A map is a small model representing a larger land unit; and while map sizes may change, ground distances don’t. To find the ratio of a map distance to the actual ground distance we use a representative map scale.
Types of Map Scale:
There are basically three forms of map scale (for a map drawn to scale) namely:
- Statement or verbal e.g. 1 cm to 2.5 kilometers (different units)
- Linear, graphic, bar, or segmented (e.g. a line on a map marked off in ground distance units)
- Representative Fraction e.g. 1: 250 000 (same unit; see Maui map)
Using a Map Scale:
To help you understand the process of calculating distances using a scale we’ll take an example:
Let us assume that the measured straight line map distance between two points, A and B is 6.9 cm. The map scale is given as 1 cm to 8 km. To find the actual ground distance in kilometers you would simply multiply 6.9 by 8 giving you 55.2 kilometers (6.9 X 8 = 55.2).
If the map scale was a representative fraction, written as 1: 800 000 you would first convert to a statement scale (e.g. 1 cm to 8 km) and then do the math.
To use a linear scale you mark the map distance on the edge of a piece of paper, for instance, and then visually determine actual ground distance using the annotated scale. This scale is useful if, for instance, you are copying a map because, as a map size changes so does the scale.
Determining a Map Scale:
Sometimes a person has a map without a scale and wants to estimate it. In that case you would work backyards. First you would pick two points, say A and B, whose real ground distance is known. If the map distance between these two points, when measured turns out to be, for example 6.9 centimeters, and the ground distance is 4 kilometers, then the initial math would be as follows: 6.9 X 4 = 27.6 km. You would then write the data as a ratio of map distance to ground distance, as follows: 6.9 cm to 27.6 km, and follow by reducing it to a base of 1 (e.g. 1 cm represents 4 km.). If written as a representative fraction (same units) it would appear as 1: 400 000.
Conversions:
A representative fraction scale is not affected by such things as miles versus kilometers: it is unit neutral. For example, 1: 100 000 can mean 1 cm to 100 000 cm (converted: 1 cm to 1 km) or 1 inch to 100 000 inches (converted: 1 inch to 1.6 miles). But you can see that using metric units is less cumbersome.
GPS Map Accuracy:
We sometimes think that GPS distance data is more accurate than on standard maps. In reality, as Garmin explains, “certain atmospheric factors and other sources of error can affect the accuracy of GPS receivers. Garmin® GPS receivers are accurate to within 15 meters on average.” As Garmin further points out, this decrease in accuracy is a result of factors such as ionosphere and troposphere delays (signal slowing), reflected signals, and a decreased number of satellites visible.
A Precautionary Note:
A map is a flat model of a round earth. If you want accuracy in distance- and there are National Map Accuracy Standards- you could be forsaking accuracy in directions, shapes or areas. Therefore, before you use an atlas map to calculate distance you might want to make sure the projection is, for instance, an zenithal equidistant.
Sources:
James Gibson - James Gibson is a retired teacher and small business owner. He is a published writer and has a wide spectrum of interests.
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