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"Geodetic Azimuth": I Think I Finally Get It!

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This post is intended to help other newcomers who may be as slow on the uptake regarding True North, Magnetic North, magnetic declination, and Geodetic Azimuth as I have been. I think I finally see the light...but if not, I'm sure the folks who helped me out through my earlier posts will chime in. [And so they did when I screwed up my first post here! ;) ]



If you pull out your magnetic compass here in eastern MA and wait till the north-pointing arrow stabilizes, it will point to magnetic north.


However, the earth's magnetic field affects your compass needle differently depending on where in the U.S. (to keep it simple) you are located. Here in the Boston area, the magnetic north pole appears to be located about 15 degrees west of the celestial north pole, the point we also refer to as true north.


[There is another even finer distinction we could make--the distinction between astronomical true north (which you could measure, for example, by sighting the stars) and geoidal true north (which I believe adjusts "true" north for the ellipsoidal nature of the shape of the planet Earth. I think, however, that the difference between these two different measures of "true" north is quite small (a couple of seconds of arc) and so for our purposes can be ignored.]


The offset you observe between true north (or celestial north) and the direction indicated by the north-pointing arrow of your compass is called "magnetic declination", or declination for short. As I said above, for Boston this declination currently appears to be about 15 degrees west (15 d W).


If I want to report a compass reading I made as a bearing relative to true north, I will need to adjust my compass reading to take account of this local declination.


One way to do this starts by considering all west declinations to be negative numbers. Under this approach, regardless of whether the declination in your area is east or west, to convert a magnetic bearing to a true bearing, you add the declination to it. As an example, in Boston, if your unadjusted compass shows you a bearing of 45d, your true bearing (geodetic azimuth) would be 30d [45 + (-15) = 30]. The (-15) above is Boston's 15d west declination.


On the other hand, if you were trying to convert a true bearing to a magnetic one under this approach, you would subtract the declination from it. For places with west declination, this has the effect of subtracting a negative number, or adding the declination to the true bearing. Again, in our Boston example, a true bearing of 30d would be adjusted to a magnetic bearing of 45d [30 - (-15) = 45].


When you adjust your magnetic compass readings to get true bearings, the adjusted bearings you come up with are referred to as geodetic bearings, or geodetic azimuths. The terms "bearing" and "azimuth" in this case are essentially synonymous. [some people make the distinction that an azimuth is measured from 0d to 360d, with north in the 0d position, while a bearing is often measured by quadrant, such as N 50d W for an azimuth of 310d, or S 20d W, for an azimuth of 200d.]


Magnetic declination varies depending on the observer's position on the earth and over time (from year to year). For example, magnetic declination in San Francisco goes the other direction from current declination in Boston, about 14.5d E as opposed to 15d W. This means that a benchmark hunter in downtown SF will have to add 14.5d to his/her observed bearings to get to "true", or geodetic, bearings. The example compass reading of 45d, if it were made in San Francisco, would become 59.5d if it were adjusted to a true bearing.


Tosborn, who thankfully unscrambled my first attempt at explaining this, describes it a little differently below, and also deals with a second formula for magnetic to true bearing adjustments or v. versa, in which all declinations are considered as positive numbers. Thank heaven for the clearer-headed! :)


So that compass users don't always have to run around with a pad, a pencil, and a calculator in order to transform their unadjusted compass readings into adjusted ones (or geodetic azimuths), many compasses have a built-in ability to "adjust for" the influence of magnetic declination. Depending on the compass model, you can turn a screw on the bottom of the compass capsule or on the side of the instrument to produce a semi-permanent "offset" of the bearings indicated by graduated circle (or the "compass rose").


So if you're using a compass that has been correctly adjusted for the correct magnetic declination in your part of the country, the bearings (or azimuths) you read off your compass dial at the north-pointing arrow will be geodetic azimuths, like those reported in the "box scores" of NGS Data Sheets. If you're in Boston, however, and you are not using a compass adjusted for magnetic declination, the geodetic azimuths given on your NGS data sheets should all be 15d out of whack with the bearings reported by your compass. For Boston, you could of course manually add the west (negative) declination back into your observed compass bearings (which has the effect of subtracting the declination from them) in order to come up with geodetic azimuths you could use in finding the reference marks for your stations when standing on the station disks.


