Great circle formulae, True cource and actual heading

"Sims" writes:

I guess i was looking for a formula to calculate my True Course +Magnetic
variation at any given point on the globe.

Formulas can tell you the true course needed at all points along the
great circle route, because it's just geometry. But the local magnetic
variation is not predictable by a formula. Just look at a map of lines
of constant variation - they're too irregular (and they move with time).

The best you can do is a table plus interpolation, or a set of functions
empirically fitted to measured data. Either way, it won't be just a
simple formula.

On the other hand, even if you knew the magnetic course you need to
follow exactly, that still wouldn't tell you the heading to fly or
sail, since the heading also needs to provide wind correction.

If you have a GPS along on your trip, it can show you whether you are to
the left or right of the ideal great-circle path between two waypoints.
The correct heading is whatever heading keeps you along the centerline
of that path. There's no better definition of correct heading.

Dave

On the other hand, even if you knew the magnetic course you need to
follow exactly, that still wouldn't tell you the heading to fly or
sail, since the heading also needs to provide wind correction.

If you have a GPS along on your trip, it can show you whether you are to
the left or right of the ideal great-circle path between two waypoints.
The correct heading is whatever heading keeps you along the centerline
of that path. There's no better definition of correct heading.


The GPS itself will indicate the amount to turn in order to reach the
correct heading. COURSE or DTK (synonyms) will change along the route as a
reflection of great circle effects. Likewise, the BEARING will also change
for great circle. While what you said is correct, a good way of staying on
course is to compare TRACK to BEARING or keep TURN to zero. This makes it
easier to find the heading that keeps the vehicle along the centerline of
the path.

Sims wrote:

"red rover" wrote in message
.. .

"Dale DePriest" wrote in message

You mean your magnetic heading. You have your actual heading. You need
a table of magnetic variations and interprolate from the table based on
your location as there is no mathmatical model that will provide this
information reliably.


(Sorry to reply here your post was cancelled).

Yes i do mean the magnetic heading.
Sorry I was not clear.

Where can i get a table to compute my magnetic heading?

Try here for a start.

http://www.ngdc.noaa.gov/seg/WMM/DoDWMM.shtml

Dale


Thanks

Sims.



--
_ _ Dale DePriest
/`) _ // http://users.cwnet.com/dalede
o/_/ (_(_X_(` For GPS and GPS/PDAs

"Sims" wrote in
:


"red rover" wrote in message
.. .

"Dale DePriest" wrote in message


You mean your magnetic heading. You have your actual heading. You
need a table of magnetic variations and interprolate from the table
based on your location as there is no mathmatical model that will
provide this information reliably.


(Sorry to reply here your post was cancelled).

Yes i do mean the magnetic heading.
Sorry I was not clear.

Where can i get a table to compute my magnetic heading?

You might take a look at the Canadian Geological Survey
Geomagnetism website:
http://www.geolab.nrcan.gc.ca/geomag/home_e.shtml
After all, the North magnetic pole is in Canada ;-)

--
Dave Patton
Canadian Coordinator, the Degree Confluence Project
http://www.confluence.org dpatton at confluence dot org
My website: http://members.shaw.ca/davepatton/
Vancouver/Whistler - host of the 2010 Winter Olympics

"John Bell" writes:

The GPS itself will indicate the amount to turn in order to reach the
correct heading. COURSE or DTK (synonyms) will change along the route as a
reflection of great circle effects. Likewise, the BEARING will also change
for great circle. While what you said is correct, a good way of staying on
course is to compare TRACK to BEARING or keep TURN to zero. This makes it
easier to find the heading that keeps the vehicle along the centerline of
the path.

I haven't heard of a GPS receiver that will tell you what heading to fly
or sail to compensate for wind or current. A GPS-only unit has no way of
knowing what your current heading is in the first place. It can tell
you how much to turn to align your heading with the desired course, but
that assumes no wind or current. In practice, you'll have to make
adjustments to that heading, while watching the cross-track error.

Dave

Dave Martindale wrote:

"John Bell" writes:


The GPS itself will indicate the amount to turn in order to reach the
correct heading. COURSE or DTK (synonyms) will change along the route as a
reflection of great circle effects. Likewise, the BEARING will also change
for great circle. While what you said is correct, a good way of staying on
course is to compare TRACK to BEARING or keep TURN to zero. This makes it
easier to find the heading that keeps the vehicle along the centerline of
the path.


I haven't heard of a GPS receiver that will tell you what heading to fly
or sail to compensate for wind or current. A GPS-only unit has no way of
knowing what your current heading is in the first place. It can tell
you how much to turn to align your heading with the desired course, but
that assumes no wind or current. In practice, you'll have to make
adjustments to that heading, while watching the cross-track error.

Dave

The III pilot does permit you to make the adjustment manually so that
you can use the GPS for guidance but it does not and cannot make this
adjustment automatically since it has no sensors to detect this.

Dale

--
_ _ Dale DePriest
/`) _ // http://users.cwnet.com/dalede
o/_/ (_(_X_(` For GPS and GPS/PDAs

In article ,
Craig Prouse wrote:
Dale DePriest wrote:

You need
a table of magnetic variations and interprolate from the table based on
your location as there is no mathmatical model that will provide this
information reliably.

