# Talk:Universal Transverse Mercator coordinate system

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## Graphics are still needed

• The 60 UTM zones overlain on a map of the world
• The process by which points are measured (eastings and northings)
• Perhaps a diagram showing how a 6° wide UTM zone wraps around the globe like a strip of paper

I will see if I can aquire any of these from other publications.

Justin 03:16, 23 August 2005 (UTC)

I've added a graphic that may satisfy the first two requirements. mdf 16:43, 29 October 2005 (UTC)
Very nice graphic, thanks! If you wouldn't mind moving a bit of the information in the image's description into the article (particularly about the discrepencies, and why they exist), that would be great. I'd do it myself, but my knowledge about the topic is only cursory, and I'm afraid I'd get something wrong. Phidauex 17:00, 29 October 2005 (UTC)
I've re-arranged things a bit, added the technicalities, and linked to the MGRS. I also marked the MGRS article as a stub. I'll see if I can make some graphics for that one.
As for UTM's exceptions: I have no idea why they exist. Two possibilites I can think of (1) for the convenience of the Norwegian people (but then, why not for the people of Edmonton?), or (2) perhaps those areas were important, or felt to become important, immediately after WWII, and the problems of converging meridians would have been a operational mess. mdf 20:10, 29 October 2005 (UTC).
On the European map, the Norwegian exception is shown slightly wrong. The boundary line between 31V and 32V should follow longitude 3°E (the middle of zone 31), but the European map shows the boundary too far east, around 4.5°E. The world map is correct, though. --Mikael R 08:58, 20 February 2007 (UTC)

The graphic provided showing the map sections was labeled as being incorrect. I commented it out. Can someone confirm if there's a problem with it?23:34, 15 March 2009 (UTC) —Preceding unsigned comment added by 67.169.145.35 (talk)

## A couple of tables?

first table two collums long(range)-UTM 0-60
second table LAt(range)-UTM A-Z
or is it the otheray around
I'll but this on my to do later list :)


--Mkouklis 12:06, 16 September 2006 (UTC)

## Notation?

In the entry, it says: "This is in longitude zone 17, and the grid position is 630084m east, 4833438m north." How do you notate.

There isn't really a standard notation, but there are conventions. The easting should be given before the northing. This would likely be most common way to write out that position:
630084 mE 4833438 mN zone 17
However, since the easting is usually given first, and the easting always has one less digit than the northing, that position could be given as: 6300844833438 zone 17. That particular style of notation isn't used very frequently anymore. - Justin 23:12, 25 October 2006 (UTC)
Note that you would also want to include which zone 17 (eg, 17T 630084E 4833438N). Some notations add an initial zero to easting to give it the same number of digits as northing. Also, some GPS receivers I have used switch the order and give Northing/Easting, but the general convention seems to be easting first.Shouriki 00:22, 5 May 2007 (UTC)

## UTM is not a map projection

UTM is not map projection. The Universal Transverse Mercator coordinate system consists of 60 zones, each of which is defined by a unique point of origin, false easting, and Transverse Mercator projection centered over a specific central meridian with a scale factor of 0.9996 The UTM coordinate system (which is the subject of this article) is a system by which locations can be specified on the globe. It uses map projections. It uses 60 specifically defined Transverse Mercator projections (60 out of an infinite number of possible Transverse Mercator projections) but it itself is not a map projection. - Justin 23:50, 27 October 2006 (UTC)

There's a bad link to MTM (Modified Transverse Mercator), which I cannot find anywhere. 70.66.184.59 01:53, 25 January 2007 (UTC)

## Trapezoidal?

Am I to understand that each lettered zone is conceived of as a perfect trapezoid, or are the east and west edges curved?--Homunq 21:41, 26 June 2007 (UTC)

