Great circle formulae, True cource and actual heading

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

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

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


Many thanks for a great page. Truly a great piece of work.

I have looked at it and found the mag var code.

I am just surprised that they vary so much depending what model is been
used.

What model is the best? And also it seems that by the poles the calculation
are somewhat wrong, is it just my imagination?

Sims

Ed,

I second the compliment on your site. I have found it useful several times.

John Bell
www.cockpitgps.com