Are sectional paths correct across "long" distances?

In article ,
vincent p. norris wrote:

You've got to go pretty big distances before GC errors start to become
significant. For example, to go from 38N/77W to 38N/122W (roughly
Washington, DC to San Francisco, CA), the rhumbline is 270 and the GC is
284.

I thought a Great Circle is the shortest possible distance between two
points on the earth. Should that read "rhumbline is 284 and GC is
270"?

vince norris

The rhumbline is a straight line drawn on a chart (or at least that's my
intuitive definition; I'm not sure what the formal definition is). Of
course, once you get into the whole concept of representing the surface
of a sphere(oid) on a flat piece of paper, and the different chart
projections used to do it, the definition of "a straight line" becomes a
little hard to pin down. I intentionally picked two points at the same
lattitude to make the rhumbline azimuth calculation trivial.

The GC route is indeed the shortest distance between two points. Try
plugging 38N/77W to 38N/122W into

http://www.aeroplanner.com/calculators/avcalcrhumb.cfm

to get the rhumbline of 2128 nm, and into

http://www.csgnetwork.com/marinegrcircalc.html

to get the GC of 2099 nm.

The rhumbline is a straight line drawn on a chart (or at least that's my
intuitive definition; I'm not sure what the formal definition is).

If I'm not mistaken, a rhumb line is a line that crosses all meridians
at the same angle.

So a rhumb line is not a straight line on a sectional chart, except in
a few special cases (e.g., the equator). Notice that on the chart
Kyler posted, the meridians are closer together at the top of the
chart than at the bottom, so that straight line crosses each meridian
ast a slightly different angle.

Of course, once you get into the whole concept of representing the surface
of a sphere(oid) on a flat piece of paper, and the different chart
projections used to do it, the definition of "a straight line" becomes a
little hard to pin down.

I don't see why. A straight line is one that can be drawn using a
straightedge. As Euclid would say, it's the shortest distance between
to points on the chart. I believe one reason the Lambert chart was
invented was to make it possible to use a straightedge to draw a great
circle route.

vince norris

vincent p. norris wrote:
If I'm not mistaken, a rhumb line is a line that crosses all meridians
at the same angle.

OK, now you gone and done it. You made me go look it up. Bowditch says:

RHUMB LINE. A line on the surface of the earth making the same oblique
angle with all meridians; a loxodrome or loxodromic curve spirals toward
the poles in a constant true direction. Parallels and meridians, which
also maintain constant true directions, may be considered special cases
of the rhumb line. A rhumb line is a straight line on a Mercator
projection. Sometimes shortened to RHUMB. See also FICTITIOUS RHUMB LINE.

So, yup, you're right.

The last time I remember flying a loxodromic spiral, I was practicing
NDB approaches for my CFI-I ride :-)

RHUMB LINE. A line on the surface of the earth making the same oblique
angle with all meridians; a loxodrome or loxodromic curve spirals toward
the poles in a constant true direction. Parallels and meridians, which
also maintain constant true directions, may be considered special cases
of the rhumb line. A rhumb line is a straight line on a Mercator
projection. Sometimes shortened to RHUMB. See also FICTITIOUS RHUMB LINE.

So, yup, you're right.

Thanks--and thanks for introducing me to the word "loxodromic," which
I had never heard.

And BTW, I do know how to spell "two."

The last time I remember flying a loxodromic spiral, I was practicing
NDB approaches for my CFI-I ride :-)

LOL! I know exactly what you mean!

vince norris

Roy Smith writes:


The GC route is indeed the shortest distance between two points. Try
plugging 38N/77W to 38N/122W into

http://www.aeroplanner.com/calculators/avcalcrhumb.cfm

to get the rhumbline of 2128 nm, and into

http://www.csgnetwork.com/marinegrcircalc.html

to get the GC of 2099 nm.


And http://gc.kls2.com/ as it makes nice visuals.

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