That is like asking whether the equator is curved or straight: it depends on what projection the map is drawn in. In a regular cylindrical projection, like Miller or ordinary Mercator, each grid zone (like 33U) appears as a perfect rectangle. However, suppose a grid zone is drawn in the UTM projection that belongs to its own zone. Then the east and west edge appear slightly curved and convex; the edge that faces the equator usually appears more curved and convex (unless it coincides with the equator: then it appears straight); the edge that faces the nearest pole also appears curved, but concave. For example, the boundary between 33U and 34U is a meridian that appears slightly curved like this ")" when drawn in UTM projection of zone 33, but appears curved the other way, "(", when drawn in UTM projection of zone 34. --Mikael R 17:47, 4 December 2007 (UTC)

## "UTM latitude zone"

I think this is in error. The latitude zones are not part of UTM as defined in DMATM 8358.2. They are part of the Military grid reference system defined in DMATM 8358.1, which is based on UTM. --David Garfield 01:19, 27 July 2007 (UTC)

You are right in theory, I think. In pure UTM notation, one would specify the hemisphere (North or South) instead of the latitude band. But using UTM zone + latitude band letter + UTM coordinates has become a quite common notation: it might be called a de facto standard. Therefore, it is no longer a good idea to use "N" and "S" to stand for north or south hemisphere, since they can be mistaken for latitude band letters. One could write "North" and "South" instead (if everyone knows enough English). Since at least one character is needed to distinguish the North and South hemisphere, why not accept the latitude band letter for this purpose? Some extra redundancy should be a good thing, since some errors might be caught. --Mikael R 17:56, 4 December 2007 (UTC)

UTM does not have a latitude zone! It is made up of the UTM Zone (1-60) N or S for North or South Hemisphere and 6 figures for Eastings with 7 figures for Northings to define a 1 metre square. What is in this wiki report is not the standard for UTM but is just adding to the confusion caused by mixing MGRS with UTM. It is not "a good idea" to add a latitude band it is nonsensical as the correct UTM offers unique locational information. To mix definitions means that computing systems and GIS could lead to ambiguous locations and potential issues Balgonie (talk) 18:22, 19 February 2009 (UTC)

I absolutely agree with Balgonie. While you will see the MGRS grid zone listed with UTM in some commerical GIS (e.g. ArcGIS's Military Analyst extension), the fact remains that, as defined by the United States Geological Survey and the National Geospatial-Intelligence Agency, UTM has no "latitude zone". By including it here in the wikipedia, we are adding to the confusion. Lets get this straight! —Preceding unsigned comment added by 72.196.233.140 (talk) 01:57, 23 March 2009 (UTC)

I absolutely agree with Balgonie. The fact is that UTM does not have latitude zones. National Geospatial-Intelligence Agency (NGA) explain the differences excelently in a document, Military Map Reading 201, on their web site. In Sweden, where i live, it's even more frustrating. The national mapping agency actually has both UTM numbering and MGRS grid designators on the maps, but unambiguously use MGRS and mentions it as UTM oan all their public maps and in almost all of their publications. Johan G (talk) 09:32, 19 June 2009 (UTC)

## Overlap of zones

I tried it allready in the first part of the article, but my english is not god enough to correct this in the article itself, so let me explain here: As I understand it, it is not correct, that...

"Distortion of scale increases in each UTM zone as the boundaries between the longitude zones are approached."

The distortion increases with the *metric* distance to the central meridian, thats why the west to east width of the UTM-Zones is limited to 800 km, btw. exactly 800 km, and that not because of the distortion but due to the concept that all eastings should have *6 digits*. That leads to the smallest valid easting of 100.000, and 900.000 as the biggest for symetry reasons (100 + 400 = 500 (central meridian) + 400 = 900km). The Zones overlap widely.

Btw. because of that, the "Norway-execption" isn't a real (systematic) eception: At these latitudes even the even zones overlap each other, witch means, in the north there are *no* places, than can only be mapped to one UTM-Zone

may be http://upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Utmzylinderrp.jpg/180px-Utmzylinderrp.jpg helps to understand?

87.160.209.176 22:52, 13 October 2007 (UTC) http://de.wikipedia.org/wiki/Benutzer:Mikl

Yes and no! It is almost true that the distortion depends on the metric distance to the central meridian. I say almost, because the latitude has a tiny effect, caused by the Earth being ellipsoid-shaped rather than spherical. However, the UTM *zones*, as the word is normally used, are *not* 800 km wide with overlap; they are 6 degrees wide (except for the Norway exceptions) and do not overlap. But a UTM *projection* can, as Mikl says, sometimes be used outside its own zone. I know of one official reason (that is, allowed by US military practice) and one non-official reason (national needs in non-Norwegian countries).

