Grid North vs True North? Calculating difference?

  • Thread starter Thread starter Dale Atkin
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Dale Atkin

I'm working on a Geocache. As part of the exercise, one has to calculate an
offset from a point on a particular bearing (relative to true north). I know
I could just use some built in function for this, but I'd really like to do
it long hand (better workout for the brain). The only thing is, I don't know
how to convert between grid north and true north, and google is strangely
uncooperative... Anyone have any good links? Or helpful suggestions? I
should I just cheat, and tell the GPS to do it for me?

Dale
 
I'm working on a Geocache. As part of the exercise, one has to calculate an
offset from a point on a particular bearing (relative to true north). I know
I could just use some built in function for this, but I'd really like to do
it long hand (better workout for the brain). The only thing is, I don't know
how to convert between grid north and true north, and google is strangely
uncooperative... Anyone have any good links? Or helpful suggestions? I
should I just cheat, and tell the GPS to do it for me?

Dale
Click to expand...

The math will depend on what map projection the grid system is using. If
you're using UTM, here's a link from Google:

http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.HTM

that has some information, but quick look doesn't show the right equation.
You want to find the convergence angle. I know the equations are either in
TM8358.2 or TM8358.1. Both are available at

http://earth-info.nga.mil/GandG/pubs.html

Melita
 
I'm working on a Geocache. As part of the exercise, one has to calculate an
offset from a point on a particular bearing (relative to true north). I know
I could just use some built in function for this, but I'd really like to do
it long hand (better workout for the brain). The only thing is, I don't know
how to convert between grid north and true north, and google is strangely
uncooperative... Anyone have any good links? Or helpful suggestions? I
should I just cheat, and tell the GPS to do it for me?

Dale
Click to expand...

If it is a conformal projection (like TM is), a decent
approximation is the difference in longitude times the sin
of the latitude. That will be good to a couple of minutes
of arc, much better than any magnetic compass (since we do
not know declination to better than a degree or so).

steve
 
isnt it just grid north = magnetic declination + true north ...?
sounds too simple
Click to expand...

too simple, indeed. No, grid north has nothing to do with magnetic
declination.

True north points towards the geographic north pole.

Grid north points along the northing grid lines of the projection used, and
the difference to true north depends on the projection *and* on the present
position. I have no fomula available, sorry.

Magnetic north points towards the magnetic north pole. The difference to
true north is small in many countries, e.g. in most parts of Europe, but it
can be up to 30 degrees or more in other parts of the worls, e.g. America.
And, if you are close to the magnetic north pole (Hudson Bay, I think) then
the magnetic north is useless at all.

Here is a link for calculation of magnetic declination at your location:
http://www.ngdc.noaa.gov/seg/geomag/magfield.shtml
 
I'm working on a Geocache. As part of the exercise, one has to calculate
an offset from a point on a particular bearing (relative to true north). I
know I could just use some built in function for this, but I'd really like
to do it long hand (better workout for the brain). The only thing is, I
don't know how to convert between grid north and true north, and google is
strangely uncooperative... Anyone have any good links? Or helpful
suggestions? I should I just cheat, and tell the GPS to do it for me?
Click to expand...

Well, you can calculate an ellipsoidal direction inverse between latitudes
and longitudes, convert the latitudes and longitudes to (UTM I suppose)
grid, calculate a grid direction inverse using basic trig on the rectangular
coordinates, and subtract one direction from the other...

Of course the GPS unit might give an accurate direction inverse between
latitudes and longitudes and will convert the latitudes and longitudes to
UTM grid...


http://pages.prodigy.net/halsteadinvest/kbh-gps.htm
 
As I understand the function of a magnetic compass, it doesn't
actually point to the Magentic North Pole, but aligns itself parallel
to the local magnetic flux lines.

So, an internal GPS declination table will let you know what the
usable offset would be while using a GPS - but a plain vanilla compass
could show something very different. The kicker: Both could be
accurate, but the users would have to depend on their understanding of
what they're looking at.

