Author Topic: More Magnetic Declination...  (Read 8291 times)

captain paranoia

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Re: More Magnetic Declination...
« Reply #15 on: November 14, 2012, 12:55:55 PM »
I've been thinking about the issue of True, Magnetic and Grid Norths, and the impending problem of the change of Grid Magnetic Angle from West to East, and the effect that will have on the use of the mnemonic 'Grid to Mag: Add; Mag to Grid: Get Rid'.  Here's my thinking...

True North
This is a physical property of the rotation of the Earth; it's point at which the the axis of rotation of the Earth meets the surface.  This changes a little, due to the changing shape of the Earth (core changes, earthquakes etc.) but not by much, and this variation can be ignored.

Celestial North
This is the imaginary point in the night sky that True North points to.  It changes with time (with a period of about 26000 years, or 1 degree in 72 years), as the Earth's rotation precesses.  Think of a spinning top as it slows down; the top still spins on its axis quite quickly, but the axis about which it rotates also rotates slowly; this is precession.  It has no impact on map and compass navigation, but does effect celestial navigation.  Slowly...

Magnetic North
The Earth's magnetic field is caused by the moving, molten, nickel-iron core of the Earth.  Lines of magnetic flux come out of the surface of the Earth at different points, at different strengths, and at different angles at different positions on the Earth's surface.  A compass aligns itself with the lines of magnetic flux as they occur at that point on the Earth's surface.  This gives the concept of a Magnetic North, as measured with a compass.  And, for a specific point on the Earth's surface, there is a Local Magnetic North, LMN.

Magnetic Declination
The concept of the difference between True North, TN, and Magnetic North due to the lines of flux is called Magnetic Declination (or Variation), and, at any point on the Earth, there is a specific Local Magnetic Declination, LMD:


Grid Convergence
The Earth is an oblate spheroid.  A map is a flat piece of paper, which attempts to represent the curved surface of the Earth; this it cannot do; try wrapping a ball with a piece of paper without leaving any creases...  Clever Mr Mercator came up with a mathematical way of drawing a map of the Earth's surface so that bearings and distances measured between two points are correct (a projection).  OSGB and UTM maps use this (Transverse) Mercator projection.  The downside of this projection is that the Grid North lines on the map, whilst being a fixed distance apart, don't point to True North.  Consider that, as we go North, the distance between lines of longitude gets smaller and smaller (until they meet at the pole).  Thus, in a map grid that maintains a fixed spacing between the Grid North lines, as we go North, the Grid North lines must diverge out from True North lines.  The only points at which Grid North and True North are aligned is on the line forming the centre of the projection space; in the OSGB projection, this occurs at 2 degrees W.  The concept of this difference between True North and Grid North is called Grid Convergence, and, at any point on the Grid, there is a Local Grid Convergence, LGC:


Grid Magnetic Angle
Now, if we look at a particular area of a Mercator Projection, i.e. we look at a map, there will be a difference between the Local Magnetic North and Local Grid North.  This difference is due to the Local Magnetic Declination (the relative position of the local magnetic field wrt True North), and the Local Grid Convergence due to the Mercator Projection of the map at that point (the relative position of Local Grid North wrt True North).  Note that Local Grid Convergence actually varies across the entire map, but this variation is relatively small, and can be ignored on large-scale (1:50k, 1:25k) printed maps*.  Let's define the Local Grid Magnetic Angle, GMA, as the difference between Local Magnetic North and Local Grid North:

GMA = (TN - LMD) - (TN - LGC)

Since, by cartographic convention, positive angles (0 <= angle <180) are E, and negative angles (-180 < angle < 0) are W, GMA measures how far Local Magnetic North is East of Local Grid North.  So, a positive GMA means LMN is E of LGN, and a negative GMA means LMN is W of LGN (as is currently the case in most of Britain).