Officially: As I remember the documentation, official US military use of UTM is to print topographic paper maps in the scale 1:50000. Of course, it would be awkward if such a map had to stop exactly at a zone boundary, so the map is allowed to continue 20 km (or was it 40 km?) into the next zone, and in the overlap, grid lines for both projections may be shown (in different colors). This makes it possible to measure distances on the map across the zone boundary. But when reporting the position of a point on the map, the coordinates must be expressed in the correct projection, namely for the zone that contains the point.

Non-officially: Finland, for example, uses the UTM projection for zone 35 for country-wide mapping, even though Finland is wider than zone 35. Is the resulting coordinate reference system an instance of UTM? No. It must be renamed in some way, to indicate the non-standard width. The coordinate system is therefore called ETRS-TM35FIN, where FIN signals that this is a national modification. If we wrote just ETRS-TM35, it would mean UTM used strictly within zone 35. (The ETRS stands for the common European geodetic datum, which coincides with WGS84 except for about half a meter. I think ETRS-UTM35 would have been a better name, but perhaps you cannot say "Universal" when you use a geodetic datum that only is defined in Europe.) See http://www.kolumbus.fi/eino.uikkanen/geodocsgb/ficoords.htm for more details.

Sweden does the same thing with UTM zone 33. It would have been nice if the resulting coordinate reference system had been called ETRS-TM33SWE, but it is not. It is called SWEREF99 TM (which is not the same as the older Swedish Grid). 28 Oct 2007, http://en.wikipedia.org/wiki/User:Mikael_R —Preceding unsigned comment added by 81.231.148.193 (talk) 21:53, 28 October 2007 (UTC)

Speaking as an idiot, I came to some grief as a consequence of ignorance over map projections and specifically UTM. Popular schoolboy impression of Mercator is a projection of the globe onto a cylinder. It isn't, it's carefully rescaled for conformality. The issue of conformality isn't very visible -0 you can Google UTM and search hard to find out a precise definition, and I thought it would be helpful to highlight that, so that anyone else contemplating coding up UTM would at least refer to e.g. Snyder. Please amend/delete if you disagree. —Preceding unsigned comment added by Monopodia (talkcontribs) 14:49, 28 December 2007 (UTC)Monopodia (talk) 14:58, 28 December 2007 (UTC)Andy Smith

## Conflicting notations (latitude band vs hemisphere) for UTM coordinates

I propose the following changes in nomenclature to eliminate confusion in the UTM entry:

• Longitude Zone -> "UTM Zone" or just plain Zone
• Latitude Zone -> Latitude Band (the terminology from the MGRS documention)
• The combination UTM Zone + Latitude Band -> Grid Zone (again this is MGSR terminology)

I also propose the following clarifications:

• The use of the Latitude Band in UTM is twofold:
• (primarily) in the exceptions in the division of the globe into UTM zones
• as optional way of specifying a UTM coordinate, e.g.,
   17T 630084 4833439


and of course the grid zone is an integral part of the MGRS.

• Document more clearly the use of the hemisphere in place of the latitude band in a UTM coordinate, e.g.,
   17N 630084 4833439


pointing out the possibility of confusion, see the last page:

   http://earth-info.nga.mil/GandG/coordsys/grids/utm_ups.pdf


and emphasizing the need to specify which convention is in use.

I'm planning on making these changes in a few days. Comments? Cffk (talk) 12:21, 24 October 2008 (UTC)

OK. Changes made. Cffk (talk) 15:10, 26 October 2008 (UTC)

Please explicitely show use of all notations!