Given a table of magnetic variations at known locations, there are
statistical methods to derive a useful mathematical model. The web site
cited in a previous article provides such a model as a polynomial.

http://williams.best.vwh.net/avform.htm#Var

http://geomag.usgs.gov/chartsdo.html

http://geomag.usgs.gov/models.html

http://www.ngdc.noaa.gov/IAGA/wg8/igrf.html

http://www.ngdc.noaa.gov/IAGA/wg8/table1.txt

http://www.freewarepalm.com/calculator/magcalc.shtml

http://www.garmin.com/manuals/GPSIII...nersManual.pdf page 78 (in document)
(page 88 in pdf file) gives 4 heading adjustment choices: auto magnetic
(using a magnetic field model driven by the current location), true, grid
(driven the UTM locatin) or user magnetic (the user states the desired
adjustment). I suppose that you could use this to include a wind adjustment?!

Other than that; get your aviation weather report and your E6B.

Randolph J. Herber, , +1 630 840 2966, CD/CDFTF PK-149F,
Mail Stop 318, Fermilab, Kirk & Pine Rds., PO Box 500, Batavia, IL 60510-0500,
USA. (Speaking for myself and not for US, US DOE, FNAL nor URA.) (Product,
trade, or service marks herein belong to their respective owners.)

Dave Martindale wrote:
"John Bell" writes:

The GPS itself will indicate the amount to turn in order to reach the
correct heading. COURSE or DTK (synonyms) will change along the
route as a reflection of great circle effects. Likewise, the
BEARING will also change for great circle. While what you said is
correct, a good way of staying on course is to compare TRACK to
BEARING or keep TURN to zero. This makes it easier to find the
heading that keeps the vehicle along the centerline of the path.

I haven't heard of a GPS receiver that will tell you what heading to
fly
or sail to compensate for wind or current. A GPS-only unit has no way
of knowing what your current heading is in the first place. It can
tell
you how much to turn to align your heading with the desired course,
but that assumes no wind or current. In practice, you'll have to make
adjustments to that heading, while watching the cross-track error.

We use GPS receivers in our gliders, and most of them can find the wind
direction and speed automatically by detecting that you have made a full 360
degree turn (happens often for gliders when searching for thermals), and
analysing the 360 degree turn you have made for drift direction and speed.

And I'm certain that the information is used to display a wind-corrected
heading.

We use Pocket-Nav http://www.cambridge-aero.com/pocketNAV.htm and others.

/Mogens

In article ,
Sims wrote:

As Steve has noted there are two things happening:
(1) The bearing to point B along a great circle/ellipsoid path
from Point A to B varies along the path. (A computer/autopilot
can be set to follow the ever varying bearing.)

Thanks

I was looking for a formula that does the same, so that i can tell my
heading at a certain point on the course.

I will look at the links given.

Again many thanks all for the help.

Sims

Here is a program that does that:

http://www.freewarepalm.com/astronomy/navigate.shtml

The idea is to compute the great circle heading and distance, divide the
great circle distance by as many legs as desired, project the initial
heading the divided distance, repeat the process from there for one
less leg until no legs remain.

E.g.: from Washington DC to Moskva, RF:

38o 51'N 77o 1' 48"W to 55o 58' 48"N 37o 30'E in 8 legs:

each leg is 607.77 miles:

bearing start
32o 46' 3.86" 38o 51'N 77o 1' 48.00"W
37o 23' 29.85" 46o 3' 58.96"N 70o 11' 54.04"W
44o 5' 15.66" 52o 44' 48.60"N 61o 24' 8.89"W
53o 47' 18.95" 58o 32' 41.37"N 49o 40' 47.65"W
67o 28' 0.55" 62o 53' 15.70"N 34o 1' 55.31"W
84o 58' 38.88" 65o 0' 21.16"N 14o 34' 48.87"W
103o 33' 33.09" 64o 20' 34.61"N 5o 56' 13.18"E
119o 26' 55.57" 61o 5' 21.89"N 23o 46' 41.62"E
55o 58' 48.00"N 37o 30' 0.00"E

Now, try to navigate that accurately. It is hard to do manually.

Randolph J. Herber, , +1 630 840 2966, CD/CDFTF PK-149F,
Mail Stop 318, Fermilab, Kirk & Pine Rds., PO Box 500, Batavia, IL 60510-0500,
USA. (Speaking for myself and not for US, US DOE, FNAL nor URA.) (Product,
trade, or service marks herein belong to their respective owners.)

"Sims" wrote in message ...

As Steve has noted there are two things happening:
(1) The bearing to point B along a great circle/ellipsoid path
from Point A to B varies along the path. (A computer/autopilot
can be set to follow the ever varying bearing.)

Thanks

I was looking for a formula that does the same, so that i can tell my
heading at a certain point on the course.

I will look at the links given.

Again many thanks all for the help.

Sims

As others have pointed out, it's all there on my web-site, but you
have to piece it together.

http://williams.best.vwh.net/avform.htm

To get the magnetic heading at each point:

(1) determine the great circle true course, TC, at each point on the
path. It varies as you progress.
(2) Correcting for magnetic variation (aka declination), you can
determine the magnetic course, MC by MC = TC +- VAR. You can get VAR
from a fit. It varies with time. If you want something quick and
dirty, use the polynomial fit. If you want to use an official model,
such as WMM2000 or IGRF2000, there's source code on my site that will
compute it.
(3) Lastly, to get magnetic *heading* from magnetic course, you need
to solve the standard flight planning wind triangle to find the wind
correction angle, WCA, using the known or forecast wind at that point
on your flight. Coding for this is also on my site. MH = MC +- WCA
(4) Even then you are not strictly finished. You need to correct
the magnetic heading to get a compass heading, CH using the listed
deviation, DEV, on the specific airplane's compass correction card.
CH = MH +- DEV