Are sectional paths correct across "long" distances?

[vincent p. norris]

>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

[Kyler Laird]

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=en&lr=&ie=UTF-8&oe=UTF-8&th=47356b4c3045b33c&seekm=c19e86%24c1s%241%40bunyip.cc.uq.edu.au#link1 0
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/kyler/tools/map_explorer?image=-455906%2C282393%2C25&scale=1&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.y=267&selected.x=411
it appears to follow the path I'd expect.
https://aviationtoolbox.org/Members/kyler/tools/map_explorer?image=-410466%2C262041%2C50&scale=50&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.y=339&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?PATH=40.412N+86.937W-37.380N+120.568W
Again, this seems to match the area on the straight-line path
drawn on the sectional.
https://aviationtoolbox.org/members/kyler/tools/map_explorer?image=673694%2C398233%2C25&scale=50&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.x=279&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

[Paul Tomblin]

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"

[Kyler Laird]

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/kyler/tools/map_image_GC?draw=line%2C1156711.566111%2C349095.3 46547%2C-1753655.440809%2C100638.192559%2C3706&scale=2&lr_Y=-1003933.23045&lr_X=1339928.06265&ul_X=-1936871.93735&ul_Y=1453666.76955
(The yellow line is straight. The red is made of ten GC segments.)

Time to start using GC calculations...

--kyler

[John Gaquin]

"Kyler Laird" > wrote in message news:h2sei1-
>
> So...anyone know the answer? Pilots are certainly accustomed to
> drawing straight lines on a sectional to find the shortest path

As a technical matter, the only chart projection on which a drawn straight
line is a great circle is a gnomonic. These are rarely used, particularly
over large areas, as they show about as much distortion as the standard
Mercator we all grew up with (remember thinking that Greenland was about
twice the size of the US?).

The Lambert Conformal projection, however, is made such that a straight
line, while not precisely a great circle, is so close that the differences
are inconsequential. Oceanic plotting charts used in aviation to monitor
navigation progress are Lamberts. The standard oceanic enroute chart is a
Mercator, but the plotting chart is Lambert.
Sectional charts are also Lamberts,iirc.

So, the short answer to your question is, just lay out the line, and go.
Note, though, that the straight line on your patched sectionals will require
you to alter heading periodically.

JG

[Eclipsme]

"John Gaquin" > wrote in message
...
>
> "Kyler Laird" > wrote in message news:h2sei1-
> >
> > So...anyone know the answer? Pilots are certainly accustomed to
> > drawing straight lines on a sectional to find the shortest path
>
> As a technical matter, the only chart projection on which a drawn straight
> line is a great circle is a gnomonic. These are rarely used, particularly
> over large areas, as they show about as much distortion as the standard
> Mercator we all grew up with (remember thinking that Greenland was about
> twice the size of the US?).
>
> The Lambert Conformal projection, however, is made such that a straight
> line, while not precisely a great circle, is so close that the differences
> are inconsequential. Oceanic plotting charts used in aviation to monitor
> navigation progress are Lamberts. The standard oceanic enroute chart is a
> Mercator, but the plotting chart is Lambert.
> Sectional charts are also Lamberts,iirc.
>
> So, the short answer to your question is, just lay out the line, and go.
> Note, though, that the straight line on your patched sectionals will
require
> you to alter heading periodically.
>
> JG
>
"the straight line on your patched sectionals will require you to alter
heading periodically" precisely because you will be flying close to a great
circle route, which requires a constantly changing heading.

Harvey

[Steven P. McNicoll]

"John Gaquin" > wrote in message
...
>
> As a technical matter, the only chart projection on which a drawn straight
> line is a great circle is a gnomonic.
>

A straight north-south line is a great circle on all the common chart
projections.

[vincent p. norris]

>>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

[John Gaquin]

"Steven P. McNicoll" > wrote in message > >
>
> A straight north-south line is a great circle on all the common chart
> projections.
>
>

Correct. Those are the two [possibly rare] exceptions to my post -- if you
happen to be flying a course of true north or south anywhere, or a course of
true east or west on the equator, then your course will layout as a straight
line and will be a great circle on any chart projection. I probably should
have mentioned it, lest someone get lost and run out of fuel.

[Roy Smith]

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.

[Dylan Smith]

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"

[Kyler Laird]

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

[vincent p. norris]

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

[vincent p. 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

[Peter Duniho]

"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

[Kyler Laird]

"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

[Peter Duniho]

"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

[Kyler Laird]

"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

[Peter Duniho]

"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

[Roy Smith]

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.

