JavaScript Navigator
- Great Circle Sailing
Below is a form using JavaScript that solve the Great Circle Sailing
problem. Please note that inputs with leading zeros will cause errors
when processed by this script.
The form has been tested with Netscape 2.02, Netscape 3.0 and MS Internet Explorer 3.0 - The full track function is not yet supported by Internet Explorer 3.0
Great Circle
A great circle is defined as a circle on the earth's surface the plane of which passes
through the centre of the earth.
For navigation purposes :
- The great circle track is the shortest distance between two places on the
earth's surface.
- The great circle track appears as a straight line on Gnomonic (great circle) charts.
- The vertices of a great circle are the two points nearest to the poles which
have a course on the great circle track due EAST / WEST.
Great Circle Sailing
To follow a great circle track, the navigator needs to adjust the ship's course
continuously because the great circle track is a curve when plotted on a Mercator Chart.
Therefore, it is not really practicable to sail on an exact great circle route.
In order to take advantage of the shorter steaming distance of the great circle track, mariners
usually divide a great circle track between the initial position and the destination
into smaller segments (way points) of about one to two day's steaming time and make course adjustment
at noon. The total distance is therefore the sum of the distances of those segments
calculated by means of Mercator Sailing.
Composite Great Circle Sailing
Although the great circle track is the shortest route between two locations, it also
usually enroutes closer to the pole (or to higher latitude) than the two places.
To avoid the danger of steaming on high latitude, which normally associates with
bad weather and icing, a careful master mariner will normally set a latitude limit on his
ocean passage plan. The ocean passage will thus consist of a first great circle track
with vertex at the latitude limit then sailing along that latitude until meeting
the vertex of a second great circle track leading to the destination. This type of
route is named as composite great circle route.
The easiest method to outline a composite greate circle route is by plotting it on
a Gnomonic chart.
The figure on the right shows the relationship between the three types of route,
the rhumb line, the great circle and the composite great circle routes for the same
set of locations.
What's new here?
The most annoying part of the great circle sailing calculation is to find out the way
points along the great circle route. The traditional way is to determine the position
of the vertex and use Napier's rules to calculate individual way point's Latitude and
Longitude. This method is not really very complex but is not suitable for
computerization as a set of conditions will need to be established in order to determine
the side of the positions.
In this script, I use a formula which was derived by myself when I was working on board
as a Second Officer. This formula uses a simple sine relationship between Latitude and
Logitude which makes the way point calculation more suitable for computerization.
The formula is :-
tan Latitude = sin (Longitude - X) * tan K
where X is the Longitude when the GC track crosses the equator from south to north
and K is the maximum Latitude of the GC track or Latitude of Vertex.
The Longitude value should be reduced to 360-degree notation measured from Greenwich towards
the East. e.g. 165 degrees West will be treat as 195 degrees.
By using the above formula, this script provides a full definition of great circle tracks
at 5-degree longitude intervals - the [Full Track] function of the form - as well as
the corresponding Latitude of any given Longitude.
[ Home ? 
]
This page hosted by 
Get
your own Free Home Page