So, we must be careful with our terminology, and must use only (Local) Grid Magnetic Angle when we wish to discuss converting between Local Grid North and Local Magnetic North; if we used the term Magnetic Declination, we would, strictly, be ignoring the Local Grid Convergence, which can be just as important a correction factor as the Local Magnetic Declination.  Generally, when map-reading, we aren't concerned with Magnetic Declination or True North; this has already been dealt with by the cartographers, who have given us a handy diagrammatic representation of magnetic, true and grid Norths.  The only way in which Magnetic Declination affects us is the change of Magnetic Declination with time, which causes the Local Grid Magnetic Angle to change with time.

Note that I have stressed the distinction between the general concepts, and the local value of those concepts, since it is essential to bear in mind that all these factors vary with position on the Earth, and in the particular mapping projection employed, and with time; they are not constants either geographically, cartographically, or temporally.

Now let's look at applying this.

Consider a point on an OS map, where the Local Magnetic North is (for example) 3 degrees West (or minus 3 degrees E) of Local Grid North.  By convention, the Local Grid North is 0 degrees.

GMA = -3 - 0 = -3
GMA = -3 degrees East, i.e. Local Magnetic North is 3 degrees West of Local Grid North (confirming what we stated above...)

Now, we can re-arrange
to give:


We can then replace these 'Norths' with actual measured bearings: Local Magnetic Bearing, LMB, and Local Grid Bearing, LGB:

LMB = LGB + GMA      Grid to Mag: Add
LGB = LMB - GMA      Mag to Grid: Get Rid

Note that, if we use the definition of GMA as above, and the E positive, W negative convention, and use signed arithmetic for the above operations, the 'Grid to Mag: Add, Mag to Grid: Get Rid' mnemonic works no matter what the values are, or where we are in the world.

nb. Unfortunately, you will often find GMA being defined as follows: "The horizontal angular difference between Grid North and Magnetic North is called GRID MAGNETIC ANGLE" (taken from the OS website below).  Note that the order in which the two terms are expressed in the 'difference' is the reverse of the above definition of GMA; when expressed arithmetically, this gives a change in sign, which makes the 'Grid to Mag: Add, Mag to Grid: Get Rid'  mnemonic completely wrong.  Sadly, they express this GMA in terms of degrees E or degrees W, rather than the more helpful, conventional +/-degrees E.

* With the rise of electronic mapping, where there is no useful North annotation in the corner of the map, some other means of finding the GMA will be required.  Ideally, the electronic mapping tool will have some means of determining GMA, probably using a look-up table of baseline and time delta values (rather like the printed map annotation).

Useful links:

You can put in any name and email address in the Geomag site...

Of course, having said all this, as I've observed above, I don't generally like mnemonics, and deal with grid to magnetic conversions in a completely different way, thinking about the relative position of local magnetic north wrt grid north...
« Last Edit: November 14, 2012, 06:37:20 PM by captain paranoia »


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Re: More Magnetic Declination...
« Reply #16 on: November 14, 2012, 06:00:13 PM »
Very very nice. Agree on the trics...just know how to explain it to yourself.


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Re: More Magnetic Declination...
« Reply #17 on: November 15, 2012, 02:46:36 PM »
CP posted Useful links:

I believe there are better links, right here on this site.

Amore detailed and better explanation of GMA (Grid Magnetic Angle) with how and why to correct for it, has already been posted on the forum

The BGS (British Geological Survey) website for GMA (Grid Magnetic Angle) is unnecessarily complicated. A easier to use site that calculates the GMA you need to use to adjust your compass with is on this forums host site

Simply move your cursor over the place you need to determine the GMA and it is displayed in the bottom right hand box.

captain paranoia

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Re: More Magnetic Declination...
« Reply #18 on: November 15, 2012, 06:41:42 PM »
The OS description of declination and GMA is pretty terse, but the advantage of the OS website it's that it carries some 'authority'...  I did have to do a double-take on the bit about calculating variation, thinking that they were going to describe calculating GMA, but, no, they describe how to determine variation starting with GMA...

