Are sectional paths correct across "long" distances?

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