Since declination is so important and changes from year to year (as well as according to the part of the country you are hunting in), NOAA has kindly provided a useful webpage for determining your local declination.


[i finally confirmed the nature of geodetic azimuths for myself by finding a station disk that had two easily intervisible reference mark disks not too far away from it (about 20-30 ft. distant), sighting the bearings from the station to each of the marks with two separate (declination-adjusted) compasses, and seeing that the bearings indicated by both compasses were within 1d or so of the geodetic azimuths of these RMs listed in the station's data sheet "box score." It worked (thank heavens!).


Hope this is helpful to others (and that I've finally get it right!)....



Edited by pgrig
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It was good of you to write up a practical guide to declination. Here are a few expansions/corrections:


1) the difference between geodetic North (which is usually what folks mean when they refer to "True North") and astronomic North is know as the Laplace correction. The formula is : Astronomic Azimuth + Laplace Correction = Geodetic Azimuth. The Laplace correction is found on NGS datasheets for adjusted marks and is calculated using the DEFLEC99 program of the NGS Geodetic Tool Kit. As you say, the Laplace correction is typically only a few arc seconds in magnitude.


2) accounting for declination in one's head can be a confusing exercise. When you have a true azimuth and you want a magnetic azimuth you have to do one thing (subtract or add the declination) depending on whether your declination is East or West. And then when you want to go from a magnetic azimuth to a true azimuth, you have to do the opposite mathematical operation. It very easy to get confused and make a mistake. That's why having a compass with the capability to set declination is so desirable.


3) In describing the declination adjustment feature on some compasses you state that "To adjust for West declination, which is negative, the graduated circle is turned counter-clockwise." Be aware that different compass manufacturers have different ways of setting declination. Some have a scale that reads from the top of the compass, others have a scale that reads from the bottom of the compass. So, clockwise...counter-clockwise.....it just depends on the way the compass is constructed and which side you are looking at.


4) Unfortunately, your examples for Boston and San Francisco of how to convert between magnetic and true azimuths are exactly opposite of what they should be.


Lets take an example. Let's pretend that you are in San Francisco standing on top of a triangulation station. You sight your compass (not adjusted for declination) at a reference mark and amazingly the azimuth you read from the compass is exactly 0.00 degrees. Of course you know this is a magnetic azimuth, so the reference mark is a point on a line between the triangulation station and magnetic North. What you need is a true azimuth. You know that the local declination is 14.5 degrees East, meaning that a magnetized needle will point 14.5 degrees East of True North. So, the True azimuth between the triangulation station and the reference mark must be 14.5 degrees. You've ADDED the declination to the magnetic azimuth in order to get the true azimuth. In your writeup, you have us SUBTRACTING the declination.


Likewise, let's say we are in Boston. Again we sight from a triangulation station to a reference mark with a compass unadjusted for declination. Again we get a magnetic azimuth of 0.00 (a.k.a. 360) degrees. In Boston we know that a magnetized needle will point 15 degrees West of True North. So the True Azimuth from the triangulation station to the reference mark must be 345 degrees. In this case we've SUBTRACTED the declination from the magnetic azimuth to get the true azimuth. In your writup you have us ADDING the declination.


Here are the rules:


4a) When going from True azimuths to Magnetic azimuths subtract east declinations, but add west declinations. (In Boy Scouts we learned the following rhyme to aide us in going from azimuths taken from a topo map (true azimuths) to correctly setting our non-declination adjusted compasses correctly (magnetic azimuths) ...EAST IS LEAST, WEST IS BEST. Meaning subtract east declinations and add west declinations to go from true to magnetic.


4b) When going from Magnetic azimuths to True azimuths, do the opposite of the above rule. In other words, add East declinations but subtract West declinations.


