Composite Sailings

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Because Land Is Hard To Swim Through

Composite Sailings are sailings that use both principles of both GC and Parallel sailings in order to cover the shortest distance between two points while avoiding an object at a given latitude. A Limiting Latitude (in these equations referred to as Lv), is the closest to the pole that trackline is allowed to go. Ice flows, land masses, or storms can cause a course to be limited to only certain latitudes to ensure safe navigation.
To Solve Composite Sailings:
Don't: Do not just draw your straight line on a gnomonic chart and sail the limiting latitude once you reach it. This route will be much longer, and thus more costly than sailing as follows.
-First, find the appropriate Gnomonic chart for your ocean region
  -Gnomonic charts are used because GC curves are represented as straight lines
-Second, find your limiting latitude
  -If you know where an ice flow or land will be, plot it on the chart so that you know to avoid it.
-From your point of departure, draw a line that will be tangent (touching at only one point) to your limiting latitude toward your point of arrival.
  -This line will be the most efficient way to reach your limiting latitude, while still approaching your destination
-From your point of arrival, draw line that will be tangent to the limiting latitude
-Between the two points where your lines meet the limiting latitude, you will sail along the limiting latitude (this will be a Parallel Sailing)
     -Use the equations at right to solve for your point of tangency; this will be the point at which your GC track become a Parallel one.
     -These equations can also be found on Bowditch page 350
-First, convert all of your positions into degrees and tenths rather than degrees and minutes
-As you know your limiting latitude already, solve for DLovx using one of the equations provided
-Either add or subtract DLovx to or from your initial or final longitude to find the longitude of each of your points of tangency
-From here, use GC and Parallel equations to find course and distance information between the points.

tan Lx =
(cos DLovx)(tan Lv)
cos DLovx =
(tan Lx) / (tan Lv)