# [Proj] Convergence

Kees Krikke kees.krikke at orange.nl
Mon Sep 15 13:42:03 EDT 2008

```Noel,

No i'm not in the south. The line with zone= and south appears because i
use the -v flag.

I always use the -v option with proj. It gives some additional
information about parameters that can be used with a projection (like
zone and south for utm) and a complete list of parameters that are
actually used. This allows you to see all the parameters including those
not set by directly by the user.

Regards,

Kees

Noel Zinn wrote:
> Pardon my proj4 syntax density, but are you in the south with TM and the
> north with LCC?  If so, that's the reason.  -Noel
>
> -----Original Message-----
> From: proj-bounces at lists.maptools.org
> [mailto:proj-bounces at lists.maptools.org] On Behalf Of Kees Krikke
> Sent: Monday, September 15, 2008 10:28 AM
> To: PROJ.4 and general Projections Discussions
> Subject: [Proj] Convergence
>
> Hello,
>
>
> I've made a piece of s/w that uses proj's convergence calculation to
> find the true north for a given grid north.
>
> When testing with a utm and lcc projection i found some confusing
> results regarding the sign (direction) of the convergence.
>
> To demonstrate this i modified proj.exe so it prints the convergence (in
> deg) at the end of the line when using the -S flag:
>
>
> C:\proj-4.6.1\src>proj -vS +proj=utm +datum=WGS84 +lon_0=3
> #Universal Transverse Mercator (UTM)
> #       Cyl, Sph
> #       zone= south
> # +proj=utm +datum=WGS84 +lon_0=3 +ellps=WGS84 +towgs84=0,0,0
> 2 52
> 431350.30       5761510.32      <0.999658 0.999658 0.999316 1.20783e-006
> 0.999658 0.999658 -0.788041>
> 4 52
> 568649.70       5761510.32      <0.999658 0.999658 0.999316 8.54066e-007
> 0.999658 0.999658 0.788041>
> 4 52.1
> 568496.62       5772632.28      <0.999658 0.999658 0.999315 0 0.999658
> 0.999658 0.789115>
>
>  From the above results it seems that for utm the convergence is
> negative when west and positive when east of lon_0.
> If you calculate two utm positions along the same longitude east of
> lon_0, you see that the easting reduces when going northwards.
>
>  From this is seems that TrueNorth = GridNorth + convergence
>
>
> I used the same points for a lcc projection:
>
> C:\proj-4.6.1\src>proj -vS +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3
> +lat_1=50 +lat_2=54
> #Lambert Conformal Conic
> #       Conic, Sph&Ell
> #       lat_1= and lat_2= or lat_0
> # +proj=lcc +datum=WGS84 +lat_0=52 +lon_0=3 +lat_1=50 +lat_2=54 +ellps=WGS84
> # +towgs84=0,0,0
> 2 52
> -68634.11       472.08  <0.999392 0.999392 0.998785 0.000355057 0.999395
> 0.999389 0.788173>
> 4 52
> 68634.11        472.08  <0.999392 0.999392 0.998785 0.000355708 0.999395
> 0.999389 -0.788173>
> 4 52.1
> 68481.15        11591.10        <0.999393 0.999393 0.998787 0.000434814
> 0.999397 0.99939 -0.788173>
>
>
> The convergence sign west and east of the origin are opposite of the
> signs found with the utm. But what confuses me is that when i calculate
> two positions along a longitude east of the origin, the easting reduces
> when going northwards just like with the utm projection.
>
>  From this is seems that TrueNorth = GridNorth - convergence
>
>
> I think that either the convergence for lcc or utm has the wrong sign.
> But i can't tell which one because i don't know how convergence is defined.
>
>
>
> Regards,
>
> Kees Krikke
>
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>

```