<div> <br>
</div>
<div> <font face="Arial, Helvetica, sans-serif">Not so. The Mercator is conformal. The scale factor is the same in all directions at any particular point. For any cylindric projection other than Mercator, you use the same formula with the caveat noted by Mr. McNierney. But on Mercator the scale factor applies in all directions.<br>
<br>
Regards,<br>
-- daan Strebe<br>
<br>
</font></div>
<div> <br>
</div>
-----Original Message-----<br>
From: Ed McNierney <ed@mcnierney.com><br>
To: PROJ.4 and general Projections Discussions <proj@lists.maptools.org><br>
Sent: Wed, 9 Jul 2008 1:45 pm<br>
Subject: Re: [Proj] Re: Distance measured in Mercator projection<br>
<br>
<div id="AOLMsgPart_3_a9749dbe-6ad2-4e34-b1ef-495fa0f2a971">
<font face="Calibri, Verdana, Helvetica, Arial"><span style="font-size: 11pt;">Shannon -<br>
<br>
Your question implies you are only interested in measuring east/west distances, and Daan’s answer is helpful for that purpose. But that answer ONLY applies to measuring a line that runs due east/west. A line running north/south, of the same length on the Earth as the east/west one, would be a different length on a Mercator projection. If you wish to measure an arbitrary line on a Mercator projection you need to also take into account the angle of that line to the Equator (as well as the latitude, and whether you’re assuming a spherical Earth).<br>
<br>
This is one of the many reasons Mercator projections are most useful to 17th-century mariners.<br>
< br>
- Ed<br>
<br>
Ed McNierney<br>
205 Indian Hill Road<br>
Groton, MA 01450<br>
<a>ed@mcnierney.com</a><br>
+1 (978) 761-0049<br>
<br>
<br>
<br>
On 7/9/08 4:21 PM, "<a>strebe@aol.com</a>" <<a>strebe@aol.com</a>> wrote:<br>
<br>
</span></font><blockquote><font face="Calibri, Verdana, Helvetica, Arial"><span style="font-size: 11pt;"> <br>
If you assume a spherical earth, the length of a meter </span></font><span style="font-size: 11pt;"><font face="Arial">on the Mercator equatorial aspect</font><font face="Calibri, Verdana, Helvetica, Arial"> is<br>
<br>
</font><font face="Arial">1m / cos (phi)<br>
</font><font face="Calibri, Verdana, Helvetica, Arial"> <br>
</font><font face="Arial">where phi is the latitude and "cos" is the cosine function. Be careful to set the calculator to degrees or else to convert the latitude to radians. The calculation is more complicated on an ellipsoidal earth.<br>
<br>
Regards,<br>
-- daan Strebe<br>
<br>
</font><font face="Calibri, Verdana, Helvetica, Arial"> <br>
-----Original Message-----<br>
From: Shannon Scott <<a>sscott@locationinc.com</a>><br>
To: <a>Proj@lists.maptools.org</a><br>
Sent: Wed, 9 Jul 2008 10:52 am<br>
Subject: [Proj] Distance measured in Mercator projection<br>
<br>
</font></span><font size="1"><font face="Tahoma, Verdana, Helvetica, Arial"><span style="font-size: 9pt;">Hello, <br>
Please forgive my ignorance, I know very little about map projections. I apologize if this list is not the appropriate place to post this question. <br>
If I
understand correctly, in the Mercator projection, 1 unit of space is equal to 1 meter at the equator. <br>
As you move away from the equator, the longitudinal lines are stretched to make the lat and long intersect at 90 degree angles. <br>
How would I calculate the length in meters of 1 unit of space in the Mercator projection at a specific latitude? <br>
Any advice of pointers are appreciated. <br>
Thank you. <br>
Shannon <br>
<br>
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