And I confess that I'd forgotten the GMA app on this website.  Naughty me...  Again, I posted the BGS site because it ought to be the definitive source of information, given that they provide the basic declination information to the OS.

My discussion was intended to provide 'another take' on the matter, for those of an arithmetic, or mathematical bent, and, in particular, the issue of magnetic north getting closer to true north, and the ensuing change of sign of GMA.  I wrote it a while back, and was prompted to post it after a couple of posts on OM where a chap was saying that variation = GMA.

Hugh Westacott

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Re: More Magnetic Declination...
« Reply #19 on: November 15, 2012, 07:11:27 PM »
I've been following this discussion and want to make a point that appears to have been overlooked.

Accurate navigation, relying solely on map and compass, in the lowland countryside of England and Wales is often more difficult than route-finding in fair weather in the mountains and moorlands of upland Britain (gasps of disbelief from the mountaineers!) for the following reasons:

1   Apart from the relatively small areas of open access, walkers are required to keep to public rights of way (PRoWs); if they don't, they are trespassing.

2   The PRoW network is often dense. In the three civil parishes that I check annually for the Ramblers Association there is a total of 19 miles of public paths.

3   PRoWs are not always visible on the ground and waymarking is often patchy.

4   The basic technique is to navigate using handrails and features such as field boundaries, woods, reservoirs, rivers etc. Contours, generally speaking, are of much less importance.

5   PRoWs are not always clear on the ground and a compass is often useful to determine the direction of cross-field paths (i.e. those that do not follow the field boundary) especially when the far side is in dead ground making the exit point invisible.

6   The most difficult areas in which to navigate accurately are popular areas such as Leith Hill, Box Hill, the Devil's Punchbowl, and Wendover Woods. The reason is that they have plenty of parking and well-meaning bodies such as the National Trust have created waymarked circular walks many of which are not shown on the map. There are animal tracks, firebreaks that are used as short cuts, and narrow paths made by courting couples seeking privacy.

7   I find that the most difficult national park in which to navigate is the New Forest. There are no PRoWs because it's common land, it is relatively flat so physical features do not stand out and, in it is  parts, densely wooded. The National Park Authority (NPA} has created a number of well-waymarked routes for walkers and riders but apart from these, exploring off-path is very difficult. I don't normally consult my satnav when walking in lowland countryside but I find it invaluable in the New Forest.

This long preamble leads me to my main point. I never make allowance for the Grid Magnetic Angle (GMA) in lowland countryside because it's not  necessary as distances between features are s short. In fact, I often guess from the map the angle that a cross-field PRoW deviates from a linear feature such as a field boundary. At a multi-path junctions, I confirm the route I want to follow by placing the compass on the map and quickly estimating the bearing. No need to bother with GMA!

Needless to say I always follow best navigation practice when walking in upland regions.



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Re: More Magnetic Declination...
« Reply #20 on: November 15, 2012, 07:19:35 PM »
Hi all,

Very interesting - the theoretical side of this is fascinating for the armchair and invaluable for the expert in the field but when trying to shape younger minds I've always found mnemonics useful (if a piece of 2x4 is unavailable).

'Add for Mag - Rid for Grid' was new to me but as has been mentioned has a limited shelf life.

I was taught 'Variation west- compass best, variation east - compass least'. It helped me when learning and has always been the way I teach others. Understanding the details is good and should always be the aim of a keen navigator but even now, when cold and tired, I check my understanding against the aide. Measure twice - walk once!



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Re: More Magnetic Declination...
« Reply #21 on: December 27, 2015, 09:10:23 PM »
This subject was one of the reasons I joined this site and purchased Mr Bs book.

I never truly understood variation, which I think is the key to everything.

"Because it is" is not the answer......but my poor bloody brain don't half hurt!!!

I get it in parts, but its probably time to dig deep until it clicks.

Oh Mother!!