"UTM zone coordinates" (zone + North/South used)

"UTM grid coodinates" (zone + latitude band)

"UTM reference coordinates" -> MGRS

Article mixes all of it into one mess with wrong images. M. —Preceding unsigned comment added by 193.8.40.119 (talk) 12:14, 3 June 2009 (UTC)

The link in the References section is no longer valid:

http://www1.nga.mil/ProductsServices/GeodesyGeophysics/GPSPreciseEphemeris/Related%20Documents/utm_ups.pdf —Preceding unsigned comment added by Hedgehog0 (talkcontribs) 10:13, 11 March 2009 (UTC)

## Conformal Projection

I believe that the statement under the "history" section that projections from a cylinder are not conformal is misleading. While it is true that standard mercator projections are not conformal, transverse mercator is considered conformal for scales of 1:500K and larger. Suggest removing this comment or changing it to say that "transverse mercator projections are considered confirm (meaning they preverse the shape) for scales of 1:500K and larger". This is especially true in the case of UTM which excludes the polar regions. —Preceding unsigned comment added by 72.196.233.140 (talk) 01:49, 23 March 2009 (UTC)

## confusion in Locating a position using UTM coordinates section

In the section Locating_a_position_using_UTM_coordinates it has links to pages easting and northing and point of origin. In point of origin it states that:

The coordinates of the origin are always all zero, for example (0,0) in two dimensions and (0,0,0) in three.

But in the Locating section it states:

The point of origin of each UTM zone is the intersection of the equator and the zone's central meridian. In order to avoid dealing with negative numbers, the central meridian of each zone is given a "false easting" value of 500,000 meters. Thus, anything west of the central meridian will have an easting less than 500,000 meters. For example, UTM eastings range from 167,000 meters to 833,000 meters at the equator (these ranges narrow towards the poles).

If the central meridian has a "false easting" value of 500,000 then how can it be the point of origin as described on that page?

On the easting and northing page it states that:

When using the Universal Transverse Mercator coordinate system, northing is the distance to the equator, while easting is the distance to the "false easting", which is uniquely defined in each UTM zone.

If this is true, then the value of 500,000 for the central meridian means 500,000 m to the "false easting" which, according to this section, is the central meridian! So the central meridian has a value of 500,000 and that means 500,000 m to the central meridian? Also, the statement When using the Universal Transverse Mercator coordinate system, northing is the distance to the equator doesn't seem to jibe with the Locating section:

In the northern hemisphere, positions are measured northward from the equator, which has an initial "northing" value of 0 meters and a maximum "northing" value of approximately 9,328,000 meters at the 84th parallel — the maximum northern extent of the UTM zones. In the southern hemisphere, northings decrease as you go southward from the equator, which is given a "false northing" of 10,000,000 meters so that no point within the zone has a negative northing value.

A value of 9,400,000 would not be 9,400,000 m to the equator. It would be in the southern hemisphere, 600,000 m from the equator. (as I understand the Locating section)

So the Locating_a_position_using_UTM_coordinates section and the easting and northing and point of origin pages don't seem to be in agreement. I think the point of origin page is probably right and the Locating_a_position_using_UTM_coordinates section is wrong. I think the easting and northing is probably wrong and the Locating_a_position_using_UTM_coordinates section is correct.

But regardless, those pages are supposed to be authoritative on those subjects and this page and section should be in agreement with them.

My Wikipedia (talk) 17:44, 29 September 2010 (UTC)

## Advantages of the UTM System over Other Systems?

Could anyone add a section about the advantages, if any, of the UTM system over other coordinate systems? --Roland 03:46, 17 January 2011 (UTC)

I second that request. I'm trying to reasons why UTM or Section/Township/Range would be desirable, because I can't think of any good ones. Ufwuct (talk) 20:14, 4 April 2012 (UTC)

## Coordinate Transformations

I just don't like the first sentence in the section with the simplified formulas. There are no "exact formula's", all formula's are series expansions. In addition, all the formula's that I have seen are "usable", they are just more complicated. Accuracy is pretty important here and I would recommned that this just be presented as a simplified formula as a point of reference. — Preceding unsigned comment added by Tomcard (talkcontribs) 19:32, 11 November 2011 (UTC)

## Simplified formulas from latitude, longitude (φ, λ) to UTM coordinates (E, N)

Hi, What means sum from j=0 to 2 and product from k=1 to j inside when j = 0 ? It looks a little like division by 0. How to write this formula not using sigma and pi notations ? Previous formulas perhaps were not so accurate (maybe not to mm), but they were very easy to use. These new ones (beginning from 03:24, 15 March 2012) are a little unclear.
Thank you.

