The first is a statement in words — Page 281, Lesson 244

Let’s start with the definition, because everything else 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 the same points. In other words, it’s the ratio between a distance measured on the paper and the real distance on the ground. There are three common ways to express scale, and I want you to know all three because you’ll meet each of them in different charts. The first is a statement in words. This is self-explanatory — you literally say it. “One inch to ten nautical miles” means a line one inch long on the chart represents a line ten nautical miles long on the Earth. Jeppesen charts often use this method. For instance, the Jeppesen E(HI) 1/2 uses a scale of 1 inch to 20 NM. The second method is a graduated scale line. These are normally depicted at the bottom of the chart, as in Figure 16.1, and they may be in nautical miles, statute miles, or kilometres. Here’s a neat trick: since one degree of latitude equals 60 nautical miles, a latitude scale on the chart in effect provides a graduated scale line, as shown in Figure 16.2. So if you ever need a quick distance reference, the latitude markings along the side of the chart can serve as your scale. The third method is the representative fraction, often abbreviated RF. This is a statement in words put into mathematical form. It’s calculated from the equation: Scale equals Chart Length divided by 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.” So on the ICAO 1:500,000 topo chart, 1 cm on the chart represents 500,000 cm on the Earth, and 1 inch on the chart represents 500,000 inches on the Earth. The ratio works regardless of the unit you choose, as long as you use the same unit top and bottom. Now, converting from a statement in words to a representative fraction. The critical rule is that you must use the same units for both the numerator and the denominator. Let’s walk through the example: converting “One inch to ten nautical miles” into a representative fraction. Substituting into the equation gives 1 inch over 10 nautical miles. But we can’t leave it like that — the units don’t match. So we multiply by 6080 to get the denominator into feet: 1 inch over 10 × 6080 feet. Then we multiply by 12 to get it into inches: 1 inch over 10 × 6080 × 12 inches. Now both numerator and denominator are in the correct units, and we get 1 over 729,600. So the RF becomes dimensionless — it will work with centimetres or any other units as long as the ratios remain the same. Let me give you the conversion factors you’ll find useful in typical scale problems. One nautical mile equals 6080 feet or 1852 metres. One metre equals 3.28 feet. One inch equals 2.54 cm. And 5.4 NM equals 10 kilometres. Keep these handy — you’ll use them constantly. Let’s finish with Example 1. On a particular chart, 5 cm represents 7 nautical miles. What is the scale? The representative fraction is chart length over earth distance, so we write 5 cm over 7 nautical miles. But we need matching units, so we multiply 7 by 1852 to convert to metres, then by 100 to convert to centimetres. That gives us 5 cm over 7 × 1852 × 100 cm. Work that out and you have your RF. The key habit to build here is always checking your units before you simplify the fraction.