Confused about great circle navigation

Not that it matters terribly much, but there's a few things I don't get.

On a WAC, which is a Lambert chart, a straight line is more or less a great
circle, right? However, to fly a great circle, you have to constantly adjust
your heading. I still can't conceptually work out why, I must say. Any
pointers?

If you had a WAC chart that displayed the entire Northern Hemisphere on one
chart, you could draw a straight line from Los Angeles to New York. Wouldn't
this be a great circle? And if it is, why couldn't you just fly the single
heading of that line? Is it that because of the fact that a chart that big
would have different magnetic north references at different meridians, and
what you would actually be drawing is a rhumb line?

And speaking of rhumb lines, if you fly one by keeping a constant magnetic
heading between two points, does that mean you actually describe a curve
over the earth's surface?

Thanks in advance, because I'm pretty confused.

OK, I'll give it a shot.

First, remember that a Lambert Conformal projection only *approximates* a sphere
for the latitudes it covers. You can't, actually, have such a chart that covers
the entire northern hemisphere because the North Pole would be the apex on the
cone of the conformal projection.

Because the chart only approximates a sphere, any line drawn between two points
only approximates a great circle. If you have access to the AOPA flight
planner, plan a route between NYC and LA. You'll see that there is a
considerable "curve" to the route plotted on the screen. That's the curve you
would have to follow, constantly changing you heading to do so.

Now use DeLorme Street Atlas or some other land-based program to draw a straight
line between the same two points. You'll see that the straight line doesn't
match up very well with the line drawn by flight planner.

To perfectly fly a great circle between two points you do have to constantly
change heading. The idea behind a rhumb line is "segment" the circle so that
you can fly a constant heading between the points that define the rhumb line.
This will make the rhumb line course slightly longer. How much longer depends
on the number of points: more points equals a closer approximation of the circle
but is harder to fly.

Unless you're flying very long distances it makes very little sense to worry
about the difference between a great circle and a straight line on a chart. For
example, the great circle between my home base here in MA and my mother's home
in SoCal would take me over terrain I don't want to fly over anyway, so the GC
is meaningless. On shorter trips the delta is so small as to be insignificant.
IOW, don't sweat it.

Dave Reinhart


xerj wrote:

Not that it matters terribly much, but there's a few things I don't get.

On a WAC, which is a Lambert chart, a straight line is more or less a great
circle, right? However, to fly a great circle, you have to constantly adjust
your heading. I still can't conceptually work out why, I must say. Any
pointers?

If you had a WAC chart that displayed the entire Northern Hemisphere on one
chart, you could draw a straight line from Los Angeles to New York. Wouldn't
this be a great circle? And if it is, why couldn't you just fly the single
heading of that line? Is it that because of the fact that a chart that big
would have different magnetic north references at different meridians, and
what you would actually be drawing is a rhumb line?

And speaking of rhumb lines, if you fly one by keeping a constant magnetic
heading between two points, does that mean you actually describe a curve
over the earth's surface?

Thanks in advance, because I'm pretty confused.

o fly a great circle, you have to constantly adjust
your heading. I still can't conceptually work out why


Consider a great circle route that takes you near the (North for example) pole.
A great circle, recall, is what a tight string between two points on a globe
describes. As you approach the pole, you will be travelling mostly North.
When you pass the pole you will be travelling mostly South. You need to change
headings somewhere! (You do so continually, although not at a constant rate)


If you had a WAC chart that displayed the entire Northern Hemisphere on one
chart, you could draw a straight line from Los Angeles to New York. Wouldn't
this be a great circle? And if it is, why couldn't you just fly the single
heading of that line?


Because that straight line is not a single heading. Note that the chart (and
the latitude lines) curve. If the latitude lines curve, a straight line must
change headings (unless it is a straight line going North South)


if you fly one by keeping a constant magnetic
heading between two points, does that mean you actually describe a curve
over the earth's surface?


