navigation question

[mah]

Was toying with my gps recently and plotted a course from my home in the
midwest to London Heathrow. I know it uses great circle routing to
calculate the distance and course. Going from west to east it shows a
course of about 45 degrees. On the return trip it shows an intial
course of 310 degrees.

Now, to my old mind, I would have thought a reciprical course of 225 .
It is something in the spherical formula used for the great circle but
I'm too rusty to work through it.

An old navigators who want to help me out?

Thanks in advance.

MAH

[ArtKramr]

>Subject: navigation question
>From: mah
>Date: 2/21/04 6:09 PM Pacific Standard Time
>Message-id: >
>
>Was toying with my gps recently and plotted a course from my home in the
>midwest to London Heathrow. I know it uses great circle routing to
>calculate the distance and course. Going from west to east it shows a
>course of about 45 degrees. On the return trip it shows an intial
>course of 310 degrees.
>
>Now, to my old mind, I would have thought a reciprical course of 225 .
>It is something in the spherical formula used for the great circle but
>I'm too rusty to work through it.
>
>An old navigators who want to help me out?
>
>Thanks in advance.
>
>MAH


I think you will have to do a Mercator solution.


Arthur Kramer
344th BG 494th BS
England, France, Belgium, Holland, Germany
Visit my WW II B-26 website at:
http://www.coastcomp.com/artkramer

[John R Weiss]

"mah" > wrote...
> Was toying with my gps recently and plotted a course from my home in the
> midwest to London Heathrow. I know it uses great circle routing to
> calculate the distance and course. Going from west to east it shows a
> course of about 45 degrees. On the return trip it shows an intial
> course of 310 degrees.
>
> Now, to my old mind, I would have thought a reciprical course of 225 .
> It is something in the spherical formula used for the great circle but
> I'm too rusty to work through it.
>
> An old navigators who want to help me out?

A reciprocal initial heading works for a rhumb line (constant heading) course,
but not for a great circle course (except along the Equator or any longitude
line. In all other cases, great circle routes are curved when plotted on a
Mercator map.

[Tarver Engineering]

"Glenfiddich" > wrote in message
...
> On Sat, 21 Feb 2004 20:09:30 -0600, mah > wrote:
>
> >Was toying with my gps recently and plotted a course from my home in the
> >midwest to London Heathrow. I know it uses great circle routing to
> >calculate the distance and course. Going from west to east it shows a
> >course of about 45 degrees. On the return trip it shows an intial
> >course of 310 degrees.
> >
> >Now, to my old mind, I would have thought a reciprical course of 225 .
> >It is something in the spherical formula used for the great circle but
>
> It's not the formula, it's the fact that the world is a sphere.
> The formula only reflects this fact.

The Earth is an oblate spheroid.

The equation he seeks is on the web.

[Cub Driver]

On Sat, 21 Feb 2004 20:09:30 -0600, mah > wrote:

>Now, to my old mind, I would have thought a reciprical course of 225 .
>It is something in the spherical formula used for the great circle but
>I'm too rusty to work through it.

You answered the question yourself: it was a Great Circle route. The
heading would change continuously in theory, at intervals in practice.
I wouldn't worry about it, if I were you. Trust your GPS. If you ever
do it in practice, you can always brush up on your celestial
navigation.

all the best -- Dan Ford
email: (requires authentication)

see the Warbird's Forum at www.warbirdforum.com
and the Piper Cub Forum at www.pipercubforum.com

[Eugene Griessel]

mah > wrote in message >...
> Was toying with my gps recently and plotted a course from my home in the
> midwest to London Heathrow. I know it uses great circle routing to
> calculate the distance and course. Going from west to east it shows a
> course of about 45 degrees. On the return trip it shows an intial
> course of 310 degrees.
>
> Now, to my old mind, I would have thought a reciprical course of 225 .
> It is something in the spherical formula used for the great circle but
> I'm too rusty to work through it.

You do not give a lat/long for your home position so a logical answer
is problematical. However a great circle from Heathrow on the angle
of departure you indicate would pass through (roughly) Upper Heyford,
Avon, Kidderminster, Highley and Westbury. However 310 is probably a
rather rough heading for calculations (I know my GPS only gives exact
degrees) so the track may lie considerably to the North or South is
the range is 309 - 311.

[mah]

Thanks to all who replied. Occasionally I need to scrape the rust off
the neurons and exercise things.

MAH