Are sectional paths correct across "long" distances?

Can you tell me how much longer the long line is?
1571.43727838 1578.04946769 6.61218931502
It's under 7nm by my simple calculations.


This makes no sense at all, and fails a basic sanity check. (and accepting
such numbers blindly the way high technology leads you to disaster).

The line looks like it goes across half the country. I'll say 1000 miles. At
the midpoint (500 miles) it is claimed that the lines are 6 miles apart. Ok,
basic trig - the longest line is the hypotenuse of a skinny right triangle.

sqrt ( 500^2 + 6^2 ) = 500.035998704093303602766435049485

So for two legs, we go an extra 0.0719974081866072055328700989694951 miles.

Google claims that a nautical mile is 6 076.11549 feet, so we end up going an
extra 437.464567122496852083885712506382 feet, or 437 feet
5.57480546996222500662855007658699 inches.

We can probably ignore the last few decimal places in the inches.

Jose


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"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.

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

"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

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

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

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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