Are sectional paths correct across "long" distances?

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

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


Can you tell me how much longer the long line is?

Jose

--
(for Email, make the obvious changes in my address)

(Teacherjh) writes:

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. That sounds about right. It's possible
to diverge quite a bit from the GC path before racking up a lot of extra distance.
(That's why searching for good slightly-off-path fuel stops is so worthwhile.)

--kyler

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


--
(for Email, make the obvious changes in my address)

In article ,
Teacherjh wrote:
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

Can you tell me how much longer the long line is?

Since it looks like it just 'bows' the line slightly the worst case would
be 2*6nm, or 12nm, and it's probably not even that.

--
Ben Jackson

http://www.ben.com/

"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