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Re: leg56. Chart vs formulas
From: Jacky Wong
Date: 1999 Jul 16, 7:34 PM

```Sailing in navigation context means the way we travel from the origin to
destination. There are two main types of sailing, the Rhumbline and Great
Circle.

- Great Circle is the shortest path on the earth surface, or a sphere, between
two points. However, we need to constantly change our course in order to follow
a Great Circle route, except between two points on the equator or of same
Longitudes.

- Rhumbline, on the othter hand, is the constant course route between two
points. The distant is longer but it is easier to follow than the Great Circle
route. Assume there is no land, if we "sail" from one point on a constant
course, except to East / West, the route will end up at one of the poles like a
spiral. That is why it is named as Rhumbline. "Plan Sailing", "Middle Latitude
Sailing" and "Mercator Sailing" are the mathmatical methods use to calculate the
Rhumbline route. Becasue the earth is not a sphere, we can't excately calculate
the actual route. Plan; middle lat. and Mercator sailing use approximation to
calculate the route. Mercator sailing based on Mercator Projection, the method
used to construct charts, is the most accurate method. But the mathmatical
solution is more complicate. For shorter routes, middle latitude sailing or plan
sailing (least accurate) can be used.

I have a small site on navigation calculation on Internet and there are some
explainations on sailings quoted from navigation books. Although it is a bit out
of maintenance, please feel free to take a look. The URL is :-

http://www.geocities.com/CapeCanaveral/2265/msail.htm

Jacky Wong
Hong Kong
______________________________ Reply Separator _________________________________
Subject: leg56. Chart vs formulas
Author:  andres ruiz  at gcn-ipo
Date:    7/16/1999 9:15 AM

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

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@orona.es

http://www.geocities.com/CapeCanaveral/Runway/3568/index.html
```
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