Great circle formulae, True cource and actual heading

Hi,

I am trying to write a formula to compute flight headings.
If i use 2 lat/lon i can get a "true course" but due to magnetic variations
the true course is not really all that useful, (knowing that my true course
is 118deg will not tell me that i should fly 93 deg).

What i mean is if i go from A to B i can calculate the True course, ('tc')
but my actual heading varies a lot depending on my position along the
course.

Is there a reliable formula to calculate my actual heading at a certain
point along the course?

Many thanks in advance.

Sims

"Sims" wrote in
:

Hi,

I am trying to write a formula to compute flight headings.
If i use 2 lat/lon i can get a "true course" but due to magnetic
variations the true course is not really all that useful, (knowing
that my true course is 118deg will not tell me that i should fly 93
deg).

What i mean is if i go from A to B i can calculate the True course,
('tc') but my actual heading varies a lot depending on my position
along the course.

Is there a reliable formula to calculate my actual heading at a
certain point along the course?

Many thanks in advance.

Sims

At least in sci.geo.satellite-nav this sort of question about
formulae has been asked numerous times, including quite recent
threads, so a search via Google Groups would likely have already
found you your answer.

Take a look at Ed Williams page about Aviation Formulary:
http://williams.best.vwh.net/avform.htm

--
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

Sims wrote:

Hi,

I am trying to write a formula to compute flight headings.
If i use 2 lat/lon i can get a "true course" but due to magnetic variations
the true course is not really all that useful, (knowing that my true course
is 118deg will not tell me that i should fly 93 deg).

What i mean is if i go from A to B i can calculate the True course, ('tc')
but my actual heading varies a lot depending on my position along the
course.

Is there a reliable formula to calculate my actual heading at a certain
point along the course?

Many thanks in advance.

Sims



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.

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

"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.


I found the post a little confusing because it seemed to be mixing
the problem of the course heading changing due to the great circle
route (mentioned in the subject) with heading changes due to changing
declination mentioned in the body. Two very different issues.

Steve

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

red rover wrote:

"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.



I found the post a little confusing because it seemed to be mixing
the problem of the course heading changing due to the great circle
route (mentioned in the subject) with heading changes due to changing
declination mentioned in the body. Two very different issues.

Steve

Yes, it was my mistake, I misread the original post by not comparing the
text to the subject line. I tried to cancel but too late, Sorry

Dale


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

"Dale DePriest" wrote in message
...

Yes, it was my mistake, I misread the original post by not comparing the
text to the subject line. I tried to cancel but too late, Sorry

Dale

Well I actually meant the original post was confusing, not your
reply.

Sims wrote:

flight headings.
If i use 2 lat/lon i can get a "true course"
but due to magnetic variations ...
actual heading varies a lot depending on my position along the
course. ...formula to calculate my actual heading at a certain
point along the course?

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.)

(2) The Earth's magnetic variation (a.k.a. declination) that affects
a magnetic compass heading varies with latitude and longitude
and also with time. This magnetic field offsets the
true great circle bearing at a given point along the path.

If one follows a rhumb line course instead of a great circle path,
the rhumb line bearing is constant. This is easier for a human
to follow at the expense of having a longer path.
One can find this on a Mercator projection map.
Again the magnetic variation offsets the rhumb line bearing
at a given point.

As Dave notes, Ed Williams' site discusses these issues.

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


The World Magnetic Model (WMM) maintained by the U.S. DoD
and others

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

predicts the components of the Earth's steady state magnetic field
for a given latitude and longitude for a given date.
The horizontal component direction corresponds to the magnetic
variation. The target accuracy is one degree over a 5-year period.

My freeware DOS command line program GCGC* calculates the great circle
bearings between two points (WGS-84 default) and then uses
the WMM to also calculate the magnetic bearings at the end points.
If one needs the true and magnetic bearings along the flight path
(certainly a reasonable thing to need in flying), one would recalculate
the great circle path to point B from the position at the moment.
One can use the included Direct function (Lat1/Long1, Bearing 1-2,
and distance 1-2 to get Lat2/Long2) to calculate positions
along the great circle path by splitting it into pieces.

I also have a program (gcb12) that does rhumb lines at my web site,
but I haven't gotten around to adding the magnetic bearings.

Cheers, 73,

Ron McConnell
w2iol

N 40º 46' 57.9" W 74º 41' 21.9"
Magnetic Variation = 13.0º W in October 2003
FN20ps77GU46 [FN20ps77GV75]

* GCGC executable and source at

http://home.earthlink.net/~rcmcc

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

"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?

Thanks

Sims.