$A=\frac{a}{1+n}\sum_{j=0}^{2}\left\{\prod_{k=1}^{j}\left(\frac{3n}{2k}-n\right)\right\}^2$

Darekk2 (talk) 20:18, 21 July 2012 (UTC)

• Is this formula correct at all ? Darekk2 (talk) 12:17, 23 July 2012 (UTC)
• This particular formula is correct. To understand it you have to accept that the product with j=0 is "empty" and the product is then defined to be unity. The horrendous notation is quite off-putting for the expression for A is simply
$A=\frac{a}{1+n}\left( 1+ \frac{n^2}{4} +\frac{n^4}{64} +\cdots \right)$
Why does this editor make things so complicated? Why not just restore the lambda-series? (see below) I have not checked the other formulae but they are basically just a rehash of the original paper by Kruger.
Peter Mercator (talk) 21:51, 24 July 2012 (UTC)
Thank you for your answer. The previous method (before march 2012) was much more transparent. Darekk2 (talk) 22:21, 24 July 2012 (UTC)
I should have said that the constant A is simply the first three terms of a series which sums to the meridian distance from equator to pole.  Peter Mercator (talk) 21:00, 25 July 2012 (UTC)
This is not important at all, but I am just curious. What is wrong here ? I implemented to Access VBA and JavaScript three other methods including previous one from Wikipedia (and one from such military manual and JavaScript from Dutch's website), they work very well, but this new one gives completely nonsensical results. So there is something wrong with transformation of formulas to the code, units or formulas. Darekk2 (talk) 22:01, 25 July 2012 (UTC)

(here was code)

Private Function tanh(x As Double) As Double
'hyperbolic tangent
tanh = (con_e ^ (2 * x) - 1) / (con_e ^ (2 * x) + 1)
End Function

• Double (and triple) check your code for A! Does it reduce to my expression?  Peter Mercator (talk) 22:57, 25 July 2012 (UTC)
• Not at all.
n = 1.6792203863837E-03
nA = a / (1 + n) * ((3 * n / (2 * 1) - n) ^ 2 + ((3 * n / (2 * 1) - n) * (3 * n / (2 * 2) - n)) ^ 2) = 4,48870082555994E-03
and A from your formula for two elements:
nA = a / (1 + n) * (1 + n ^ 2 / 4 + n ^ 4 / 64) = 6367.44914582342
but final results are still nonsensical. Darekk2 (talk) 23:55, 25 July 2012 (UTC)
• Always simplify algebra before coding. Your expression for A omits the leading '1' inside the brackets. If that doesn't work (as you claim) I can't help. Check your code. Have a look at a reliable source. I trust the paper by Karney at [1] and also see [2]. The expressions and notation are slightly different so beware. See if they work! I also suggest that you remove your code from this talk page as it is inappropriate here. Peter Mercator (talk) 09:52, 26 July 2012 (UTC)
• So, could you write correct expression with that leading '1' ? Thank you in advance. And thank you for link to Karney publication with formulas. I have used so far in the past Dutch's JavaScript based on his formulas from his webpage, such military manual (part 1 and part 2, or here) and previous Wikipedia formulas. They all work very well, however previous Wikipedia formulas and military manual lack some simple formulas which can be obtained from Dutch's JavaScript. — Preceding unsigned comment added by Darekk2 (talkcontribs) 12:51, 26 July 2012 (UTC)
• deleted code, because it is really inapropriate here nd only occupies space. Previous versions of this talk are still available ... Darekk2 (talk) 13:09, 29 July 2012 (UTC)
• Here are data and results of sample calculations. Could anyone explain, whrere is beginning of the mistake ?
phi = 43,642567
lambda = -79,387139
lambda0 = -81
f = 298,257223563
n = 1,6792203863837E-03
a = 6378,137
A = 6367,44914582342
alpha1 = 8,37731818819254E-04, alpha2 = 7,60849695869916E-07, alpha3 = 1,20348778759666E-09
beta1 = 8,37732164082144E-04, beta2 = 5,90611086371992E-08, beta3 = 1,67699117943797E-10
delta1 = 3,35655144862887E-03, delta2 = 6,57191319317269E-06, delta3 = 1,76774599620756E-08
t = 0,223340108128025
xi_prim = 4,4009769892643
eta_prim = 36,413486361909
rho = 8,12700371895615E+85
tau = 2,64903350164501E+86
E0 = 500
k0 = 0,9996
N0 = 0
E = 8,62126392920262E+88
N = 2,81013984547736E+89

