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Great/Small Circles and Rhumb Lines

  • sydpilot
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sydpilot created the topic: Great/Small Circles and Rhumb Lines

Hi Bob,

With reference to Great and Small Circles and Rhumb Lines, can you confirm if the below statements are indeed true.

1. All parallels, including the equator, are rhumb lines, since they cross all meridians at 90 degrees. They are also small circles
(excluding the equator)
2. All meridians are rhumb lines, in addition to being great circles.
3. A rhumb line always spirals toward one of the poles, unless its direction is true east, west, north, or south, in which case the rhumb
line forms a parallel of latitude (small circle) or a meridian of longitude.

I was a bit confused as I only associated parallels of latitude with small circles and meridians of longitude with great circles.


Thanks.
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bobtait replied the topic: Great/Small Circles and Rhumb Lines

Statement 1. Correct. A rhumb line is a line that crosses every meridian at the same angle. By definition that means rhumb lines are lines of constant direction. All parallels of latitude are both rhumb lines and small circles [except for the equator which is a rhumb line and a great circle].

Statement 2. Correct. Meridians run exactly true north and true south so they are rhumb lines. Each meridian together with its anti-meridian forms a great circle.

Statement 3. Correct. Apart from parallels of latitude and meridians, rhumb lines are loxodromes - they spiral about one of the poles.

Remember also that although the parallels of latitude are small circles, they are not the only ones. There are an infinite number of small circles that can be drawn on any sphere. Any cutting plane that does not pass through the earth's centre forms a small circle.

Also, although the meridians are great circles, they are not the only ones. There are an infinite number of great circles that can be drawn on any sphere. Any cutting plane that passes through the earth's centre forms a great circle.

Bob
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  • sydpilot
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sydpilot replied the topic: Great/Small Circles and Rhumb Lines

Excellent. Thanks Bob.
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  • gregk
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gregk replied the topic: Great/Small Circles and Rhumb Lines

Great stuff guys, thanks. But the puzzle lives on in my head!

Bob/Richard can you clarify for me what i am flying, either Great Circle or Rhumb line if I plan a straight track due west from say Sydney to wherever for example.

My logic based on what i read in the text suggests it is in fact a great circle on a VNC or WAC as they are conic projections and meridians are not parallel. Although, it would be very close to a rhumb line also over the distance displayed on a WAC if I read correctly. The rhumb line would take me just north of the track i would estimate if I cross the meridians at exactly the same angle on one of these charts.

This then poses the quandary, when would I plan a rhumb line course? If you can clear that one up for me it would be very much appreciated just feel my concrete brain is missing something simple.

Cheers, Greg
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