Saturday, February 7, 2009

Great Circle Tracking Charts

The Coast Guard uses questions which refer to great circle tracking charts. If you are testing for a mates license you could easily have one of these questions on your exam. Below are six example problems with a explanation. These examples should give you a sense of how to reach the answers to problems of this type. If you can get charts WOXZC 5270 and WOXZC 5274 you can follow the explanations with each of the 6 example problems below.

Example Problem 1:
A great circle track would be most advantageous when compared to the rhumb line track on which of the following routes? (Use gnomonic track­ing chart WOXZC 5274 - North Atlantic)

A. Cayenne (Lat. 4°40.0' N, Long. 52°15.0' W) to Sao Tome (Lat. 0°00.0', Long. 3°15.0' W)
B. Palm Beach, FL to the English Channel
C. Natal, Brazil to Reykjavick, Iceland
D. Recife, Brazil to Monrovia, Republic of Liberia

Step 1: Using a pencil and straightedge lightly draw in a line between the points listed in each of the above choices.

Step 2: Eliminate choice A. Cayenne and Sao Tome are both so near the equator (which is a great circle) that a rhumb line track between them would not be appreciably longer than a great circle.
Step 3: Choice B is the correct choice. It represents the situation where a great cir­cle is advantageous, a voyage between points in the middle latitudes with a significant difference of longitude between the points.

Step 4: Eliminate choice C. Natal, Brazil is almost due south of Iceland, the rhumb line between the places does not diverge significantly from being a meridian which is a great circle.

Step 5: Choice D may be eliminated because the two points are in the vicinity of the equator rather than the middle latitudes. In addition, the distance between the points is relatively short which decreases the advantage of great circle over rhumb line tracks.

Example Problem 2:
You are planning a voyage from Cape May (Lat. 38°45.0' N, Long. 74°­45.0' W) to Lisbon (Lat. 38°37.0' N, Long. 9°45.0' W). Which of the fol­lowing is true? (Use gnomonic chart WOXZC 5274)

A. Because the latitudes are almost the same, a great circle track approxi­mates parallel sailing.
B.The northern hemisphere vertex is approximately at longitude 42°10.0 W
C.The distance is measured by using the length of one degree of the meridian at the position of the vertex.
D. A composite sailing must be plotted to remain south of a limiting lati­tude of 44° N

Step 1: Use a straight edge to draw a line between the two points on the chart.

Step 2: Eliminate choices A, C, and D for the following reasons.

Choice A - The great circle track diverges significantly, from parallel sailing. This can be seen if a line is drawn along latitude 38°40 to compare with the great circle. A rhumb line track like a parallel sailing would be much longer.

Choice C - The distance is not measured by the method stated. Measurement of distance on a Gnomonic chart can not be done by direct methods.

Choice D - The latitude of the vertex of this great circle is 43.8° N. This is less than the limiting latitude of 44° N. So composite sailing is not required.

Step 3: Choice B is correct. The great circle track reaches its maximum north latitude 43.8 degrees north (vertex) at approximately 42.1° W longitude.

Example Problem 3:
On a voyage via the southern tip of Nova Scotia (Lat. 43°20.0' N, Long. 65°35.0' W) you wish to sail the shortest route to La Corunna, Spain (Lat. 43°20.0' N, Long. 8°24.0' W). Which of the following will require you to plot a composite sailing? (Use gnomomic sailing chart WOXZC 5274)

A. Shoals extending 15 miles from Sable Island
B. Sea ice reported 68 miles ESE of St. Johns, Newfoundland
C. Icebergs reported extending to west to west-northwest from Lat. 47°00.0' N, Long. 35°00.0' W
D. Naval exercises using live ammunition being conducted within a 150 mile radius of Lat. 49°00.0' N, Long. 20°00.0' W.

Step 1: Use a straightedge to draw a great circle track between the two points.

Step 2: Choice A may be eliminated because your great circle track will pass more than one degree of latitude (60 miles) north of Sable Island avoiding any shoals extending 15 miles from the island.

Step 3: Choice B is eliminated because this great circle track passes well away from the sea ice reported 68 miles ESE (112.5° T) from St. John.

Step 4: The icebergs reported extending west to west-northwest (270° to 292.5° T) from Lat. 47°00.0' N, Long. 35°00.0' W lie astride the track. A composite sailing can be used to avoid this hazard. This is the correct answer.