In most cases yes. Consider lines of latitude, which have a constant heading
(90 degrees, or 270 degrees). Except for the equator, they are all curved.
You can do the same with "magnetic latitude" as with "true latitude"
(referencing the magnetic pole as opposed to the rotational pole) and it comes
out the same. You see this most easily near the pole, hence the puzzle "you go
South for one mile, East for one mile, North for one mile, and end up where you
started. You then see a bear. What color is it?"

Jose






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

A straight line on a Lambert chart is not a single heading. The heading
changes depending on where you measure the line.

thanks to all!

The penny has dropped.


"Julian Scarfe" wrote in message
...
"xerj" wrote in message
...
If you had a WAC chart that displayed the entire Northern Hemisphere on
one
chart, you could draw a straight line from Los Angeles to New York.
Wouldn't
this be a great circle? And if it is, why couldn't you just fly the
single
heading of that line?

If the other answers haven't done it for you, here's another angle. Look
carefully at the meridians (lines of longitude) on a WAC chart and note
that
they are not quite parallel. You measure your track by the angle between
the straight line you drew and the meridian representing north. So if
they're not parallel, your straight line will cross them at slightly
different angles.

Julian Scarfe

"xerj" wrote in message
...
If you had a WAC chart that displayed the entire Northern Hemisphere on
one
chart, you could draw a straight line from Los Angeles to New York.
Wouldn't
this be a great circle? And if it is, why couldn't you just fly the single
heading of that line?

If the other answers haven't done it for you, here's another angle. Look
carefully at the meridians (lines of longitude) on a WAC chart and note that
they are not quite parallel. You measure your track by the angle between
the straight line you drew and the meridian representing north. So if
they're not parallel, your straight line will cross them at slightly
different angles.

Julian Scarfe

you will notice on Lambert Conformal charts in the northern hemisphere.. the
lines of longitude tend to converge the farther north you go so they are not
parallel.
Remember that you measure heading reference in correlation to the lines of
longitude (normally)
so now as you draw your "straight" line, you will notice that the course
line continuously intersects the longitude lines at different angles.

For shorter distances, measure the heading at mid course and fly that
heading, you will not fly over your ground plotted track, but you will be
close to the destination at the end of the course.

make sense?

"xerj" wrote in message
...
Not that it matters terribly much, but there's a few things I don't get.

On a WAC, which is a Lambert chart, a straight line is more or less a
great
circle, right? However, to fly a great circle, you have to constantly
adjust
your heading. I still can't conceptually work out why, I must say. Any
pointers?

If you had a WAC chart that displayed the entire Northern Hemisphere on
one
chart, you could draw a straight line from Los Angeles to New York.
Wouldn't
this be a great circle? And if it is, why couldn't you just fly the single
heading of that line? Is it that because of the fact that a chart that big
would have different magnetic north references at different meridians, and
what you would actually be drawing is a rhumb line?

And speaking of rhumb lines, if you fly one by keeping a constant magnetic
heading between two points, does that mean you actually describe a curve
over the earth's surface?

Thanks in advance, because I'm pretty confused.

"xerj" wrote in message
...
Not that it matters terribly much, but there's a few things I don't get.

On a WAC, which is a Lambert chart, a straight line is more or less a
great
circle, right? However, to fly a great circle, you have to constantly
adjust
your heading. I still can't conceptually work out why, I must say. Any
pointers?

Wrong. A Lambert Conformal is a conical projection, the WAC is just a
larger scale than a sectional. You can't draw a Great Circle Route on a
conical projection using a straight edge.
The easiest test is to use a globe. Stretch a string around the globe
from Los Angeles to New York and note some geographical point (city,
mountain, etc.) at or near the middle of the string. Then draw a straight
line between LA and NY on a Lambert conical projection. Where is the
mid-point of that line in relation to the string line around the globe?
A rhumb line is not the same as the GCR. An RL is a constant
navigational heading that would take the navigator from one spot to another.
The GCR on the other hand does require adjustment. The GCR is the shortest
distance (over the surface, not through a tunnel) between two points on the
globe.

For more than you ever wanted to know about GCR navigation, include
formulae you can pack onto your PocketPC or PDA, go to:
http://williams.best.vwh.net/avform.htm