Topographical Maps and Map Reading — Page 229, Lesson 206

I want to walk you through the concept of scale on topographical maps — this is one of the most fundamental ideas in navigation, because without scale, a chart is just a picture with no usable distance information. Scale is defined as the relationship between the length of a line drawn between two positions on a chart and the distance on the Earth between the same two points. In other words, if you measure a distance on the paper chart, scale tells you what that distance represents in the real world. There are three common methods of expressing scale, and you need to be comfortable with all of them. The first is a statement in words. This is exactly what it sounds like — a plain English statement. For example, "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 and direct. The second method is the Representative Fraction, often abbreviated as RF. This takes the statement in words and puts it into mathematical form. The equation is: Scale equals Chart Length divided by Earth Distance. By convention, the chart length is always set to 1. The dimensions above and below the line — the numerator and denominator — are the same unit, so they cancel each other out, making the fraction dimensionless. That's why it's called "representative" — it represents the ratio regardless of what unit you measure in. Let me give you a concrete example. On the ICAO 1:500,000 topographical chart — that's the standard ICAO 1 to 500,000 scale chart — 1 centimetre on the chart represents 500,000 centimetres on the Earth. And equally, 1 inch on the chart represents 500,000 inches on the Earth. The ratio stays the same because the units cancel. Now, let's convert that earlier statement — "One inch to ten nautical miles" — into a representative fraction. One nautical mile is 6,076 feet, and there are 12 inches per foot, so one nautical mile is 72,912 inches. Ten nautical miles is therefore 729,120 inches. So the representative fraction becomes 1:729,120, or written as a fraction, 1 over 729,120. The third method is the Graduated Scale Line. These are normally depicted at the bottom of the chart, as shown in Figure 13.1. They may be marked in nautical miles, statute miles, or kilometres. Now here's a very practical point: since one degree of latitude is equal to 60 nautical miles, the latitude scale printed along the edge of the chart effectively provides a graduated scale line as well. That's shown in Figure 13.2 — the latitude scale itself can be used to measure distances in nautical miles. So to summarise: you have three tools — a statement in words, a representative fraction, and a graduated scale line. In professional navigation, you'll use the graduated scale line most often for quick measurements, but you need to understand the representative fraction for chart calculations and conversions.