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Plane Sailing - Basic geometry applies here, it's basically just a few lines and angles and all that
stuff we learned in early high school. Here are the equations you'll need to remember.
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sin C = p/D
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cos C = l/D
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tan C = p/l
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To convert from C (course angle) to Cn (true course), first determine the rough direction of travel. In
the drawing presented, we are moving toward the Northwest, and therefore C would be labeled as N30°W.
-To find the Cn from C, in this case (NW) you would subtract 30° from 360°.
-If C were to the SW, you would add C to 180°.
-If C were to the SE, you would subtract C from 180°.
-If C were to the NW, C=Cn.
To Solve For Course and Distance:
If given lat and long for P1 and P2, solve or convert for l
and final latitude in degrees and tenths, and solve for DLo in minutes, then enter into the equation
p=DLo cos L2 to solve for p. Then solve for C using the equation tan
C= p/l to find C. Next, to find the distance traveled, plug what you know into the equation
sin C = p/D to solve for the distance traveled in nautical miles.
Example
To Solve for Final Position:
If given P1 and a course and distance, work backward through the equations to find what you need.
Use sin C = p/D to solve for the displacement, then solve for l using tan C = p/l. p
can then be converted into DLo using p = DLo cos L2. As you know the initial
L1 and l1,
simply add or subtract l and DLo to find L2 and l2.
Example
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