If you do not have paper charts on board then you will need to draw one. This is a very old skill. In the days when there was terra incognita, explorers drew their charts as they sailed. You can do the same.

First decide on the scale. The longitude scale is constant and the ratio of longitude to latitude is 1: secant of your latitude. A secant is the inverse of a cosine, or one divided by the cosine of your latitude. If you are in latitude 50° north or south then you need the secant of 50° or 1 / Cos 50°. The answer is 1.5557. In other words the ratio

At 0° N/S |
1' Longitude equals 1cm |
1' Latitude equals 1cm |

At 10°N/S |
1' Longitude equals 1cm |
1' Latitude equals 1.015 cm |

At 20° N/S |
1' Longitude equals 1cm |
1' Latitude equals 1.064 cm |

At 30° N/S |
1' Longitude equals 1cm |
1' Latitude equals 1.154 cm |

At 50° N/S |
1' Longitude equals 1cm |
1'Latitude equals 1.556 cm |

At 80° N/S |
1' Longitude equals 1cm |
1' Latitude equals 5.759 cm |

At 89° N/S |
1' Longitude equals 1cm |
1' Latitude equals 57.299 cm |

At 89.90°N/S |
1' Longitude equals 1cm |
1' Latitude equals 572.958 cm |

At 90° N/S |
1' Longitude equals 1cm |
1' Latitude equals Infinity |

19.1 Mercator Charts Latitude Versus Longitude

19.1 Mercator Charts Latitude Versus Longitude between longitude and latitude is 1:1.5557 and on your hand-drawn chart it means: 1' of longitude = 1mm, cm or whatever unit you chose.

And:

1' of latitude = 1.5557 mm, cm or whatever unit you chose. You must use the same units for both latitude and longitude.

If you are unable to work out the secant of your latitude then decide upon a suitable longitude scale and find the latitude scale graphically (Figures 19.2 to 19.5 show you how).

It is best to keep home-made charts to one degree of latitude, especially if you are sailing in high latitudes where small changes in latitude can have a disproportionate effect on scale. In the real world Australia is far larger than Greenland, but not on a Mercator map.

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