Without a course to steer all your effort in working out direction from the stars, sun and moon, and how to steer by the seat of your pants, is wasted. You need to know what direction to aim the bows rather than pointing towards the horizon and declaring, 'Thataway'!
If you know the latitude and longitude of both your start point and your destination then working out the course to steer is easy (see Figure 18.2).
Finish Latitude and
DIFFERENCE IN LONGITUDE LonaitUd<e which means
Sine A = BC /AC which means f If names instead of letters
BC = Dep = Sine A x AC^r are used these equations can be rewritten as:
rD'lat = Cosine Course x Distance and
Dep = Sine Course x Distance ' To turn a Departure (Difference in Longitude in nautical miles) into a Difference in Longitude in degrees called D'long the equation is
D'long = Departure/ cosine of new Latitude.
Turn minutes and seconds of degrees into decimals by dividing by 60.
EXAMPLE
Course 040° T Distance Sailed 96nm
D'lat = Cos Course x Distance = Cos 40 x 96 = 73.5 = 1° 13.5' New Lat = 49° 23' + 1° 13.5' = 50° 36.5'N
D'long = Dep / Cos New Lat = 61.7 / Cos 50.61 * = 97.2 = 1° 37.2' New Long = 1° 37.2' - 1° 04' = 0° 33.2 E **
Turn minutes and seconds of degrees into decimals by dividing by 60.
^Start Latitude and Longitude
Always work out if you are sailing north or south and east or west - and add or subtract differenc es accordingly.
18.1 Daily Work
Finish Latitude
18.1a Plane Sailing
Difference in Longitude it is called the Departure and written as Dep.
When the difference in Longitude is in degrees it is called the Difference in Longitude
(confused? You should be) and it is written as D'Long
Finish Latitude and
LoLgitudu
18.1b Plane Sailing
Finish Latitude and
LoriLitnUe
D'Long in Degrees or Departure in nautical miles f Q
i"
The coordinates of your start and finish points will give you your D'lat and D'long but to work out the course you must turn the D'long into a Departure. The equation is k Dep = D'long x cos Lat
Start Lat 52° 27.9'N Start Long 04° 32.4E L End Lat 54° 04.8'N End Long 00° 11.2W D'Lat 1° 36.9' D'Long 04° 43.6'
= 04° 43.6 x Cos 56° 16.4' = 283.6 x Cos 56.27° = 157.6'
The equation* to find your
Course = Tan Departure / D'lat = Tan 157.5 / 69.9 = Tan 1.6253 = 58°
You know from your coordinates that you are ' steering North and West and the course to steer is found by subtracting 58 from 360.
Start Latitude and Lgnuitude
18.2 Course to Steer
Finish Latitude
Finish Latitude
18.3 Distance to Sail Distance to Sail
The second question is, how far? Once again, traverse tables provide the answer (see Figure 18.3). Be careful, plane sailing is good up to about 400 nautical miles, beyond which the answers become increasingly doubtful.
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