The document discusses concepts related to navigation including: - Angles are measured in degrees, minutes, and seconds in a sexagesimal system with 360° in a circle. - Latitude and longitude define positions on Earth and are measured in degrees from the equator and prime meridian, respectively. - Great circle tracks provide the shortest distance between two points on a globe but converge at higher latitudes compared to rhumb lines. - Convergence, change of azimuth, and departure are concepts that relate the angles between great circle and rhumb line tracks. - Formulas are provided to calculate distances and angles based on latitude, longitude, and great circle track changes between positions.

1. Do you really know where you are?

2. Feb-12 Alejandro Menéndez , MA 2

3. PROPERTIES:
•Circle = 360º
Sexagesimal system: •1º = 60’
•1’ = 60’’
Directions always refered to a datum (North, Prime
Meridian or Equator)
Cartesian System (x,y)
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4. PROPERTIES:
Always mesured in clockwise direction
from the reference datum
Recap trigonometry!
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5. 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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7. PROPERTIES:
• 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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8. DEFINITION: Shortest angular distance
between the Prime Meridian and the
meridian passing through that point
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10. PROPERTIES:
• 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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11. DEFINITION: Shortest angular distance along a
meridian between two parallels of latitude.
D LAT: Minutes
CH LAT: Degrees and minutes
*Exercises!
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12. DEFINITION: Shortest angular distance along a
parallel between two meridians
D LONG: Minutes
CH LONG: Degrees and minutes
*Exercises!
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13. DEFINITION: Algebraic middle value of latitude
for two positions.
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14. DEFINITION: Algebraic middle value of
longitude for two positions.
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15. 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.
Basis for Position Creates a Cartesian
Reference System System
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17. DEFINITION: Longitudinal distance along a
parallel of latitude between two
predetermined meridians
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18. D = (2 π R/360) β
r
NP
d d = (2 π r / 360) β
D
β = CHLong
R
000º
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19. r
α = LAT r = R Cos α = R Cos LAT
R
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20. d = (2 π r / 360) β β = CHLong r = R Cos LAT
d = (2 π /360) R CosLAT CHLong
Departure (d) = 60 CHLong CosLAT
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21. D = 60(nm/º) CHLong Cos(Lat)
For every GC: 1nm = 1’ -> 60nm = 1º
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22. 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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23. PROPERTIES:
• 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
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25. CALCULATION:
CONVERGENCY : CHLong x Sin (LAT)
CONVERGENCY: GCTTin - GCTTfin
¡ Convergency between two positions on different latitudes
might be calculated using the mean latitude !
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27. DEFINITION: Difference in direction between
the GC track and the RL track running
through two positions, observed at any of
the points
C.A. = ½ CONVERGENCY
C.A. = 0.5 CHLong Sin MLat
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31. The GC track will always be closer to the
nearest pole than a RL
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33. What 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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