The foregoing assumes that ones treats both East and West declinations as positive numbers. At one point in your writeup you did bring up the idea that West declinations can be considered negative and East declinations positive. But then you didn't seem to follow through with that distinction in your examples. However, if one consistently treats West declinations as negative numbers and East declinations as positive numbers, the following formulas can be used. In the end, it works out identical to the above two rules.


True azumith = Magnetic azimuth + magnetic declination (where West Declinations are negative), and

Magnetic azimuth = True azimuth - magnetic declination (where West Declinations are negative)


5) In addition to spatial and long run secular changes in declination, there is also daily variation and irregular variation. Daily variation in the US averages 8 arc minutes. It is furthest East at around 8 in the morning and furthest West at around 1:30 in the afternoon. In terms of irregular variation, it can be as much as 1 degree resulting from electrical storms and magnetic disturbances. Then there are local sources of attraction such as iron-bearing rocks, etc which can cause deflection in a magnetic needle. Also, things worn by the individual can cause the needle to deflect. There is the story about the surveyor from the 1800's who's bearings were consistently different from what current-day surveyors would find when they retraced his lines. One day, the mystery was solved when a photo of the old surveyor surfaced. It showed him standing next to his waist-high compass with a large pistol strapped to his hip. Now you know the rest of the story.

Edited by tosborn
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But wait, have you heard of Geomagnetic Reversal?


Recent geomagnetic reversals.

Wikipedia link.

And just when we think we understand everything, it could change in a heartbeat.



PS: Your post is long but, just might help someone understand things a little better. :)

Me? - I let John figure out that stuff...:unsure:


A good point!


However, the reality of it will be a bit more disconcerting for compass users.

While the reversals are rather sudden in geologic terms, the evidence seems to indicate a period of several hundred to thousands of years for a complete reversal. While nobody knows for certain, some of the theorists think there will be a period when there is little or no magnetic field at all.


Considering what the magnetosphere does to protect us from space radiation, I think a poorly functioning compass will probably be among the least of our worries.


Of course, until it happens it's all speculation...


A different Wikipedia link.


EDITED: To add the link.

Edited by AZcachemeister
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" astronomical true north (which you could measure, for example, by sighting the stars) and geoidal true north (which I believe adjusts "true" north for the ellipsoidal nature of the shape of the planet Earth."


(Not "geoidal true north"-- dunno that such a term exists, but if it does it probably means astronomic north.)


If the earth were actually ellipsoidal then the plumbline would always point to a point on the earth's axis, and astro north would always coincide with geodetic north. But if you're on the west slope of a large mountain range the plumb-bob will usually be pulled toward it a bit (i.e. eastward) which means "astro north" will point east of the earth's pole.


In an extreme case, like on the big island of Hawaii, the plumbline might point about a minute away from "geodetic vertical".

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One thing I miss from Topozone is the local magnetic declination being shown in the corner of the map.


If the declination shown on the Topozone maps is the same as the indicator on the printed maps, then it could be considerably off. Certainly better than nothing, but if the map was created 20-30 years ago (as many that are still in print were), the declination has definitely changed.


Better to visit here and get the latest value. It might be a good idea to retrieve values for several localities in your state if you are really going to rely on a magnetic compass.


Of course, once the reversal starts, you are on your own... :rolleyes:

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Yep, learned that many years ago (Boy Scouts maybe?). The "N" end of the compass needle is the North SEEKING end of the needle. Which actually makes it the South magnetic end of the needle.

Interesting, huh?

I thought it was the other way around, the the compass needle was the correct polarity, with the North Magnetic Pole and the Magnetic North Pole being on opposite sides of the globe. Here's what wiki says: LINK, and the Canadian Geological Survey's page (on the bottom of the page): LINK with a pretty good drawing here.

Edited by coggins
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"North" and "South" as names for poles of a magnet are completely ambiguous and about as useful as useful for names as "Pink" and "Green". They can describe the concepts but you cannot deduce the polarity.


The terms "North Seeking" and "Earth's North magnetic pole" are not ambiguous. You can make sense of statements like "The Earth's south magnetic pole is a north-seeking pole."

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