EPSG:9805

Mercator (variant B)

Attributes

Data source: OGP

Information source: EPSG guidance note #7-2, http://www.epsg.org

Revision date: 2019-05-03

Remarks: Used for most nautical charts.

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Definition: OGP XML

<div class="syntax"><pre><span class="cp">&lt;?xml version=&quot;1.0&quot; encoding=&quot;UTF-8&quot;?&gt;</span> <span class="nt">&lt;gml:OperationMethod</span> <span class="na">xmlns:epsg=</span><span class="s">&quot;urn:x-ogp:spec:schema-xsd:EPSG:1.0:dataset&quot;</span> <span class="na">xmlns:gml=</span><span class="s">&quot;http://www.opengis.net/gml/3.2&quot;</span> <span class="na">xmlns:xlink=</span><span class="s">&quot;http://www.w3.org/1999/xlink&quot;</span> <span class="na">gml:id=</span><span class="s">&quot;iogp-method-9805&quot;</span><span class="nt">&gt;</span> <span class="nt">&lt;gml:metaDataProperty&gt;</span> <span class="nt">&lt;epsg:CommonMetaData&gt;</span> <span class="nt">&lt;epsg:alias</span> <span class="na">alias=</span><span class="s">&quot;Mercator (2SP)&quot;</span> <span class="na">code=</span><span class="s">&quot;14882&quot;</span> <span class="na">codeSpace=</span><span class="s">&quot;urn:ogc:def:naming-system:EPSG::7301&quot;</span><span class="nt">&gt;</span> <span class="nt">&lt;epsg:remarks&gt;</span>This was the method name used prior to October 2010. However it is ambiguous as it is also applicable to variant C (method code 1044).<span class="nt">&lt;/epsg:remarks&gt;</span> <span class="nt">&lt;/epsg:alias&gt;</span> <span class="nt">&lt;epsg:informationSource&gt;</span>EPSG guidance note #7-2, http://www.epsg.org<span class="nt">&lt;/epsg:informationSource&gt;</span> <span class="nt">&lt;epsg:revisionDate&gt;</span>2019-05-03<span class="nt">&lt;/epsg:revisionDate&gt;</span> <span class="nt">&lt;epsg:changes&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2004.320&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2004.430&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2010.058&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2010.098&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2015.021&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:changeID</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:change-request:EPSG::2019.018&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;/epsg:changes&gt;</span> <span class="nt">&lt;epsg:show&gt;</span>true<span class="nt">&lt;/epsg:show&gt;</span> <span class="nt">&lt;epsg:isDeprecated&gt;</span>false<span class="nt">&lt;/epsg:isDeprecated&gt;</span> <span class="nt">&lt;/epsg:CommonMetaData&gt;</span> <span class="nt">&lt;/gml:metaDataProperty&gt;</span> <span class="nt">&lt;gml:metaDataProperty&gt;</span> <span class="nt">&lt;epsg:CoordinateOperationMethodMetaData&gt;</span> <span class="nt">&lt;epsg:isOperationReversible&gt;</span>true<span class="nt">&lt;/epsg:isOperationReversible&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8823&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8802&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8806&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:signReversal</span> <span class="na">changeSign=</span><span class="s">&quot;false&quot;</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8807&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;epsg:example&gt;</span>For Projected Coordinate System Pulkovo 1942 / Caspian Sea Mercator Parameters: Ellipsoid Krassowski 1940 a = 6378245.00m 1/f = 298.300 then e = 0.08181333 and e^2 = 0.00669342 Latitude of first SP = 42°00&#39;00&quot;N = 0.73303829 rad Longitude of natural origin = 51°00&#39;00&quot;E = 0.89011792 rad False Eastings FE = 0.00 m False Northings (at equator) FN = 0.00 m Forward calculation for: Latitude = 53°00&#39;00.00&quot;N = 0.9250245 rad Longitude = 53°00&#39;00.00&quot;E = 0.9250245 rad gives ko = 0.744260894 Easting E = 165704.29 m Northing N = 5171848.07 m Reverse calculation for same easting and northing first gives : t = 0.336391288 chi = 0.921795958 Latitude = 53°00&#39;00.000&quot;N Longitude = 53°00&#39;00.000&quot;E<span class="nt">&lt;/epsg:example&gt;</span> <span class="nt">&lt;/epsg:CoordinateOperationMethodMetaData&gt;</span> <span class="nt">&lt;/gml:metaDataProperty&gt;</span> <span class="nt">&lt;gml:identifier</span> <span class="na">codeSpace=</span><span class="s">&quot;IOGP&quot;</span><span class="nt">&gt;</span>urn:ogc:def:method:EPSG::9805<span class="nt">&lt;/gml:identifier&gt;</span> <span class="nt">&lt;gml:name&gt;</span>Mercator (variant B)<span class="nt">&lt;/gml:name&gt;</span> <span class="nt">&lt;gml:remarks&gt;</span>Used for most nautical charts.<span class="nt">&lt;/gml:remarks&gt;</span> <span class="nt">&lt;gml:formula&gt;</span>Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided. The formulas to derive projected Easting and Northing coordinates are: ko = cos(latSP1)/(1 - e^2*sin^2(latSP1))^0.5 where latSP1 is the absolute value of the first standard parallel (i.e. positive). E = FE + a*ko(lon - lonO) N = FN + a*ko* ln{tan(pi/4 + lat/2)[(1 - esin(lat))/(1 + esin(lat))]^e/2} where logarithms are natural. The reverse formulas to derive latitude and longitude from E and N values are: lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi) + (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi) + (7e^6/120 + 81e^8/1120) sin(6chi) + (4279e^8/161280) sin(8chi) where chi = pi/2 - 2 arctan t t = B^((FN-N)/(a*ko)) B = base of the natural logarithm, 2.7182818... and ko is calculated as for the forward transformation above. lon = ((E - FE)/(a*ko)) + lonO<span class="nt">&lt;/gml:formula&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8823&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8802&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8806&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;gml:generalOperationParameter</span> <span class="na">xlink:href=</span><span class="s">&quot;urn:ogc:def:parameter:EPSG::8807&quot;</span> <span class="nt">/&gt;</span> <span class="nt">&lt;/gml:OperationMethod&gt;</span> </pre></div>
<?xml version="1.0" encoding="UTF-8"?>
 <gml:OperationMethod xmlns:epsg="urn:x-ogp:spec:schema-xsd:EPSG:1.0:dataset" xmlns:gml="http://www.opengis.net/gml/3.2" xmlns:xlink="http://www.w3.org/1999/xlink" gml:id="iogp-method-9805">
  <gml:metaDataProperty>
    <epsg:CommonMetaData>
      <epsg:alias alias="Mercator (2SP)" code="14882" codeSpace="urn:ogc:def:naming-system:EPSG::7301">
        <epsg:remarks>This was the method name used prior to October 2010. However it is ambiguous as it is also applicable to variant C (method code 1044).</epsg:remarks>
      </epsg:alias>
      <epsg:informationSource>EPSG guidance note #7-2, http://www.epsg.org</epsg:informationSource>
      <epsg:revisionDate>2019-05-03</epsg:revisionDate>
      <epsg:changes>
        <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2004.320" />
        <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2004.430" />
        <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2010.058" />
        <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2010.098" />
        <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2015.021" />
        <epsg:changeID xlink:href="urn:ogc:def:change-request:EPSG::2019.018" />
      </epsg:changes>
      <epsg:show>true</epsg:show>
      <epsg:isDeprecated>false</epsg:isDeprecated>
    </epsg:CommonMetaData>
  </gml:metaDataProperty>
  <gml:metaDataProperty>
    <epsg:CoordinateOperationMethodMetaData>
      <epsg:isOperationReversible>true</epsg:isOperationReversible>
      <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8823" />
      <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8802" />
      <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8806" />
      <epsg:signReversal changeSign="false" xlink:href="urn:ogc:def:parameter:EPSG::8807" />
      <epsg:example>For Projected Coordinate System Pulkovo 1942 / Caspian Sea Mercator

