{"id":463,"date":"2024-06-06T21:38:39","date_gmt":"2024-06-06T20:38:39","guid":{"rendered":"https:\/\/sailorvikas.com\/?p=463"},"modified":"2024-06-12T18:28:49","modified_gmt":"2024-06-12T17:28:49","slug":"mercator-sailing-calculations","status":"publish","type":"post","link":"https:\/\/sailorvikas.com\/index.php\/2024\/06\/06\/mercator-sailing-calculations\/","title":{"rendered":"Mercator sailing calculations"},"content":{"rendered":"\n<p class=\"has-white-color has-black-background-color has-text-color has-background has-link-color has-medium-font-size wp-elements-58e7692bdce8e583865e1063121ed85e\"><strong>Mercator charts have been described in the module for chart projections. Here, we will shortly discuss some principles involved in the construction of the mercator chart and then learn the calculations involving mercator sailing.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"992\" height=\"563\" src=\"https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015740.png\" alt=\"\" class=\"wp-image-466\" srcset=\"https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015740.png 992w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015740-300x170.png 300w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015740-768x436.png 768w\" sizes=\"(max-width: 992px) 100vw, 992px\" \/><\/figure>\n\n\n\n<p class=\"has-white-color has-black-background-color has-text-color has-background has-link-color has-medium-font-size wp-elements-a8f4b6f6f35e18f83e14c9bbc19d78d3\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-amber-color\">Some Principles involved in calculation of Mercator chart:<\/mark><\/strong><\/p>\n\n\n\n<ul class=\"has-black-background-color has-background wp-block-list\">\n<li class=\"has-medium-font-size\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\"> <strong>Mercator chart is based on \u201cCylindrical Orthomorphic Projection\u201d. <\/strong><\/mark><\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-amber-color\">Latitudes appear as parallel horizontal straight lines to the equator. In actuality, we know that the longitudes coverage at the poles. Hence, the distance between the longitudes is maximum at the equator and reduces as latitude increases towards the poles. <\/mark><\/strong><\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">In the mercator chart, meridians are represented by equidistant parallel straight lines. Therefore the east-west distortion on chart increases as the latitude increases. <\/mark><\/strong><\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-amber-color\">To maintain the orthomorphic property of the chart, it is therefore necessary to deliberately introduce an equal north-south distortion, which is just like the east-west distortion and should increase towards the pole. <\/mark><\/strong><\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">Due to the reason mentioned above, the distance between successive parallels of latitude on Mercator chart will increase towards the pole.<\/mark> <\/strong><\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-amber-color\">As the nautical mile is defined as the length of the meridian between two geographic latitudes which differ by 1\u2019 (i.e. 1\u2019 of d\u2019lat) \u2013 on the mercator chart, the length of a nautical mile on increases pole ward \u2013 as nautical miles are measured on the latitude scale. <\/mark><\/strong><\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-white-color\">As seen earlier, on a Mercator chart, since the length of the meridian between two parallel of latitude increases towards the pole a concept of Meridional part has been introduced.<\/mark><\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"827\" height=\"523\" src=\"https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015657-1.png\" alt=\"\" class=\"wp-image-467\" srcset=\"https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015657-1.png 827w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015657-1-300x190.png 300w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015657-1-768x486.png 768w\" sizes=\"(max-width: 827px) 100vw, 827px\" \/><\/figure>\n\n\n\n<p class=\"has-white-color has-black-background-color has-text-color has-background has-link-color has-medium-font-size wp-elements-78482160dba395c275ac41d377342765\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-amber-color\">Definition of a \u201cMeridional Part\u201d<\/mark><br>The \u201cMeridional parts\u201d for any latitude is the length of the meridian between the equator and that latitude on a mercator chart measured in units of longitude scale, i.e. the number of times one minute of longitude can be laid along a meridian between the equator and that latitude, on a Mercator chart. This value is tabulated in the nautical tables, assuming the earth to be a spheroid in shape<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"342\" src=\"https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015717-1024x342.png\" alt=\"\" class=\"wp-image-465\" srcset=\"https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015717-1024x342.png 1024w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015717-300x100.png 300w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015717-768x257.png 768w, https:\/\/sailorvikas.com\/wp-content\/uploads\/2024\/06\/Screenshot-2024-06-07-015717.png 1217w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-white-color has-black-background-color has-text-color has-background has-link-color has-medium-font-size wp-elements-fad9401c7bbee02df8c91debf4731078\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-amber-color\">Calculations<\/mark> &#8211;<br>Look at the figure which shows a Mercator chart. Mercator sailing is recommended to be<br>used when the distance between two positions exceeds 600 nautical miles, in order to get more accurate results than by plane and parallel sailing methods. Mercator sailing method is used to find the rhumb line course and distance between two positions, the latitudes<br>and longitudes of which are known. Refer to the Figure above The Rhumb line course is laid from A to B AB is the distance from A to B Angle OAB is the course AO is the D\u2019lat<br>and OB is the D\u2019long<br>Formulas used:<br>D\u2019long \/ DMP = tan course<br>Distance = D\u2019lat x sec course.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mercator charts have been described in the module for chart projections. Here, we will shortly discuss some principles involved in the construction of the mercator chart and then learn the calculations involving mercator sailing. Some Principles involved in calculation of Mercator chart: Definition of a \u201cMeridional Part\u201dThe \u201cMeridional parts\u201d for any latitude is the length 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