Are sectional paths correct across "long" distances?

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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"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...

"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

"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

"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.

"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.

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=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

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

wrote in message . com...
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=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

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