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In coastal navigation I use the charts for navigation, but when the distance 
is outside of the chart, for me is easier to use a calculator with 
trigonometric functions in order to obtain the DR position, or to find the 
rhumb to a point.
I've compared the Mid-Latitude Sailing, the RhumbLine, and the Great Circle 
Sailing of the point 2) of the Leg 56, and here are the results.
The distance is a great one, because of this the best method is to divide the 
GC track in small legs, and sail between them by a rhumbline, from a waypoint 
to another.
    Lat1
             Lon1
             R
             d
             Lat2
             Lon2


            LatitudMed
             R, d ?
             -42.6633
             -98.8583
             124.3904
             1487.5287
             -56.6667
             -67.25


            Loxodromica
             R, d ?
             -42.6633
             -98.8583
             124.5705
             1480.7388
             -56.6667
             -67.25


            Ortodromica
             R, d ?
             -42.6633
             -98.8583
             135.9026
             1466.8856
             -56.6667
             -67.25


            Ortodromica
             WayPoint
             -42.6633
             -98.8583
             135.9026
             506.8132
             -48.4098
             -90

            Ortodromica
             WayPoint
             -48.4098
             -90
             129.5663
             245.2815
             -50.9095
             -85

            Ortodromica
             WayPoint
             -50.9095
             -85
             125.7533
             222.4828
             -52.9731
             -80

            Ortodromica
             WayPoint
             -52.9731
             -80
             121.8148
             204.0477
             -54.6645
             -75

            Ortodromica
             WayPoint
             -54.6645
             -75
             117.7777
             189.2925
             -56.0348
             -70

            Ortodromica
             WayPoint
             -56.0348
             -70
             113.6634
             177.6471
             -57.1245
             -65

            Ortodromica
             WayPoint
             -57.1245
             -65
             289.4892
             78.6791
             -56.6667
             -67.25

If you want, in the address below, you can find the algorithm for mercator 
sailing and rhumbLines. The titles are in Spanish, but the algorithm are 
mathematics, universal language.
http://www.geocities.com/CapeCanaveral/Runway/3568/index.html [Navigation] [Mercator sailing]
I translate some words for anyone interested:
Rumbo y distancia Course and distance
Posicion. La estima Dead reckoning
Loxodromica Loxodromic or rhumbLines
Partes meridionales Meridional parts
I don't know what is the difference between mercator sailing and rhumbline, for me is the same ??
Andr?s Ruiz
e-mail: aruiz@XXX.XXX
http://www.geocities.com/CapeCanaveral/Runway/3568/index.html

   

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