Are sectional paths correct across "long" distances?

In article , Roy Smith 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. 14 degrees on a coast to coast trip.

The error will be less still on an aviation chart, which is a Lambert
Conformal Conic projection rather than Mercator. Over the distances of a
typical sectional chart, the difference between a GC and a line on the
chart is irrelevant.

--
Dylan Smith, Castletown, Isle of Man
Flying: http://www.dylansmith.net
Frontier Elite Universe: http://www.alioth.net
"Maintain thine airspeed, lest the ground come up and smite thee"

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

Peter, you saved me the effort of replying further; your replies
stated essentially what I would have said.

One comment: The reason I asked for the greatest distance between a
GC line and a straight line was that it looked to me, on Kyler's
chart, as though it was never more than a few miles. That would
indirectly indicate the difference between the distance to destination
of the two routes could not be more than a few miles.

I can't remember ever planning a flight of more than a couple hundred
miles that did not involve dodging around one or more restricted areas
or MOAs, so the question about the difference between a straight line
and a GC over a long distance is only of academic interest.

vince norris

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

"Kyler Laird" wrote in message
...
It's personal until you cut across restricted airspace by that much.
Then it gets *really* personal.

Huh? The error should be with respect to whether you're really flying the
shortest path between two points. It should not have anything to do with
how you navigate, nor should it affect your spatial orientation, your
knowledge of where you are at any given time.

Even if it did affect your navigation (and it shouldn't), I sure hope you're
not depending on dead reckoning to keep you out of restricted airspace.

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'm not sure why vince asked that question. The point of widest divergence
isn't something anyone should care about. What's important is how much
extra *length* is added to the trip, as Jose asks.

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.

If you fly the route plotted, then the route plotted is the one you fly.
Simple, no?

Regardless of whether you fly a true great circle route, a collection of
great circle intervals, or a straight line on a sectional, you need
something else to keep you on the route you've chosen. It's *that* which
will affect whether you fly through restricted airspace, not the method of
chosing the route (assuming you've chosen the route to avoid restricted
airspace, of course).

Pete

"Peter Duniho" writes:

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

Huh? The error should be with respect to whether you're really flying the
shortest path between two points. It should not have anything to do with
how you navigate, nor should it affect your spatial orientation, your
knowledge of where you are at any given time.

No, but it does affect planning. I like to plan for "straight"-line paths
that keep me out of restricted airspace. Makes my life a lot easier.

I'm not sure why vince asked that question. The point of widest divergence
isn't something anyone should care about.

It's something that matters to me. Am I going to have to think about
where I'm going around some airspace/mountain/...? Do I have to explain
my plans to Center?

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.

If you fly the route plotted, then the route plotted is the one you fly.
Simple, no?

Simple except that it doesn't match the plot on the GPS I use to double-
check my progress.

I'm a horrible person for wanting to simplify flying...blah, blah, blah...
I'll never earn my "aviator balls"...blah, blah, blah...Yeah, I know.

--kyler

"Kyler Laird" wrote in message
...
No, but it does affect planning. I like to plan for "straight"-line paths
that keep me out of restricted airspace. Makes my life a lot easier.

That doesn't make any sense to me. Either a straight line between your
origin and destination will keep you out of restricted airspace, or it
won't. The origin, destination, and restricted airspace aren't moving.
It's not like there are multiple "straight line" paths. In reality there's
only one.

However, that's all irrelevant. If you are close enough to restricted
airspace that a Lambert "straight line" versus a great-circle makes the
difference between in or out, you need more than just a plotted route to
ensure you remain clear of the restricted airspace.

I don't know when the last time you flew a perfect straight line is. Maybe
it was yesterday. But I've never managed to do so.

It's something that matters to me. Am I going to have to think about
where I'm going around some airspace/mountain/...? Do I have to explain
my plans to Center?

That still doesn't explain why you are worried about the difference between
great-circle and a sectional straight line. You never have to explain your
planning to Center, and you always have to think about where you're going
around some airspace or mountain. How you plot the route is irrelevant. If
you have to go around, you have to go around.

