Reasons For The Sailings
The sailings get their name from the days of sail when charts were reference sources for the navigator and were almost never used for plotting. In those days, determination of future DR position, voyage planning, prediction of ETA, and most other evolutions which are now done on charts or plotting sheets, were done mathematically. These mathematical methods are known as the "sailings". In actuality there are seven different types of sailings. The choice of which would be used was primarily dependent on the distance and direction to be traveled and some other factors. While the sailings were used extensively in times past, they are seldom used today. The availability and use of relatively inexpensive and highly accurate charts in coastal navigation, along with great circle sailing charts (Gnomonic projections) and modern ship routing services have relegated the sailings to a matter of academic interest. While seldom used in actual practice today, they do remain in one place the deck officer license exam.
Terminology of Sailing Problems
The various values which are given or found in sailing problems have been given certain abbreviation symbols. Some of them might be familiar to you or self explanatory, others will be new. You should be familiar with the symbol and brief descriptions given below.
L1 - Latitude of the point of departure (position the vessel is leaving from)
Lo1 - Longitude of the point of departure
L2 - Latitude of the point of arrival (position the vessel is going to)
Lo2 - Longitude of the point of arrival
Lm - The latitude mid-way between L1 and L2
I - Difference of latitude between L1 and L2. It is assigned a sign, "N" or "S," depending on the direction of L2 from L1 or course of the vessel (N for courses in the NW and NE quadrants, S for courses in the southerly quadrants).
Note: When L1 and L2 are on different sides of the equator, the difference of latitude (l) is the sum of the two latitudes.
Dlo - Difference of longitude between Lo1 and Lo2. It is assigned a sign "E" or "W," depending on the course of the vessel or the direction of L2 from L1.
Note: Dlo is always less than 180°. When one point is in east longitude and the other in west, Dlo is measured either across the prime (0°) meridian or the 180th meridian by the shortest distance. For example, when Lo1 is 165°00.0' E and Lo2 is 170°00.0' W, Dlo is 25°00.0' (E).
p - Departure - The number of miles measured east or west between Lo1 and Lo2 (it has the same sign, E or W, as Dlo).
Here is a example, true course (Cn) 166° T is in the SE'ly quadrant. Course angle (C) would be 14°.
D - The distance the vessel travels. It may be determined from the vessel's speed and the time travelled.
M1 - The number of meridional parts of L1.
M2 - The number of meridional parts of L2.
m - The meridional parts difference between M1 and M2. Meridional parts are assigned to each minute of latitude from the equator to the pole in table 5 of Bowditch, Volume II. Meridional parts aid in constructing of Mercator charts and solving problems in Mercator sailing.
Note: When L1 and L2 are on different sides of the equator, meridional difference (m) is equal to the sum of Ml and M2.
Methods Of Solving Sailing Problems
There are two basic methods which may be used to solve the sailings problems which might be in the license exam. One is by mathematical formulas and the other is by the tables in Bowditch, Volume II. The sailing formulas are all listed in Bowditch, Volume II, a publication which is available for you to use in the exam room. The sailings chapter contains explanations on how to solve all types of sailings. You should remember where these formulas are in Bowditch in case your memory starts to fail while taking the exam. A hand-held calculator is the preferred method of solution. Your calculator must have the capability of multiplying and dividing with Sine, Tangent, and Cosine trigonometric functions. All the formulas are very basic and a modestly priced calculator is all that you need for these problems.
Parallel Sailing
Parallel sailing is used for vessels that are sailing along a parallel of latitude. Its course must be either east (090° T or west (270° T. There are two categories of parallel sailing problems:
1. Problems where the latitude and longitude of the point of departure are given. The vessel then proceeds on course 090° T or 270° T for a given distance. You must find the longitude of the point of arrival.
2. Problems where the coordinates of two positions along the same parallel of latitude are given, and you must find the course and distance between them.
Middle Latitude Sailing
Middle Latitude, or Mid-Latitude sailing problems are used when the vessel is proceeding along a course other than north (000°), south (180°), east (090°) or west (270°). There are two different types of Mid-Latitude problems which the Coast Guard can give you in the exam.
1. The coordinates of the points of departure and arrival are given. The course and distance between them must be found.
2. The coordinates of the point of departure and the vessel's course and the distance travelled are given. The coordinates of the point of arrival must be found.
Mercator Sailing
The Mercator sailing problems are the next level of complexity of the sailing problems found in the license exam. A solution by Mercator sailing is appropriate whenever the distance between the points of departure and arrival exceeds a few hundred miles.
Mercator sailing problems are of two general types:
1. The coordinates of the points of departure (Ll and Lol) and arrival (L2 and Lo2) are given. The course (Cn) and distance (D) between them must be found by Mercator sailing. This course and distance is along the rhumb line joining the two points.
2. The coordinates of the point of departure (Ll and Lol) are given along with the course (Cn) and the distance (D) that the vessel travelled. The coordinates of the point of arrival (L2 and La2) must be found by Mercator sailing. This type problem is sometimes called a "reverse Mercator sailing".
In up coming blogs I will show you how you can solve Mercator, Parallel, and Mid-Latitude sailings problems found on the Coast Guard exams.
