**Composite Great Circle Sailing**

**On 5 March 2005 at 1200 hours local time, a vessel is expected to depart from port Elizabeth (South Africa) to arrive at Melbourne (Australia) with a General average speed of 12.5 knots. The Master intends to follow a composite great circle track with a limiting latitude of 42° S from: **

**Departure position: 34° 05′ S 026° 00′ E.Landfall position: 39° 00′ S 143° 50′ East.The Pilotage distance from port Elizabeth to the departure position is 45 miles and from the landfall position to berth Melbourne is 84 miles. Calculate following: **

**The total distance of the voyage.ETA local time at landfall position?**

Dlong = 143**°** 50′ – 026**°**00′ = 117**°** 50′

**Composite Great Circle Sailing**

△ PAV1 , V1 = 90**°**

PA = 90**°** – 34**°** 05′ = 55**°** 55′

PV1 = 90**°** – 42**°** = 48**°**

By using Napiers rule,

Sin (90 – P1) = tanPV1.tan(90-PA)

cos P1 = tan 48**°** . tan 34**°** 05′

P1 = 41.28**°**

Again using Napiers rule,

sin AV1 = cos (90- P1) . cos(90 – PA) = sin P1 . cos (90 – 55**°**05′)

sin AV1 = sin 41.28**°** . cos 34**°** 55′

AV1 = 33.12**°** = **1987.3′**

Now, In △ PBV2 , V2 = 90**°**

PB = 90**°** – 39**°**00′ = 51**°**

PV2 = 90**°** – 42**°** = 48**°**

By using Napiers rule,

sin (90 – P3) = tan (90 – PB) . tan PV2 = tan (90 – 51**°**) . tan (48**°**)= tan 39**°** . tan 48**°**

cos P3 = 0.899

P3 = 25.93**°**

Again using Napiers rule,

sin BV2 = cos (90- P3) . cos(90 – PB) = sin P3 . cos (90 – 51**°**) = sin 25.93**°** . cos 39**°**

BV2 = 19.86**°** = **1191.97′**

Now, P2 = dlong – (P1+P3) = 117**°** 50′ – (25.93**°** + 41.28**°**) = 50**°** 37.4′

Distance (departure) = dlong P2 * cos m’lat = 50**°** 37.4 * cos 42**°**

= **2257.2 miles**

Total distance = **1987.3′** + **1191.97′** + **2257.2** ‘ + **45 ‘ + 84 ‘** = **5565.4 miles** (Ans.)

Distance upto Landfall position = 5565.4 – 84 = 5481.4′

Time required = 5481.4 / speed = 5481.4 / 12.5 = 438.5 hours = 18d 6h 30m

Departure time = 05d 12h 00m (Local time)

Time required = 18d 6h 30m

So, LMT at landfall = 23d 18h 30m

Clock advanced = 9h 00m 00s

So, LMT at landfall (with clock) = 24d 3h 30m (Ans.)