{"id":28,"date":"2025-06-28T04:08:45","date_gmt":"2025-06-28T03:08:45","guid":{"rendered":"https:\/\/nottagemews.uk\/utilities\/?page_id=28"},"modified":"2025-10-11T13:55:05","modified_gmt":"2025-10-11T12:55:05","slug":"course-distance","status":"publish","type":"page","link":"https:\/\/nottagemews.uk\/utilities\/course-distance\/","title":{"rendered":"Course &amp; Distance"},"content":{"rendered":"\n\t<section class=\"section\" id=\"section_1590195801\">\n\t\t<div class=\"bg section-bg fill bg-fill  bg-loaded\" >\n\n\t\t\t\n\t\t\t\n\t\t\t\n\n\t\t<\/div>\n\n\t\t\n\n\t\t<div class=\"section-content relative\">\n\t\t\t\n\n<div class=\"row\"  id=\"row-361100939\">\n\n\n\t<div id=\"col-384522711\" class=\"col medium-4 small-12 large-4\"  >\n\t\t\t\t<div class=\"col-inner\"  >\n\t\t\t\n\t\t\t\n\n\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\n\t\n\n\t<div id=\"col-575629239\" class=\"col medium-4 small-12 large-4\"  >\n\t\t\t\t<div class=\"col-inner\"  >\n\t\t\t\n\t\t\t\n\n\n\n<input type=\"text\" id=\"nameInput\" placeholder=\"Your name here\">\n\n\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\n\t\n\n\t<div id=\"col-2003340956\" class=\"col medium-4 small-12 large-4\"  >\n\t\t\t\t<div class=\"col-inner\"  >\n\t\t\t\n\t\t\t\n\n\n\n<button id=\"submitBtn\">Submit<\/button>\n\n<a class=\"button primary is-shade box-shadow-3 box-shadow-5-hover lowercase submitButton\"  style=\"border-radius:5px;\">\n  <i class=\"icon-user\" aria-hidden=\"true\" ><\/i>  <span>Submit 2<\/span>\n  <\/a>\n\n\n\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\n\t\n\n<\/div>\n\n\t\t<\/div>\n\n\t\t\n<style>\n#section_1590195801 {\n  padding-top: 30px;\n  padding-bottom: 30px;\n}\n<\/style>\n\t<\/section>\n\t\n\t<section class=\"section\" id=\"section_2120981567\">\n\t\t<div class=\"bg section-bg fill bg-fill  bg-loaded\" >\n\n\t\t\t\n\t\t\t\n\t\t\t\n\n\t\t<\/div>\n\n\t\t\n\n\t\t<div class=\"section-content relative\">\n\t\t\t\n\n<div class=\"row\"  id=\"row-1140258163\">\n\n\n\t<div id=\"col-1971077417\" class=\"col small-12 large-12\"  >\n\t\t\t\t<div class=\"col-inner\"  >\n\t\t\t\n\t\t\t\n\n<h2>Definitions<\/h2>\n<h3>Nautical Mile<\/h3>\n<p data-start=\"206\" data-end=\"244\">A <strong data-start=\"208\" data-end=\"225\">nautical mile<\/strong> (NM) is <strong data-start=\"229\" data-end=\"240\">defined<\/strong> as <strong data-start=\"248\" data-end=\"264\">1,852 metres.<\/strong><\/p>\n<p data-start=\"206\" data-end=\"244\">The earth is an oblate spheroid (it is flattened at the poles) and 1 minute of latitude varies from 1,843m at the equator to 1,861 at the poles. The average distance is 1,852 &#8211; the nautical mile.<\/p>\n<p data-start=\"206\" data-end=\"244\">But for most surface navigation, the Earth can be assumed to be a <strong data-start=\"1359\" data-end=\"1392\">sphere with radius \u2248 6,371 km.<\/strong><\/p>\n<p data-start=\"206\" data-end=\"244\"><em>How do you calculate the NM from this<\/em><\/p>\n<p data-start=\"206\" data-end=\"244\">For simplicity, marine navigation and charting are based on the <strong data-start=\"382\" data-end=\"412\">spherical Earth assumption.<\/strong><\/p>\n<h3 data-start=\"206\" data-end=\"244\">The Mercator Chart<\/h3>\n<p data-start=\"159\" data-end=\"257\">A <strong data-start=\"161\" data-end=\"179\">Mercator chart<\/strong> is a <strong data-start=\"192\" data-end=\"223\">standard navigational chart<\/strong>\u00a0used in marine navigation. It is based on the <strong data-start=\"279\" data-end=\"302\">Mercator projection<\/strong>, which is a cylindrical projection of the globe onto a flat surface.