Great Circle Sailing Example 2
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Problem

You are on a great circle track departing from 2530.0'N, 07700.0'W and your initial course is 061.7T. The position of the vertex is 3720.0'N, 02545.0'W. There is a floating pub at the vertex. If you leave at 0800, April 3 and travel at 20 knots, when will you be seated with a drink in hand?

L1: 2530.0'N
Lv: 3720.0'N
λ1: 07700.0'W
λv: 02545.0'W

Horizontal Divider 1

How to Solve:
-First establish what you need to know and what you do already know from the information provided.
-Second, solve for what you don't know. In this case, we do not yet know DLo, so we will solve by subtracting λfrom λ1.

-Lastly, now that you only have one unsolved variable, solve for your Dv and ETA using the appropriate equations (see right).

Back to GC Sailings

sin Dv =
(cos L1)(sin DLov)

What you need:
What you know:
L1
2500' N
DLo
???

Horizontal Divider 1

Solving

λ1
07700.0'W
λv
02545.0'W
DLo
λ1v = 5115.0' (E)

sin Dv = (cos L1)(sin DLov)
sin Dv = (cos 25.5)(sin 51.25)
sin Dv = 0.70391
Dv = 44.7 = 2684.5 nm

Time = Distance / Speed
Time = 2684.5nm / 20kts
Time = 134.225 hrs = 5 days 14 hours 14 minutes

Departure
0800, 3 Apr
Time in Transit
5d 14h 14m
Arrival
2214, 8 Apr with a beer in hand