# [Proj] RE: Distance measured in Mercator projection

strebe strebe at aol.com
Wed Jul 16 16:09:33 EDT 2008

```(laugh!) Apologies for getting distracted. I meant to look it up but then forgot I hadn't. Thanks, Cliff.

Regards,
-- daan Strebe

On Jul 16, 2008, at 11:44:02 AM, "Clifford J Mugnier" <cjmce at lsu.edu> wrote:
From:   "Clifford J Mugnier" <cjmce at lsu.edu>
Subject:    RE: [Proj] Re: Distance measured in Mercator projection
Date:   July 16, 2008 11:44:02 AM PDT
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
I'd suggest something other than zero for the eccentricity of the WGS84 ellipsoid.  Say, e squared being 0.00669437999013, more or less ...

Cliff Mugnier
LOUISIANA STATE UNIVERSITY

From: proj-bounces at lists.maptools.org on behalf of strebe
Sent: Wed 16-Jul-08 13:39
To: PROJ.4 and general Projections Discussions
Subject: [Proj] Re: Distance measured in Mercator projection

Shannon,

The scale factor in any direction at a given point on the ellipsoidal equatorial Mercator is:

h = √(1 - e^2 x sin^2 (phi)) / cos (phi)

where √ is the square root of the expression; e is the eccentricity of the ellipsoid (0.0 for WGS84); ^2 means the square of the expression; and other symbols and semantics as given before.

Therefore you would multiply 1m x h to find the map distance of one meter at full scale. As you can see, this is the same as the original expression but just multiplied by the factor that adjusts for the eccentricity.

Don't hesitate to ask for clarification if you need it. Good luck.

Regards,
-- daan Strebe

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