<\/p>\n<p data-start=\"374\" data-end=\"394\">On a Mercator chart:<\/p>\n<ul>\n<li data-start=\"399\" data-end=\"470\"><strong data-start=\"399\" data-end=\"433\">Meridians (lines of longitude)<\/strong> are <strong data-start=\"438\" data-end=\"469\">vertical and equally spaced<\/strong>.<\/li>\n<li data-start=\"475\" data-end=\"609\"><strong data-start=\"475\" data-end=\"508\">Parallels (lines of latitude)<\/strong> are <strong data-start=\"513\" data-end=\"527\">horizontal<\/strong> but <strong data-start=\"532\" data-end=\"554\">not equally spaced<\/strong> \u2014 they get farther apart as you move toward the poles.<\/li>\n<li data-start=\"614\" data-end=\"807\">This spacing distortion compensates for the curvature of the Earth to preserve <strong data-start=\"693\" data-end=\"724\">angles and compass bearings<\/strong>, which is why <strong data-start=\"739\" data-end=\"781\">rhumb lines (constant compass courses)<\/strong> appear as straight lines.<\/li>\n<li data-start=\"810\" data-end=\"950\">The result is a <strong data-start=\"826\" data-end=\"843\">conformal map<\/strong>: angles and shapes are preserved locally, but <strong data-start=\"890\" data-end=\"922\">area and scale are distorted<\/strong>, especially near the poles.<\/li>\n<\/ul>\n<h3 data-start=\"206\" data-end=\"244\">Meridional Parts<\/h3>\n<p data-start=\"206\" data-end=\"244\">A <strong data-start=\"182\" data-end=\"201\">Meridional Part<\/strong> is the <strong data-start=\"209\" data-end=\"264\">length of a meridian (a line of constant longitude)<\/strong> from the equator to a given latitude, <strong data-start=\"303\" data-end=\"335\">measured on a Mercator chart<\/strong>. It&#8217;s expressed in <strong data-start=\"355\" data-end=\"373\">minutes of arc<\/strong>, like nautical miles, and it accounts for how the Mercator projection stretches the vertical (north\u2013south) scale with increasing latitude.<\/p>\n<h3 data-start=\"206\" data-end=\"244\">Plain Sailing<\/h3>\n<p data-start=\"160\" data-end=\"416\">Plane Sailing is a method of navigation that assumes the Earth is flat over short distances. It uses <strong data-start=\"261\" data-end=\"283\">plane trigonometry<\/strong> to calculate the course and distance between two points based on the differences in latitude and departure (the east-west distance).<\/p>\n<ul data-start=\"418\" data-end=\"843\">\n<li data-start=\"418\" data-end=\"480\">\n<p data-start=\"420\" data-end=\"480\"><strong data-start=\"420\" data-end=\"432\">Used for<\/strong>: Short voyages (typically &lt; 600 nautical miles)<\/p>\n<\/li>\n<li data-start=\"481\" data-end=\"517\">\n<p data-start=\"483\" data-end=\"517\"><strong data-start=\"483\" data-end=\"494\">Assumes<\/strong>: Earth is a flat plane<\/p>\n<\/li>\n<li data-start=\"518\" data-end=\"653\">\n<p data-start=\"520\" data-end=\"545\"><strong data-start=\"520\" data-end=\"544\">Calculations involve<\/strong>:<\/p>\n<ul data-start=\"548\" data-end=\"653\">\n<li data-start=\"548\" data-end=\"579\">\n<p data-start=\"550\" data-end=\"579\">Difference in latitude (\u0394Lat)<\/p>\n<\/li>\n<li data-start=\"582\" data-end=\"614\">\n<p data-start=\"584\" data-end=\"614\">Departure (East\u2013West distance)<\/p>\n<\/li>\n<li data-start=\"617\" data-end=\"631\">\n<p data-start=\"619\" data-end=\"631\">Course angle<\/p>\n<\/li>\n<li data-start=\"634\" data-end=\"653\">\n<p data-start=\"636\" data-end=\"653\">Distance traveled<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"654\" data-end=\"843\">\n<p data-start=\"656\" data-end=\"670\"><strong data-start=\"656\" data-end=\"667\">Formula<\/strong>:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">tan\u2061(Course)=Departure\u0394Latitudeand<\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"654\" data-end=\"843\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Distance=Departuresin\u2061(Course)tan(text{Course}) = frac{text{Departure}}{Deltatext{Latitude}} quad