Strange values begin from rho i tau - maybe cosh and sinh are incorrectly computed ? Perhaps the formulas lack some additional explanations regarding for example units.

Darekk2 (talk) 23:16, 3 August 2013 (UTC)

## More on coordinate transformations

I would like to make a few observations on the previous topics. Interested watchers should read the article on the Transverse Mercator projection: all references quoted are to be found there. The detailed seies are in the article Transverse Mercator: Redfearn series.

1. There is an exact form of the transverse Mercator projection. The analytic formulae, involving incomplete elliptic integrals, were obtained by E.H. Thompson in 1945 but not published until a paper of L.P.Lee in 1976 (ref8). This solution is very interesting because it is a bounded projection--it does not tend to infinity in any direction. See illustration in Transverse Mercator projection.
2. The exact solution provides a yardstick against which approximate series solution may be assessed. Two such approximations were published by Kruger in 1912 (ref6): one is an expansion (the lambda-series) in the longitude measured from the central meridian and the other an expansion (the n-series) in the flattening parameter . The latter is more accurate over a given interval in longitude.
3. The lambda-series is the one chosen for the UTM projections. The details of the full series are given in J.P.Snyder, Working manual, and in the US Defense Mapping Agency (Hager et al) manual (ref14). The formulae given in the Transverse Mercator: Redfearn series are those used by the OSGB: they differ only in sub-millimeter terms.
4. To agree with the "official" UTM maps one must use the same formula in calculating transformations. The n-series should not be used. The fact that the n-series is more accurate is irrelevant.
5. The so-called "simplified formulae" are based on the n-series. This is quite misleading and I suggest that this section be deleted. I personally consider these formulae to be horrendously complicated and not at all transparent. If it is felt necessary to have formulae in this article, as against refs to TM article and the online literature, I would advocate restoring the previous formulae based on truncated lambda-series (but with refs to actual series used). I have meant to do this for some time but perhaps someone else can have a go.
6. Finally, I suspect that the simplified series introduced by user 官翁 (talk | contribs)‎ were in fact put in place by the same Kawase he references. This is a case of a user introducing his own original research on a wiki page. The same has been done in Meridian arc.

## More on simplified series

I have again unpacked the horrendous expression given for A_0. The truncated series is entirely in keeping with the truncated expressions for the other term. Please remember that this is a geodesy page: it is not a mathematics article. The concept of the product over the empty set will be unknown to most readers who arrive here: it has clearly confused at least two readers already. The generalisation to an arbitrary term is irrelevant here. Once again may I suggest that this material goes to the page Transverse Mercator: flattening series. Comments from third parties please.  Peter Mercator (talk) 09:07, 10 September 2012 (UTC)

Amen. I do not understand the rationale for providing an infinite series for one element when the rest consists of truncations. Strebe (talk) 04:16, 11 September 2012 (UTC)

## World Polyconic Grid

Many old military etc maps were published using the World Polyconic Grid (WPG), which preceded UTM. Please add info about this to the article and WP. Are there any online tools for converting from WPG? -96.237.4.73 (talk) 20:55, 9 January 2013 (UTC)

According to it's docs (not tried) GeoTools has support for world polyconic. GeoTools is a component in Geoserver and uDig, so that means they do too. I don't think QGIS uses GeoTools, so no information on if it does polyconic. Try using a proj4 file to force it to. — Preceding unsigned comment added by 81.133.50.94 (talk) 12:05, 29 January 2014 (UTC)