the intersection of the surface of the earth with a plane passing
through the two points of interest (A and B) and the center of
the earth?  

> If you shoot a beam of light directly from A to B, even if it

were to follow the curved surface of the earth, I don’t believe
this would always result in a great circle route.

Think of it this way. Wherever you stand on the surface of the
earth, there is an imaginary straight line between you and the
centre of the earth. When you shoot a beam of light (or a radio
wave) from where you are (point A) to point B, that also forms a
straight line. Those two straight lines intersect at point A and
by definition describe a plane which (a) passes through the
centre of the earth and (b) contains the beam of light as it
follows the earth’s surface. Therefore, the beam of light *must*
follow a great circle.

> Sorry guys, a VOR radial isn’t a GCc. It is a magnetic course. Need a
> magnetic heading to stay on it. A GCc, by nature(i.e., spherical trig),
> is a constant curve (i.e., constantly changing mag course), albeit, on
> short legs it would be hard to tell the difference.

It’s only aligned with magnetic north at the station (sometimes not even
then).  A radio wave doesn’t know magnetic from nothing, it travesl in
a straight line.

A Great Circle course is not a curve except over the curvature of the
earth.  What is constantly changing is the heading because the relative
direction of "north" changes as you fly most courses.

-Ron

I hadn’t thought of it that way, but yes, of course that’s correct.  If
you follow a VOR radial along the lower altitude limit of reception,
you’ll keep climbing to stay within reception range, but your ground track
will certainly be a great circle.

–
Roy Smith <r…@nyu.edu>
Hippocrates Project, Department of Microbiology, Coles 202
NYU School of Medicine, 550 First Avenue, New York, NY 10016
"This never happened to Bart Simpson."

Yup, that sounds good.

>  If you shoot a beam of light directly from A to B, even if it were
>  to follow the curved surface of the earth, I don’t believe this would
>  always result in a great circle route.

Yes it would.  Although visible light won’t follow the curvature of the
Earth’s surface, if you try some other sort of electromagnetic radiation of
a slightly lower frequency (say, 1 MHz), it’ll follow the surface just fine,
and yes indeed, it will trace out a great circle.

The problem is that great circles are hard for people to visualize (take a
course in celestial navigation, and you’ll be cured of that problem) because
they’re used to looking at globes with lat/long lines painted on them.  Just
remember, there is nothing magic about lat/long.  It’s just a somewhat
arbitrary coordinate system that’s in common use.  If you wanted to, you
could draw a lat/long-like coordinate system using any point on the Earth’s
surface as the north pole.  That’s essentially what you’re doing when you
draw great-circles from A to B; you’re using A as your "north pole", and
putting B on a meridian.
—
Roy Smith <r…@nyu.edu>
Hippocrates Project, Department of Microbiology, Coles 202
NYU School of Medicine, 550 First Avenue, New York, NY 10016
"This never happened to Bart Simpson."

VOR signals do not need to follow the curve of the earth.  They are line
of
sight.  But they still travel in straight lines, and a give VOR radial
will
be a plane that follows the area over the great circle.

-Ron

: The "magnetic heading" (actually magnetic track) required to stay on a
: radial will be constant *only* if that radial happens to lie along an
: isogonic line.

Oh, my… here I am responding to my own post!  While staring at a Canadian
WAC chart this afternoon and observing the isogonic lines (running nearly
E-W), I suddenly realized that my above statement is not correct!  An
isogonic line is a line of constant difference between *true* and
*magnetic* direction.  If the radial and isogonic line I referred to above
lie in any direction other than (true) N-S, the true course will be
changing along the radial and the magnetic course will be changing as
well – maintaining a constant offset with the true course, *not* a
constant magnetic course.

So although I still stand by the first paragraph of my response, I hereby
retract the second paragraph, above.

(I feel so much better now…)

Isogonic lines have nothing to do with it.

> In article <31E707FE….@vgernet.net>, robe…@vgernet.net says…
> >Sorry guys, a VOR radial isn’t a GCc. It is a magnetic course. Need a
> >magnetic heading to stay on it. A GCc, by nature(i.e., spherical trig),
> >is a constant curve (i.e., constantly changing mag course), albeit, on
> >short legs it would be hard to tell the difference.
> Yep, this is what the PPLs are taught, no doubt.
>   Now here’s the scoop.
> Electromagnetic waves travel in straight lines
>  ( ignoring the numerous refractive and releativistic cases).
> Imagine a thin, thin  fan beam of light shining from a transmitter site,
>  with its thin dimension horizontal and its wide dimension vertical and
> its other long dimension starting out along a magnetic radial.
> It travels in a straight line.
> If you follow this fan of light at constant height above the Earth’s
>  surface, you follow a great-circle.

  Maybe someone already responded to this, but if not I’ll raise the
  question… Isn’t it required for a great circle route to be the
  intersection of the surface of the earth with a plane passing
  through the two points of interest (A and B) and the center of the
  earth?  

  If you shoot a beam of light directly from A to B, even if it were
  to follow the curved surface of the earth, I don’t believe this would
  always result in a great circle route.

  If I’m wrong, I have no doubt I’ll be shown the error of my ways!

  —Tom T.

: Sorry guys, a VOR radial isn’t a GCc. It is a magnetic course. Need a
: magnetic heading to stay on it. A GCc, by nature(i.e., spherical trig),
: is a constant curve (i.e., constantly changing mag course), albeit, on
: short legs it would be hard to tell the difference.

WRONG.  A VOR radial is a great circle defined by a magnetic bearing from
the station.  This is because radio signals tend to travel the path of
*least distance* between transmitter and receiver – and a great circle is
just such a least distance path along the earth’s surface.

The "magnetic heading" (actually magnetic track) required to stay on a
radial will be constant *only* if that radial happens to lie along an
isogonic line.

>Sorry guys, a VOR radial isn’t a GCc. It is a magnetic course. Need a
>magnetic heading to stay on it. A GCc, by nature(i.e., spherical trig),
>is a constant curve (i.e., constantly changing mag course), albeit, on
>short legs it would be hard to tell the difference.

>R.A.

Yep, this is what the PPLs are taught, no doubt.
  Now here’s the scoop.
Electromagnetic waves travel in straight lines
 ( ignoring the numerous refractive and releativistic cases).

Imagine a thin, thin  fan beam of light shining from a transmitter site,
 with its thin dimension horizontal and its wide dimension vertical and
its other long dimension starting out along a magnetic radial.
It travels in a straight line.
If you follow this fan of light at constant height above the Earth’s
 surface, you follow a great-circle.

 Yep, there it is.
Now; live with it.

brian