Topographical Maps and Map Reading — Page 229, Lesson 206

Let’s start with the very idea of scale, because everything on a chart hangs off it. Scale is the relationship between the length of a line drawn between two positions on a chart and the distance on the Earth between those same two points. In other words, it’s the ratio that tells you how much the real world has been shrunk down to fit on the paper. There are three common ways to express scale, and you need to be comfortable with all of them. The first is a statement in words. This is self-explanatory. For example, the statement “One inch to ten nautical miles” means that a line one inch long on the chart represents a line ten nautical miles long on the Earth. Simple, direct, and it tells you exactly what you’re dealing with. The second method is the Representative Fraction. This is that statement in words put into mathematical form. It’s calculated from the equation: Scale equals Chart Length over Earth Distance. By convention, the chart length is always 1, and the dimensions above and below the line are the same, so they cancel each other out and make the fraction dimensionless — that’s why it’s called “representative.” It doesn’t matter what units you use, because they cancel. Let me make that concrete. On the ICAO 1:500,000 topographical chart, 1 centimetre on the chart represents 500,000 centimetres on the Earth, and 1 inch on the chart represents 500,000 inches on the Earth. Same fraction, different units, because the ratio is unitless. Now, here’s a nice conversion to see how the statement in words becomes a representative fraction. “One inch to ten nautical miles” becomes a representative fraction of 1 over 729,600, or 1:729,600. Why that number? Because ten nautical miles, converted into inches, gives you 729,600 inches. So one inch on the chart equals 729,600 inches on the Earth. The third method is the Graduated Scale Line. These are normally depicted at the bottom of the chart, as in Figure 13.1, and they may be in nautical miles, statute miles, or kilometres. It’s a drawn bar with divisions marked off, so you can physically measure a distance on the chart and read it off directly. And here’s a clever point: since one degree of latitude is equal to 60 nautical miles, the provision of a latitude scale in effect provides a graduated scale line, as shown in Figure 13.2. So the latitude markings along the edge of the chart double as a distance scale, because latitude and nautical miles are tied together that way. So to sum up: scale is the ratio between chart distance and Earth distance. You can state it in words, as a representative fraction, or as a graduated scale line. And remember, the latitude scale is your built-in graduated scale line, because one degree of latitude equals 60 nautical miles.