What is the overlap between different UTM zones?

[JohnBrown1]

Hello,

I know my question does not have an exact answer (it will depend on the region of the globe we're talking about), but I wanted to know what's the overlap between two UTM zones? Centimeters, meters, hundreds of meters? The same question applies for different latitude bands.

I'll localize a robot in region close to the intersection of two zones and two bands (therefore I might be in 4 different zones) and would rather force the Lat/Long-to-UTM conversion to always use the same zone. I know the further I get from the meridian the less precise it will be, but what's an acceptable distance I could cross from a zone and still force it to project it into another zone? Again, I just need want to know an order of magnitude. If I get some 100 kilometers out from one zone into another, what's the magnitude of the error I should expect?

If anyone has any references on where I could go about calculating all these more precisely, I'd appreciate.

[JoeBorgione]

Hello,

I know my question does not have an exact answer (it will depend on the region of the globe we're talking about), but I wanted to know what's the overlap between two UTM zones? Centimeters, meters, hundreds of meters? The same question applies for different latitude bands.

I'll localize a robot in region close to the intersection of two zones and two bands (therefore I might be in 4 different zones) and would rather force the Lat/Long-to-UTM conversion to always use the same zone. I know the further I get from the meridian the less precise it will be, but what's an acceptable distance I could cross from a zone and still force it to project it into another zone? Again, I just need want to know an order of magnitude. If I get some 100 kilometers out from one zone into another, what's the magnitude of the error I should expect?

If anyone has any references on where I could go about calculating all these more precisely, I'd appreciate.

To my knowledge, utm zones don't overlap each other.  Take a look at Melita Kennedy's classic publication Understanding Map Projections.  Go to page 105 for a description; no mention of overlaps there. In the glossary, it lists:

UTM
Universal Transverse Mercator.  A projected coordinate
system that divides the world into 60 north and south
zones, six degrees wide.

Not sure I've answered your question, but hope this helps none the less

[HardolphWasteneys]

John,

I think I see what you've driving at:  As Joe said UTM zones do not overlap by definition, but that does not mean that you cannot project features existing in one zone using an adjacent one.  The issue is not immediate locational error, but progressive shift, map distortion and therefore area and length.  Depending on how far north you are you can probably use an adjacent UTM zone as the projection say half way across a few hundred km  ... or anywhere say 3 degrees of longitude before things start to get noticeably out of shape and if projected out of alignment by say a meter at mid latitudes. 

That is why there are other projections like Albers to preserve area across several zones.  But project to excess across a few zones and you will see shifts and severe area distortion like these shots of Lake Superior in a screen projection of UTM Zone 15N (with a background map in NAD84 Web Mercator Auxialiary Sphere).  The progessive  offset was the result of projecting a shapefile from zone 15N into 14, 13, 12, 11, 10 and 9 shown overlapping to the west with the zone 9 on top.   In 14 there is only about a meter of offset but the area is also significantly changed in the shapefile.   Progressive westward errors in meters from the zone 15N projection; UTM14N = 1m, UTM13N = 25m, UTM 12N = 314m, UTM 11N = 2500m, UTM10N = 18000m, UTM9N= 102,000m.  Areas are displayed as square meters in a jumble with the minimum being the zone 15N projection and the max 9N.  The larger red number is the area in a continental Albers projection.

So based on that you have to decide what precision you can tolerate whether you are using a UTM projection or Albers.

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Hardolph

[JoeBorgione]

Hardolph makes a great point, and I wondered if that's what John meant.

I live and work in Utah and the western boundary of Utah/eastern Nevada is 5 minutes west of the UTM zone line.  For that much (or little) the typical practice is to call the entire State in the same zone and project as such.  As you might imagine there really isn't a whole lot going out there so any compromises in spatial data integrity are generally accepted.

[JohnBrown1]

John,

I think I see what you've driving at:  As Joe said UTM zones do not overlap by definition, but that does not mean that you cannot project features existing in one zone using an adjacent one.  The issue is not immediate locational error, but progressive shift, map distortion and therefore area and length.  Depending on how far north you are you can probably use an adjacent UTM zone as the projection say half way across a few hundred km  ... or anywhere say 3 degrees of longitude before things start to get noticeably out of shape and if projected out of alignment by say a meter at mid latitudes. 

That is why there are other projections like Albers to preserve area across several zones.  But project to excess across a few zones and you will see shifts and severe area distortion like these shots of Lake Superior in a screen projection of UTM Zone 15N (with a background map in NAD84 Web Mercator Auxialiary Sphere).  The progessive  offset was the result of projecting a shapefile from zone 15N into 14, 13, 12, 11, 10 and 9 shown overlapping to the west with the zone 9 on top.   In 14 there is only about a meter of offset but the area is also significantly changed in the shapefile.   Progressive westward errors in meters from the zone 15N projection; UTM14N = 1m, UTM13N = 25m, UTM 12N = 314m, UTM 11N = 2500m, UTM10N = 18000m, UTM9N= 102,000m.  Areas are displayed as square meters in a jumble with the minimum being the zone 15N projection and the max 9N.  The larger red number is the area in a continental Albers projection.

So based on that you have to decide what precision you can tolerate whether you are using a UTM projection or Albers.

[ATTACH=CONFIG]15195[/ATTACH]


Hardolph

Hardolph  and Joe,

Thanks for your answers. Indeed, UTM zones do not overlap, but as Hardolph pointed out, I could still project on a different zone. I really appreciate Hardolph's example, it helped me understand UTM more clearly. However, I will be navigating a robot, so precision is quite important to me and a 1m offset is way more than I can tolerate. On your example, I understand Lake Superior is on zone 15N and was projected into 14N (and others), right? How far was the Lake from zone 14N's border?

One more thing, just to see if I got it right: the close I am to the Equator, the larger my offset will be?

[JoeBorgione]

google utm zones; you'll find cool links like

this one

and this one

etc...

[HardolphWasteneys]

John, 

Actually most of Lake Superior is in zone 16:  the 1 meter offset would have implied more than the full 6 degree width of the UTM zone at that latitude since most of Lake Superior is actually in UTM zone 16N with west boundary at 90 W.   The east edge of Lake Superior that I used as an example is at 84.5degW and the east side of UTM zone 14 is at 90, almost 850 km away.  Right next to the zone boundary there would be zero offset and it would ramp up in a slightly non-linear relation to the other side.

Upon remeasure with a zone 16N projection of the Lake against a zone 15N projection at the eastern side of Lake Superior, which is a good 430 km from the east side of zone 15N and almost to the east side of zone 16N,  I get an error of only 10 cm in the projection.   So if you are operating up to 100 km into an adjacent UTM zone at mid lat, I would expect less than 2 cm error max.  At the equator you could probably go 150 km with that error.

thanks for prompting the question John, I would not have thought of measuring this otherwise.

Hardolph


one little afterthought; if you really go too far with misprojections like a zone 16 feature projected to zone 8 they will get chopped by the algorithms which only support 90 degrees of UTM projection display and you can visualize orthogonals to a flat tangential projection plane laid flat on the real zone start to have really low incident angles and in the limit are tangents to the earth themselves.    H