Step 5: Choice D can be eliminated as your track takes you south of the naval exercises extending a 150 mile radius around Lat. 49°00.0' N, Long. 20°00.0'W.

Example Problem 4:
You are planning a voyage from departure Seattle (Lat. 48°30.0' N, Long. 125°00.0' W) to a position at Lat. 44°00.0' N, Long. 161°00.'0 E. Which of the following statements is true? (Use gnomonic chart WOXZC 5270)

A. You must plot a composite sailing to remain south of the Aleutian Islands.
B. The northern hemisphere vertex lies to the west of your arrival position.
C. Military exercises north of 53° N between longitudes 150° W to 165° W will not effect your voyage.
D. At your highest latitude, the sun will be visible at upper and lower / transit if the voyage occurs near 21 June.

Step 1: Use a straightedge to draw a line bewteen the points of departure and arrival which were given.

Step 2: Eliminate choice A. The great circle track passes south of the southern most of the Aleutian Islands.

Step 3: Eliminate choice B. The northern hemishere vertex is at about Lat. 52°45.0' N, Long. 155°00.0' W between the points of departure and arrival.

Step 4: Choice C is the correct choice. The statement that the voyage will not be effected by military exercises is true. The great circle track passes just south of the exercice area above 53° N between 150° W tp 165° W.

Step 5: Eliminate choice D. In order to see the sun at upper and lower transit about June 21, the track would have to go above latitude 66°30.0' N (the Arctic Circle).

Example Problem 5:
You are planning a voyage by great circle from Lat. 59°00.0' N, Long. 07°00.0' W via Lat. 38°00.0' N, Long. 61°30.0' W. Which of the following statements is true? (Use gnomonic tracking chart WOXZC 5274)

A. You are east of the northern hemisphere vertex.
B. When plotted on a Mercator chart the track line will be concave to Cape Farwell.
C. All courses are in the southwest quadrant of the compass.
D. Distance is measured by using the length of a degree of latitude at the midpoint of the trackline.

Step 1: Use a straight edge to draw a line between the coordinates of the points given.

Step 2: Eliminate choice A. The northern hemisphere vertex is east of the point of departure. It is located approximately 59°15.0' N, 01°00.0' E.

Step 3: Eliminate choice B. Great circles between points which lie in the northern hemisphere are concave to the equator. Therefore, this trackline is convex, not concave, to Cape Farwell (south tip of Greenland) which lies to the north of the track.

Step 4: Choice C is the true statement. Inspection of the angle at which the track­line intersects each meridian between departure and arrival indicates all the courses to be steered will fall in the southwest quadrant (between 180° T and 270° T).

Step 5: Eliminate choice D. Distance may not be measured directly on gnomonic charts. The method given for measurements is true for Mercator chart pro­jections not gnomonic projections.

Example Problem 6:
In planning a North Pacific voyage, you wish to steam the minimum dis­tance from Lat. 48°30.0' N, Long. 124°45.0' W, to Lat. 44°00.0' N, Long. 150°00.0' E, while remaining south of 51° N latitude. Which of the follow­ing tracks meets these requirements? (Use gnomonic tracking chart WOXZC 5270)

A. A Mercator sailing from departure to the mid-longitude at 51° N, which is great circle to arrival.

B. A great circle between departure and arrival with parallel sailing between the longitudes where the great circle intersects 51°N.

C. A great circle, tangent to 51°N, from departure to the mid-longitude, then a great circle to arrival.

D. A great circle from departure to Lat. 51° N, Long. 148°, parallel sailing to Lat. 51° N Long. 171° W, then a great circle to arrival.

The shortest distance between two positions when there is a limiting lati­tude is called a "composite sailing". Choice D exactly describes the method of plotting a composite sailing track and it is the correct choice.

Choice A has the ship traveling by rhumb line for 42.6 degrees of longi­tude between departure and the mid-longitude. This is half the trip by a less economical route.

Choice B is even less efficient than A. On the direct great circle route the ship would reach the limiting latitude of 51° N at 133° W. It would then travel by rhumb line until the direct great circle returns to 51° N at 168° E. This would mean traveling for 59 degrees of the total difference of longi­tude, which exceeds 85 degrees, by rhumb line.

Choice C is a fairly efficient route but its combination of two great circles lies south of the composite sailing route for its entire length. This indicates it is longer than the composite sailing. Which means the composite route lies closest to the direct great circle route and will save the greatest distance while conforming to the limiting latitude restriction.