Very cool: http://geomag.usgs.gov/flash/declination_fla.html
 
As part of the exercise, one has to calculate an
If you're in the USA, take a look at a USGS 7.5' topo map. It shows the
differences between grid north, true north, and magnetic north. Magnetic north
could have moved slightly in the years since the map was produced, but the
relation between grid north and true north remains constant.

Steve
 
Dale said:
I'm working on a Geocache. As part of the exercise, one has to calculate an
offset from a point on a particular bearing (relative to true north). I know
I could just use some built in function for this, but I'd really like to do
it long hand (better workout for the brain). The only thing is, I don't know
how to convert between grid north and true north, and google is strangely
uncooperative... Anyone have any good links? Or helpful suggestions? I
should I just cheat, and tell the GPS to do it for me?
Click to expand...


Maybe I'm missing the bleeding obvious here.

Grid north is parallel to the line of longitude up the centre of the UM
zone.

True north is parallel to the line of longitude you're sitting on.

If you're at a pole, the angle between these two lines will be equal to
the difference in angular longitude. The angle will be equal to 1 x
(long<zone centre> - long<point of interest>)

If you're at the equator, they're going to be parallel. The angle will
be equal to 0 x (long<zone centre> - long<point of interest>)

There's some function for latitudes in between which will tell you what
factor, call it Z, to apply to the same basic equation such that the
angle will be equal to Z x (long<zone centre> - long<point of interest>).

Without even drawing up complicated diagreams and working it all out,
I'm pretty confident that Z = sin (latitude).
 
The thing that is bing discussed is known as "grid convergence". See
http://www.tpub.com/content/USMC/mcr3161a/css/mcr3161a_70.htm
(Go down first column until the subject starts.)

Most conversion programs like Corpscon (free and recommended) will output
when converting.

A more technical reference is
ftp://164.214.2.65/pub/gig/tm8358.2/TM8358_2.pdf

A related topic is the "scale factor" which corrects for distances in UTM.
 
If you're in the USA, take a look at a USGS 7.5' topo map. It shows the
differences between grid north, true north, and magnetic north. Magnetic north
could have moved slightly in the years since the map was produced, but the
relation between grid north and true north remains constant.
Click to expand...
One caveat:

The sketch showing their relation should not be relied on for angle.
Instead, use the numbers printed.

Also, the map gives the declination for Magnetic North vs True North,
and also the rate of change in declination as of when the map was
produced. If it has been more than 10 years, it would be best to use
an up-to-date resource, perhaps one of the web sites mentioned by
others.

Also, before you get too deep into the difference between grid North
and True North, you might figure a ballpark idea of the discrepancy
over the distance you are doing. If it is rather small, you might not
need to bother depending on the overall accuracy of what you doing.

If you think it through, the difference will increase as you travel
from the Equator to the Pole.

Happy trails,
Gary (net.yogi.bear)
 
.........a wee thing they taught us back in the pre gps days was 'mag to
grid, get rid.......................grid to mag, add'........of course you
have to know the amount to 'get rid' or 'add'........so when converting from
magnetic bearing to grid bearing, subtract the declination....and reverse
for magnetic to grid conversion............using prismatic compasses over
distances typically less than ten miles in a leg, it was not worth bothering
with for normal nav purposes.
 
........a wee thing they taught us back in the pre gps days was 'mag to
grid, get rid.......................grid to mag, add'........of course you
have to know the amount to 'get rid' or 'add'........so when converting from
magnetic bearing to grid bearing, subtract the declination....and reverse
for magnetic to grid conversion............using prismatic compasses over
distances typically less than ten miles in a leg, it was not worth bothering
with for normal nav purposes.
Click to expand...
The little sayings like that are specific to which side of the zero
declination line you happen to be on. Here in New England the
declination ranges from 14 to 17 degrees one way, and in the Cascades
it is about 15 degrees the other way. I have also seen advice from
people living near the zero line that declination is not a major
thing.

Many people hiking will do everything in magnetic bearings, even
drawing parallel lines aligning with MN. As long as your whole group
is consistent, this works out fine.

Happy trails,
Gary (net.yogi.bear)
 

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