of latitude between two predetermined meridians
8 Apr 2023
Alejandro Menéndez , MA 17
DEPARTURE
8 Apr 2023
Alejandro Menéndez , MA 18
D = (2 π R/360) β
d = (2 π r / 360) βd
DR
r
000º
NP
β = CHLong
DEPARTURE
8 Apr 2023
Alejandro Menéndez , MA 19
r
α = LAT
Rr = R Cos α = R Cos LAT
DEPARTURE
8 Apr 2023
Alejandro Menéndez , MA 20
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
8 Apr 2023
Alejandro Menéndez , MA 21
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
8 Apr 2023
Alejandro Menéndez , MA 22
EARTH CONVERGENCY
PROPERTIES:
8 Apr 2023
Alejandro Menéndez , MA 23
• 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
8 Apr 2023
Alejandro Menéndez , MA 24
EARTH CONVERGENCY
CALCULATION:
8 Apr 2023
Alejandro Menéndez , MA 25
CONVERGENCY : CHLong x Sin (LAT)
CONVERGENCY: GCTTin - GCTTfin
¡ Convergency between two positions on different latitudes might be calculated using the mean latitude !
EARTH CONVERGENCY
8 Apr 2023
Alejandro Menéndez , MA 26
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
8 Apr 2023
Alejandro Menéndez , MA 27
C.A. = ½ CONVERGENCY
C.A. = 0.5 CHLong Sin MLat
EARTH CONVERSION ANGLE
8 Apr 2023
Alejandro Menéndez , MA 28
EARTH CONVERSION ANGLE
8 Apr 2023
Alejandro Menéndez , MA 29
EARTH CONVERSION ANGLE
8 Apr 2023
Alejandro Menéndez , MA 30
EARTH CONVERSION ANGLE
The GC track will always be closer to the nearest pole than a RL
8 Apr 2023
Alejandro Menéndez , MA 31
EARTH CONVERSION ANGLE
8 Apr 2023
Alejandro Menéndez , MA 32
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
8 Apr 2023
Alejandro Menéndez , MA 33