Mercator Charts - Scale — Page 320, Lesson 284

Let’s pick this up right where the numbers left off. We were working out the chart length for a distance of 2400 minutes of longitude at 40°N, and we got an Earth distance of 1838.4 NM. Now I want to show you the final step, because this is where the unit conversion catches people out. We have a chart at a scale of 1 in 10 million. That means 1 unit on the chart equals 10 million of the same units on the Earth. So the chart length is the Earth distance divided by 10 million. That gives us 1838.4 NM divided by 10 million. But that answer is in nautical miles, and we don’t want the chart length in nautical miles — we want it in centimetres. So we convert. One nautical mile is 1852 metres, and one metre is 100 centimetres. So to go from nautical miles to centimetres, we multiply by 1852 and then by 100. That’s the 1838.4 × 1852 × 100 in the numerator, all over 10 million. Work that out and you get 34 centimetres. That’s the chart length. Now, the really important concept for practical navigation: the idea of a “constant” scale. For real-world flying, we treat a chart as having constant scale in any area where the scale is within 1% of the correct scale. That’s the tolerance we accept — within 1%. On a Mercator chart, the scale is constant and “correct” only along the Equator. That’s the one line where the chart scale exactly matches the true scale. Away from the Equator, the scale changes because the parallels are stretched. But here’s the practical rule: the scale is within 1% of correct within a band of 8° of latitude either side of the Equator. So from 8°N down to 8°S, we can treat the chart as constant scale for navigation. And there’s a note for the exam: that 8° figure can be quoted as 480 nautical miles or 500 nautical miles. So if you see 480/500 NM in a question, that’s the same band of latitude expressed as a distance. So the takeaway: the Mercator scale is only truly correct at the Equator, but within 8° of latitude either side — about 480 to 500 NM — the error stays under 1%, and that’s good enough for practical navigation.