Parameters:
Ellipsoid  Krassowski 1940   a = 6378245.00m   1/f = 298.300
then e = 0.08181333 and e^2 = 0.00669342

Latitude of first SP = 42°00'00"N = 0.73303829 rad
Longitude of natural origin = 51°00'00"E = 0.89011792 rad
False Eastings FE = 0.00 m
False Northings (at equator) FN = 0.00 m
Forward calculation for: 
Latitude = 53°00'00.00"N = 0.9250245 rad
Longitude = 53°00'00.00"E  = 0.9250245 rad

gives 
  
ko = 0.744260894
Easting E = 165704.29 m 
Northing N = 5171848.07 m

Reverse calculation for same easting and northing first gives :
t = 0.336391288
chi = 0.921795958
Latitude = 53°00'00.000"N
Longitude = 53°00'00.000"E</epsg:example>
    </epsg:CoordinateOperationMethodMetaData>
  </gml:metaDataProperty>
  <gml:identifier codeSpace="IOGP">urn:ogc:def:method:EPSG::9805</gml:identifier>
  <gml:name>Mercator (variant B)</gml:name>
  <gml:remarks>Used for most nautical charts.</gml:remarks>
  <gml:formula>Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

The formulas to derive projected Easting and Northing coordinates are:

ko = cos(latSP1)/(1 - e^2*sin^2(latSP1))^0.5 
where latSP1 is the absolute value of the first standard parallel (i.e. positive).

E = FE + a*ko(lon - lonO)              
N = FN + a*ko* ln{tan(pi/4 + lat/2)[(1 - esin(lat))/(1 + esin(lat))]^e/2} where logarithms are natural.

The reverse formulas to derive latitude and longitude from E and N values are:

lat = chi + (esq/2 + 5e^4/24 + e^6/12 + 13e^8/360) sin(2chi) 
+ (7e^4/48 + 29e^6/240 + 811e^8/11520) sin(4chi)
+ (7e^6/120 +  81e^8/1120) sin(6chi)  + (4279e^8/161280) sin(8chi)

where chi = pi/2 - 2 arctan t
t = B^((FN-N)/(a*ko)) 
B = base of the natural logarithm, 2.7182818...
and ko is calculated as for the forward transformation above.
lon  =  ((E - FE)/(a*ko)) + lonO</gml:formula>
  <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8823" />
  <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8802" />
  <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8806" />
  <gml:generalOperationParameter xlink:href="urn:ogc:def:parameter:EPSG::8807" />
</gml:OperationMethod>