[vincent p. 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).

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

[Kyler Laird]

"Peter Duniho" > writes:

>There is absolutely no basis for Center ever asking you to justify your
>choice in flight planning.

My use of "explain" was apparently ambiguous. I've not been asked to
justify my route (that I recall), but I have been asked to elaborate on how
I'm going to deal with airspace barriers. I got the feeling that they
wanted more than "I'm going to avoid them."

>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.

Again, that's off the subject. I don't know that I'm capable of providing
further clarification on my preference to have all of my maps (and paths)
be aligned.

That's my own laziness though. I'm perfectly happy justifying the use of
Great Circle paths for the tools I build solely because it's The Right
Thing to do.

--kyler

[Roy Smith]

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 :-)

[vincent p. norris]

>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

[[email protected]]

Kyler Laird > wrote in message >...
> 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=en&lr=&ie=UTF-8&oe=UTF-8&th=47356b4c3045b33c&seekm=c19e86%24c1s%241%40bunyip.cc.uq.edu.au#link1 0
> 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/kyler/tools/map_explorer?image=-455906%2C282393%2C25&scale=1&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.y=267&selected.x=411
> it appears to follow the path I'd expect.
> https://aviationtoolbox.org/Members/kyler/tools/map_explorer?image=-410466%2C262041%2C50&scale=50&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.y=339&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?PATH=40.412N+86.937W-37.380N+120.568W
> Again, this seems to match the area on the straight-line path
> drawn on the sectional.
> https://aviationtoolbox.org/members/kyler/tools/map_explorer?image=673694%2C398233%2C25&scale=50&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.x=279&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

As a rule of thumb:

Use this equation to draw the bow. It gives the distance offset from
a straight line for the circle route.

A: Lat
A: Longitude

B: Lat
B: Longitude

A and B are the two locations.

C: km of rhumb line.


Nathanial Bowdich has an equation there for this method and is
forgotten, but available from his Navigation Book.

Except his method is to find the equation that fits the geometer's
rhumb line, meaning Bowdich only has a method of navigation and not
the true rhumbline solution.

Making my equation a constant for the earth sphere type, where only
the geometry of all spheres allows the applied line!! That is geometer
talk btw.

C*1.3 seconds= Alat

C*1.3 seconds= Blat

Two simulatanous equations to solve for C, the rhumbline. Longitude is
the reason for the 1.3 seconds of time arc, as a constant.

Meaning just take the time of the trip and lengthen until the A and
the B are equal latitudes!

That is it.

Douglas Eagleson
Gaithersburg, MD USA

[David Lesher]

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.

--
A host is a host from coast to
& no one will talk to a host that's close........[v].(301) 56-LINUX
Unless the host (that isn't close).........................pob 1433
is busy, hung or dead....................................20915-1433

[[email protected]]

wrote in message >...
> Kyler Laird > wrote in message >...
> > 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=en&lr=&ie=UTF-8&oe=UTF-8&th=47356b4c3045b33c&seekm=c19e86%24c1s%241%40bunyip.cc.uq.edu.au#link1 0
> > 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/kyler/tools/map_explorer?image=-455906%2C282393%2C25&scale=1&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.y=267&selected.x=411
> > it appears to follow the path I'd expect.
> > https://aviationtoolbox.org/Members/kyler/tools/map_explorer?image=-410466%2C262041%2C50&scale=50&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.y=339&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?PATH=40.412N+86.937W-37.380N+120.568W
> > Again, this seems to match the area on the straight-line path
> > drawn on the sectional.
> > https://aviationtoolbox.org/members/kyler/tools/map_explorer?image=673694%2C398233%2C25&scale=50&draw=line%2C1156711.566111%2C349095.346547%2C-1756203.849778%2C112012.534211%2C3706&selected.x=279&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
>
> As a rule of thumb:
>
> Use this equation to draw the bow. It gives the distance offset from
> a straight line for the circle route.
>
> A: Lat
> A: Longitude
>
> B: Lat
> B: Longitude
>
> A and B are the two locations.
>
> C: km of rhumb line.
>
>
> Nathanial Bowdich has an equation there for this method and is
> forgotten, but available from his Navigation Book.
>
> Except his method is to find the equation that fits the geometer's
> rhumb line, meaning Bowdich only has a method of navigation and not
> the true rhumbline solution.
>
> Making my equation a constant for the earth sphere type, where only
> the geometry of all spheres allows the applied line!! That is geometer
> talk btw.
>
> C*1.3 seconds= Alat
>
> C*1.3 seconds= Blat
>
> Two simulatanous equations to solve for C, the rhumbline. Longitude is
> the reason for the 1.3 seconds of time arc, as a constant.
>
> Meaning just take the time of the trip and lengthen until the A and
> the B are equal latitudes!
>
> That is it.
>
> Douglas Eagleson
> Gaithersburg, MD USA

Aslo note that to solve, the definition of seconds is a distance for
the place. A place on the map selected for the rhumbline. And here,
the 1/2, the distance of the straight route line is the selected
point.

