CHAPTER - 13
CHAPTER - 13
GREAT CIRCLES AND RHUMB LINES
GREAT CIRCLES AND RHUMB LINES
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Learning Outcomes
Learning Outcomes
1. Understand Basic Concepts
1. Understand Basic Concepts
Define a Great Circle as the largest circle that can be drawn on a sphere, dividing it into two equal halves.
Define a Rhumb Line (or loxodrome) as a line crossing all meridians at the same angle, representing a constant compass direction.
Explain the differences between Great Circles and Rhumb Lines in terms of navigation and distance.
2. Apply Great Circle Navigation
2. Apply Great Circle Navigation
Understand that the shortest distance between two points on the Earth’s surface is along a Great Circle.
Plot a Great Circle route on a nautical chart.
Calculate initial and final courses and distances for a Great Circle voyage.
Understand the need for course adjustments when following a Great Circle.
3. Apply Rhumb Line Navigation
3. Apply Rhumb Line Navigation
Understand that a Rhumb Line keeps a constant compass bearing but is longer than a Great Circle route over long distances.
Plot a Rhumb Line course on a Mercator chart.
Calculate distance and course for Rhumb Line navigation.
4. Compare and Choose Navigation Methods
4. Compare and Choose Navigation Methods
Compare the advantages and disadvantages of Great Circle vs. Rhumb Line navigation.
Decide when to use a Great Circle (for long distances) and when to use a Rhumb Line (for easier course-keeping).
5. Solve Practical Navigation Problems
5. Solve Practical Navigation Problems
Calculate the difference in longitude (D'Lo) and latitude (D'Lat) for both Great Circle and Rhumb Line routes.
Determine positions and distances along both types of paths during voyage planning.
6. Use Navigation Instruments and Tools
6. Use Navigation Instruments and Tools
Use navigational instruments and electronic systems to assist in plotting Great Circle and Rhumb Line routes.
Interpret data from nautical charts, GPS, and ECDIS related to these navigation methods.
7. Communicate and Record Navigational Data
7. Communicate and Record Navigational Data
Record route plans clearly, specifying whether the course follows a Great Circle or Rhumb Line.
Communicate navigational plans effectively during voyage preparation and reporting.
A great circle is defined as any circle on a sphere whose plane divides the sphere into two equal parts. Examples of this are the meridians and the equator. An infinite number of great circles can be inscribed on a sphere and the section of such a circle passing between two points provides the shortest distance between these points. However, a great circle will intersect the meridians at different angles, the only exception being the equator. The navigator using his compass would be required to continuously change his course in order to accurately follow a great circle route. Since this would be impractical, it is customary to steer a constant course from point to point.
A great circle is a circle drawn on a sphere such that its plane passes through the centre of the sphere the radius of G.C is the same as the radius of the sphere. AB is G.C between A & B and is the shortest distance between them.
A small circle is a circle on a sphere, the plane of which does not pass through the centre of the sphere.
Rhumb line
Rhumb lines. If a curve is drawn on a sphere so that it cuts all Meridians at the same angle it is called a Rhumb Line.
This constant course line is known as a rhumb line or loxodromic curve. The rhumb line will cut all meridians through which it passes at the same angle: examples of this are parallels of latitude.
The only time that a vessel can follow a rhumb line and also a great circle is on the equator or when steaming along a meridian.
On ocean passages when a great circle route may result in considerable saving in distance it is usual to plot several points along the great circle route and to steer rhumb lines between successive points.
Vertex of great circle
Vertex of great circle
The point on a G.C. nearest to the pole is called the vertex.
Every G.C. has two vertices
At vertex, G.C. Lines E.W // to equator
G.C cut the equator midway between two vertice( 90° of D. Long either side of each vertex )
Course of G.C. At equator is equal to Co-Lat of the vertex.
A great circle track can be drawn on the sphere, on our globe, having vertex, the maximum and highest latitude on its tra ck in this case as 35° North and South as per below figures.
If we travel along this track, our course when we pass the equator is the complement of the vertex angle, 55°(055°T). Overview of the track can be shown as below figure.
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