Rendezvous Position Sunrise

Rendezvous Position Sunrise

At 0450 GMT on 18 June 2006, a tanker in position 39° 42′ N, 145° 06′ W has an injured seafarer requiring urgent medical attention onboard. At the same time a passenger vessel in position 40° 00′ N, 148° 07′ W heading

076° T at 26 knots, has a doctor on board and has agreed to assist. It will maintain Course and speed.

It has been agreed that the transfer will take place at sunrise the next morning. Find the following: 

• GMT of sunrise 
• Rendezvous position 
• The course and speed of the tanker to rendezvous at sunrise. 

Rendezvous Position Sunrise

Solution

Step 1 1st Approximation

LMT sunrise for 40 N (18-6-06) = 04 31

Increment for 0000

LMT sunise for 40° 00′ N = 04 31

Longitude in time (148° 07′ W) = + 09 52

GMT sunrise (1st approx) = 14 23 (based on the position at 0450 GMT)

Initial GM = 04 50 

Difference = 09 33

Speed = 26 knots

Distance to run = 248.3′ 

Step 2

Pass Vsl Co 076° (T) = N 76° E

For course 076° T and distance 248 3′, d.lat and Departure are:

dlat = Cos Course x Distance = Cos 076° x 248.3’=60.1′ N (1° 0′.1)

Dep = Sin Course x Distance = Sin 076° x 248.3′ = 240.9′ E

Latitude = Lat of Pass V/L – d.lat

= 40° 00’N – 01° 00.1′ N = 41° 00.1′ N

Mean Latitude = 40° 30.05′ N

d.long = Dep / Cos Mean Lat

= 240.9′ /Cos 40° 30.05′ N= 316′.8 E = 005° 16.8′ E

Longitude = Long Pass V/L – d.long

= 148° 07′ W – 005 16.8′ E = 142° 50.2′ W

Step 3

2nd Approximation for a reined time of sunrise

LMT sunrise for 40° N = 04 31

Increment for O1° 00.1′ = 00 03

LMT sunrise for 41° 00.1′ N = 04 28

Longitude in time (142° 50.2′ W) = O9 31

GMT Sunrse (2nd Appx) = 13 59 (based on 1st approximation of position)

Initial GMT = 04 50 

Difference = 09 09 

Speed = 26 knots 

Distance to run = 237.9′

Step 4

For course 076° T and distance 237.9′, d.lat and Departure are:

d.lat = Cos Course x Distance = Cos 076° x 237.9′ = 57.6′ N

Dep = Sin Course x Distance = Sin 076° x 237.9′ = 230.8′ E

Arrived latitude = Lat of Pass V/L – d.lat

= 40° 00.0′ N – 57.6′ N

= 40° 57.6′ N 

Mean Latitude = 40° 28.8′ N

d.long= Dep/ Cos Mean Lat

230′.8 / Cos 40° 28.8′ N= 303.4 E=005° 03.4′ E

Arrived Long = Long Pass VIL +/- d.long

= 148° 07′ – 005° 03.4′ E = 143° 03.6′ W  

The cargo vessel will have to head for the position of the passenger’s vessel at Sunrise (1359), ie., 40° 57.6′ N, 143° 03.6′ W (Rendezvous position).

Step 5

Cargo vessel’s position at 0450 GMT = 39° 42′ N 145° 06′ W

Passenger Vessel’s position at Sunrise = 40° 57′.6 N 143° 03.6 W 

d.lat = 01° 15.6′ N = (75.6′) ; d.long = 002° 02.4′ E = (122.4′) 

M Lat 40° 19′.8 N

Dep = d.long x Cos M Lat = 122′.4 x Cos 40° 19.8′ = 93.3′ 

Tan Course = Dep /d.lat = 93′.3/75.6′ = 1.23413 = Course N 51° E

Distance d.lat / Cos Course = 75.6′ / Cos 51° = 120.1 Nautical miles

Speed = Distance/ Time = 120.1 / 09 09 = 13.13 Knots

GMT Sunrise = 1359 ;; Course N 51° E ;; Speed= 13.1 Knots ;; Rendezvous Position, Lat= 40° 57.6′ N Long= 143° 03.6′ W