This makes the time to go one half the route a time for the least
pleasent route to navigate. Does a new rhumbline for the half the
original route have to be mathematically converging??? Ha ha!

Never, because another system of equations would be encountered. A
short trip!!

So, the reason for the clarification is to cause the time to equal the
rhumbline. A simple rule of thumb. Time will equal distance
navigationally.
A nonphysics solution because it is caused by the relation of location
to the definer of location, as the time of rotation. The lattitude
and longitude are time locations!

Douglas Eagleson
Gaitherbsurg, MD USA

[F1]

"Kyler Laird" > wrote in message
...
> "Peter Duniho" > writes:
>
> >There is absolutely no basis for Center ever asking you to justify your
> >choice in flight planning.
>
> My use of "explain" was apparently ambiguous. I've not been asked to
> justify my route (that I recall), but I have been asked to elaborate on
how
> I'm going to deal with airspace barriers. I got the feeling that they
> wanted more than "I'm going to avoid them."
>
> >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.
>
> Again, that's off the subject. I don't know that I'm capable of providing
> further clarification on my preference to have all of my maps (and paths)
> be aligned.
>
> That's my own laziness though. I'm perfectly happy justifying the use of
> Great Circle paths for the tools I build solely because it's The Right
> Thing to do.
>
> --kyler

When flying VFR, I've been asking about my planned route of flight before.
The controller is just doing his/her job and wants to get the heads up.

[F1]

"Roy Smith" > wrote in message
...
> In article >,
> (Paul Tomblin) wrote:
<snip>
> 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.


And it is all moot anyhow, since you'd be IFR and not using VFR charts...

[Peter Duniho]

"F1" > wrote in message
...
> When flying VFR, I've been asking about my planned route of flight before.
> The controller is just doing his/her job and wants to get the heads up.

Did the controller ask you to explain why you chose one route versus
another? I doubt they did. That is the issue here, not a controller's
general interest in which way you're going.

[Roy Smith]

In article >,
"Peter Duniho" > wrote:

> "F1" > wrote in message
> ...
> > When flying VFR, I've been asking about my planned route of flight before.
> > The controller is just doing his/her job and wants to get the heads up.
>
> Did the controller ask you to explain why you chose one route versus
> another? I doubt they did. That is the issue here, not a controller's
> general interest in which way you're going.
>
>

I've had controllers ask me "how I'm navigating" while VFR. But I
believe the intent of the question has generally been, "Can you give me
a heads-up where you're heading so I can anticipate your flight path
better?" Sometimes I think it's been, "Based on where you said you were
going, I'm wondering if you're lost; do you need some help?"

In all cases, if I've come back with something like, "We're going to be
maneuvering in the area of X for a while", or "We're going to be
following X, Y, and Z", (no matter how absurd or circuitous that path
might have been), that's seem to satisfy the controller.

[Peter Duniho]

"Roy Smith" > wrote in message
...
> [...]
> In all cases, if I've come back with something like, "We're going to be
> maneuvering in the area of X for a while", or "We're going to be
> following X, Y, and Z", (no matter how absurd or circuitous that path
> might have been), that's seem to satisfy the controller.

Exactly. That was my point. The controller doesn't care, and has no reason
to care, why you pick a particular route. They just want to know what the
route is (and much of time, they aren't too terribly concerned about that
either, if you're VFR).

Pete

[vincent p. norris]

> The controller doesn't care, and has no reason
>to care, why you pick a particular route. They just want to know what the
>route is (and much of time, they aren't too terribly concerned about that
>either, if you're VFR).

An amusing incident: 20 or 30 years ago, I left central PA for
Rochester, NY, and asked for flight following. (Pretty wild country
much of the way.)

Since thre ae no VORs along that route, Center asked me for my route.
I said "Direct Rochester." A pause. Then he asked, "Do you have
RNAV?"

I said, "No, I have a line on a chart."

There was a long period of silence. I guess it was a young controller
who had never heard that before.

vince norris