lines on the earth contradiction??

[ramshorn]

Hi everyone.
Just wondering if somebody could explain to me how the equator and meridians can be both rhumb lines and great circles,as i'm sure most of you will know that rhumb lines have a constant track direction and great cirles have a constantly changing track direction.This would seem like a contradiction?I would guess the answer is reasonably straightforward,but would be most grateful if anyone can fill me in?!
Thanks.:confused:

[Alex Whittingham]

A better definition would be that rhumb lines have a constant true track direction whereas great circles are the shortest distance between two points and USUALLY have a changing track direction. The exceptions are, as you say, the equator and meridians. As an example, the shortest distance between A (51°N 000°W) and B (46°N 000°W) is along the greenwich meridian, and therefore a great circle, but has a constant track direction of 180°T and is therefore also a rhumb line.

[Pirate]

The definition of a rhumb line is that it is a regularly curved line which cuts all meridians at a constant angle. It is something of an anachronism in an age where computerised navigation systems can make the constant small changes required to keep a vehicle on the most efficient path between two points - the great circle. However, in past times navigators on water and in the air needed a line crossing meridians at a constant angle for ease of application and it was for this reason that the rhumb line was introduced. As an example, sailing ships needed to sail a sequence of straight lines to optimise wind usage. It was also the best system for use on a Mercator projection, where a straight line is a rhumb line.

To answer the original question, meridians and the equator are the only Great Cirles to also be rhumb lines as they are the limiting cases covered by the definition, i.e. the meridians cross themselves effectively at zero angle and the equator at 90 degrees.

confundemus

[ramshorn]

Thankyou both very much for your help.Got a bonus history lesson thrown in too!Always interesting.Back to the studys.
Cheers

Hi again guys!
Still on the same subject,the example given in alex\'s reply is on the greenwich meridian.Is it the case that not all meridians of longitude are rhumb lines aswell as great circles.just the greenwich meridian and antimeridian?
Hope i,m not stating the obvious?;)

[parris50]

All meridians are great circles.

All meridians are rhumb lines as they have a constant direction i.e. 0 degrees

[Pirate]

The thing to remember is that the equator is a geographical fact - there is, and can be, only one equator. Meridians, on the other hand are man-made conveniences for navigation and as such there can be an infinite number since any straight line joining the poles is a meridian. All are rhumb lines, since they are all crossing meridians (themselves) at zero angle.

confundemus

[ramshorn]

Thanks guys/gals
All cleared up! :ok: