Are sectional paths correct across "long" distances?

Awhile ago I pointed out in rec.aviation.piloting that one of my
tools will generate a map using stitched sectionals for a given
route.
http://groups.google.com/groups?hl=e....edu.au#link10
Ben Jackson mentioned that it didn't look correct to just draw a
straight line between two points so far away (across multiple
sectionals). I have looked into it a few times but I haven't
come up with a definitive answer.

So...anyone know the answer? Pilots are certainly accustomed to
drawing straight lines on a sectional to find the shortest path
between two points, and I've never been taught to do anything
other than align sectionals by sight to plan multi-sectional
flights. Does this not work over long distances?

One path I know fairly well is LAF-MER. The Great Circle path
happens to go right near Denver (where I usually stop). If that
path is plotted as a straight line on the sectionals
https://aviationtoolbox.org/Members/...selected.x=411
it appears to follow the path I'd expect.
https://aviationtoolbox.org/Members/...selected.x=427

Also, there's an easily-identified area on that path where Iowa,
Illinois, and Missouri meet. Take a look at the Great Circle
route.
http://gc.kls2.com/cgi-bin/gcmap?PAT....380N+120.568W
Again, this seems to match the area on the straight-line path
drawn on the sectional.
https://aviationtoolbox.org/members/...selected.y=324

Anyone know for sure whether or not this is an accurate way of
depicting Great Circle paths in the conUS?

Thank you.

--kyler

In a previous article, Kyler Laird said:
Anyone know for sure whether or not this is an accurate way of
depicting Great Circle paths in the conUS?

No. Straight lines on Lambert Conformal maps are not great circles. We
use it normally because within one section it doesn't make a huge
difference, but if you're crossing several, the errors add up.


--
Paul Tomblin http://xcski.com/blogs/pt/
"Pilots are reminded to ensure that all surly bonds are slipped before
attempting taxi or take-off"

No. Straight lines on Lambert Conformal maps are not great circles.

It's my understanding that the Lambert Conformal is better than any
other flat surface at representing the curved surface of the earth in
such a way that a straight line on the chart comes very close to being
a Great Circle.

Any straight line through the exact center of a chart, regardless of
direction, will be precisely a Great Circle. A line across a corner
of the chart will be the poorest representation of a Great Circle, but
still "good enough for government work." Probably as close as the
average GA pilot can hold a course, anyway.

vince norris

vincent p. norris writes:

Any straight line through the exact center of a chart, regardless of
direction, will be precisely a Great Circle. A line across a corner
of the chart will be the poorest representation of a Great Circle, but
still "good enough for government work." Probably as close as the
average GA pilot can hold a course, anyway.

I decided to finally test this. I drew Great Circle segments on top of
the straight line path. The difference is small but significant.
https://aviationtoolbox.org/Members/...=1453666.76955
(The yellow line is straight. The red is made of ten GC segments.)

Time to start using GC calculations...

--kyler

Any straight line through the exact center of a chart, regardless of
direction, will be precisely a Great Circle. A line across a corner
of the chart will be the poorest representation of a Great Circle, but
still "good enough for government work." Probably as close as the
average GA pilot can hold a course, anyway.

I decided to finally test this. I drew Great Circle segments on top of
the straight line path. The difference is small but significant.

That's a very interesting chart, Kyler.

I can't see the red GC line very well except against the dark brown of
the higher elevations; but it seems as if the two lines are only about
a line-width apart. I wouldn't consider that "significant," but of
course that's a personal judgment.

My reaction is the opposite of yours: I'm impressed by how well the
straight line follows a Great Circle.

Can you tell me how many nautical miles separate the two lines, at the
point of widest divergence?

Thanks. vince norris

vincent p. norris writes:

I can't see the red GC line very well except against the dark brown of
the higher elevations; but it seems as if the two lines are only about
a line-width apart. I wouldn't consider that "significant," but of
course that's a personal judgment.

It's personal until you cut across restricted airspace by that much.
Then it gets *really* personal.

My reaction is the opposite of yours: I'm impressed by how well the
straight line follows a Great Circle.

I'm pursuing perfect solutions. As usual, the more I get to know
something, the more I realize how little I knew about it, but I know
how to handle this now.

Can you tell me how many nautical miles separate the two lines, at the
point of widest divergence?

-102.934677557 40.1266731277 5.99724483075
6nm

I don't fly that path non-stop though. With a landing at Centennial,
the max. error is under 2nm on the leg from Indiana, and under 1nm on
the next leg to California.

I have discarded routes because the straight paths clipped some
restricted airspace by only a mile or two. I expect any tool that I
use to be accurate enough to tell me whether or not that's going to
happen.

--kyler

In article ,
(Paul Tomblin) wrote:

In a previous article, Kyler Laird said:
Anyone know for sure whether or not this is an accurate way of
depicting Great Circle paths in the conUS?

No. Straight lines on Lambert Conformal maps are not great circles. We
use it normally because within one section it doesn't make a huge
difference, but if you're crossing several, the errors add up.

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. 14 degrees on a coast to coast trip. If you're flying it nonstop
in a jet, it makes sense to take that into account. For most of us
flying spam cans, we just can't fly long enough legs for it to become
significant.

I just tried another one. From 38N/77W to 38N/100W is just under 1100
nm, or about the limit for the longest legged GA airplane I know of.
Again, a rhumbline of 270, CG of 277 (7 degrees correction).

For most of us, CG routes are just not something to worry about.

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

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