text{and} quad text{Distance} = frac{text{Departure}}{sin(text{Course})}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">tan<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord\">Course<\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">\u0394<span class=\"mord text\">Latitude<\/span><span class=\"mord text\">Departure<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord text\"><span class=\"mord\">and<\/span><\/span><span class=\"mord text\"><span class=\"mord\">Distance<\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord text\">Course<\/span><span class=\"mclose\">)<\/span><span class=\"mord text\">Departure<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"206\" data-end=\"244\">Mercator Sailing<\/h3>\n<p data-start=\"888\" data-end=\"1150\">Mercator Sailing is a method used for long-distance navigation that takes into account the Earth&#8217;s curvature. It uses a <strong data-start=\"1008\" data-end=\"1031\">Mercator projection<\/strong>, in which meridians and parallels are straight lines, allowing navigators to plot a straight-line course (rhumb line).<\/p>\n<ul data-start=\"1152\" data-end=\"1624\">\n<li data-start=\"1152\" data-end=\"1189\">\n<p data-start=\"1154\" data-end=\"1189\"><strong data-start=\"1154\" data-end=\"1166\">Used for<\/strong>: Long-distance voyages<\/p>\n<\/li>\n<li data-start=\"1190\" data-end=\"1252\">\n<p data-start=\"1192\" data-end=\"1252\"><strong data-start=\"1192\" data-end=\"1203\">Assumes<\/strong>: Earth is a sphere, mapped onto a Mercator chart<\/p>\n<\/li>\n<li data-start=\"1253\" data-end=\"1433\">\n<p data-start=\"1255\" data-end=\"1280\"><strong data-start=\"1255\" data-end=\"1279\">Calculations involve<\/strong>:<\/p>\n<ul data-start=\"1283\" data-end=\"1433\">\n<li data-start=\"1283\" data-end=\"1316\">\n<p data-start=\"1285\" data-end=\"1316\">Difference in longitude (\u0394Long)<\/p>\n<\/li>\n<li data-start=\"1319\" data-end=\"1398\">\n<p data-start=\"1321\" data-end=\"1398\">Meridional parts (logarithmic values accounting for convergence of meridians)<\/p>\n<\/li>\n<li data-start=\"1401\" data-end=\"1433\">\n<p data-start=\"1403\" data-end=\"1433\">Rhumb line course and distance<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"1434\" data-end=\"1624\">\n<p data-start=\"1436\" data-end=\"1450\"><strong data-start=\"1436\" data-end=\"1447\">Formula<\/strong>:<\/p>\n<\/li>\n<\/ul>\n<h3>Rhumb Line<\/h3>\n<p data-start=\"1436\" data-end=\"1450\">A rhumb line is an <span class=\"AraNOb\">imaginary<\/span>\u00a0line on the earth&#8217;s surface cutting all\u00a0<span class=\"AraNOb\">meridians<\/span>\u00a0at the same angle, used as the standard method of\u00a0<span class=\"AraNOb\">plotting<\/span>\u00a0a ship&#8217;s course on a chart.<\/p>\n\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\n\t\n\n<\/div>\n\n\t\t<\/div>\n\n\t\t\n<style>\n#section_2120981567 {\n  padding-top: 30px;\n  padding-bottom: 30px;\n}\n<\/style>\n\t<\/section>\n\t\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-28","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/pages\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/comments?post=28"}],"version-history":[{"count":9,"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/pages\/28\/revisions"}],"predecessor-version":[{"id":49,"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/pages\/28\/revisions\/49"}],"wp:attachment":[{"href":"https:\/\/nottagemews.uk\/utilities\/wp-json\/wp\/v2\/media?parent=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}