If you fly the route plotted, then the route plotted is the one you fly.
Simple, no?

Simple except that it doesn't match the plot on the GPS I use to double-
check my progress.

In other words, you wouldn't be flying the route plotted. My statement is
still true.

I don't recall you ever stipulating that you needed a plotted route that
matched your GPS's great-circle calculations. I would agree that if what
you want to fly is a great-circle route, then you need to plot a
great-circle route.

Personally, I'd use the GPS to show restricted airspace and to ensure I'm
WELL clear. If I wanted to navigate using the GPS, and I had found that a
straight line plotted on a sectional kept me clear of the restricted
airspace, I'd simply add a waypoint to the GPS-direct route near the
airspace, on the line I plotted on the sectional. Likewise other obstacles.
If you're that close to stuff like that, you need something more reliable
(such as looking out the window) to ensure you avoid what you're trying to
avoid anyway.

I'm a horrible person for wanting to simplify flying...blah, blah, blah...
I'll never earn my "aviator balls"...blah, blah, blah...Yeah, I know.

I have no idea what that's all about. IMHO, you are making things more
complicated, not simplifying things. You are falling into the usual trap of
allowing your technology to provide you with false precision, overanalyzing
the flight to the point of distraction.

Maybe you're the best pilot around, and you can actually stay on centerline
when your GPS has a great-circle route for you to fly. Me, I know for a
fact that I'm doing good to keep headings that keep me within a half mile to
a mile of course, even with GPS or Loran.

Using a VOR, my precision goes down even more. I know better than to cut
things close to obstacles and restricted airspace using only my radio
navigation, simply because I can't fly that precisely by radio navigation.
I need outside references to cut things that close, and if I have those,
then I don't need to worry about the difference between a sectional
straight-line course and a true great-circle route.

More power to you if you always remain within a hundred feet or so of your
intended centerline throughout an entire cross-country. I guess if that's
the case, then you shouldn't feel worried at all about trusting your GPS to
guide you just past an obstacle or restricted airspace, and nothing I've
written is relevant to your operations.

Pete

"Peter Duniho" writes:

Either a straight line between your
origin and destination will keep you out of restricted airspace, or it
won't.

Yes. (If we're calling the Great Circle path a "straight line.)
That's why I want it to be exact.

I don't know if this would realistically affect me or not. I've never
planned long trips without GC paths. I don't want to deal with the
inconsistency though.

It's something that matters to me. Am I going to have to think about
where I'm going around some airspace/mountain/...? Do I have to explain
my plans to Center?

That still doesn't explain why you are worried about the difference between
great-circle and a sectional straight line. You never have to explain your
planning to Center,

And yet I've been asked on more than one occasion. Is this one of those
Wubba-logic things where "never" means "5% of the time" and I'm just
supposed to forget my experiences, or by "never have to" are you just
meaning that you can not divulge the information and remain in compliance
with FAA regs (even though they'll probably drop you and call you names)?

--kyler

"Kyler Laird" wrote in message
...
[...]
And yet I've been asked on more than one occasion. Is this one of those
Wubba-logic things where "never" means "5% of the time" and I'm just
supposed to forget my experiences, or by "never have to" are you just
meaning that you can not divulge the information and remain in compliance
with FAA regs (even though they'll probably drop you and call you names)?

There is absolutely no basis for Center ever asking you to justify your
choice in flight planning. Their job is to control airspace -- to keep you
from hitting other airplanes.

I have never had any controller ask me to justify my route of flight. I
won't go so far as to say you never have either, but it boggles my mind that
you would have, and that you'd think there's any reason you'd be required
to.

But frankly, that's just a red herring anyway. There's no way in hell that
any controller would want to know why you flew a sectional straight line
instead of a great-circle route or vice a versa. The difference is just
noise to them.

If it makes you feel better, feel free to detail the instances in which ATC
has asked you to justify your route. It's such a bizarre concept, I'm sure
we'd all learn something new from that. But it still has nothing to do with
this thread.

Pete

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.