Scale and distance on maps

Transcription

1 Scale and distance on maps This section explains how to use and convert different types of scales. It also discusses how to measure distances on maps. By the end of this section you should be able to: Measure curved and straight distances Use the scale to convert map distances to real distances Convert (change) one scale to another. Topographic maps show man-made features such as houses, roads, railroads, windmills, etc., as well as natural features such as rivers and mountains. Part of a 1: topographic map of the Ogongo area

2 Let s visit my uncle at the Agricultural college. Can we walk from Oshitutuma to the college? I don t know, let us look at our map. It has a 1: ratio scale. On the map it is about 7 cm from Oshitutuma to the college. The formula is: map distance scale, so 7 cm cm is cm. Now we must divide cm by cm to convert the distance to kilometres. So the real distance is = 3.5 km. Yes, we will be able to walk to the college. Different units can be used in a word scale, for example, if 1 cm equals 0.5 km then 1 mm equals 0.05 km Ruben and Selma are using a topographic map to find their way to the college. To work out what the real distance will be, they must know how to use the scale of the map. They must also know how to measure distances on the map. Map scales A map scale shows us the relation between a distance on a map and the corresponding distance on the surface of the earth. There are three types of scales: word scales, ratio scales and linear scales. 1 Word scales If 1 cm on the map represents cm in reality, then 1 cm also represents 0.5 km. 2 Ratio scales If the ratio scale is 1:50 000, then 1 cm equals cm. Here are examples of other ratio scales: 1: :4 000

3 To convert a word scale to a ratio scale you must follow two rules: 1 A ratio scale must always start with 1. 2 The measurements before and after the colon (:) must be in the same unit. For example, to convert the word scale 4 cm equals 2 km, you must apply both rules. Therefore you must first convert 2 km to cm ( = ) and then you must divide 4 by 4 (=1). Remember that you must also divide the by 4 (= ). The ratio scale is therefore 1: Linear scale A linear scale consists of a line, divided into primary units, with secondary units to the left of the 0. Remember that the primary units to the left of the 0 must be exactly the same size or length as the primary units to the right of the 0. The above example of a linear scale means that 1 cm on the map equals 1 km on the ground. Study the following two examples and try to convert them to word scales. Don t worry if you can t do it. We will explain more about scale conversions later. 2 cm = 3 km or 1cm = 1.5 km The following steps will help you to draw a linear scale. They are used in the example below to show you how you go about drawing a linear scale. Example: Draw a linear scale with primary and secondary units where 2 cm equals 100 m. Step 1: Draw a linear scale (line) (draw a line of any length)

4 Step 2: where 2 cm (divide line into 2 cm units) Step 3: equals 100 m (every 2 cm equals 100 m) Step 4: Subdivide the units to the left of the 0 into smaller secondary units of your own choice. How to convert scales One type of scale can be converted to another type of scale. Look at the example below to see how. Example: Word scale: 1 cm represents 0.5 km Convert to: Ratio scale: Linear: Word scale: 1 cm represents 1 km

5 To be able to convert one scale to another scale or one unit to another unit, you must know the following: To convert from: mm in 1 km mm to km you by cm in 1 km cm to km you by m in 1 km m to km you by cm in 1 m cm to m you by mm in 1 m mm to m you by Measuring distance On a map, distances can be measured in two ways: along a straight line or along a curved line. Along a straight line To measure a straight line, simply use your ruler. For example, the distance from A to B shown here is 5.6 cm.

6 1 Along a curved line To measure a curved line you need a piece of paper with a straight edge. Step 1: Put the paper strip with the straight edge on the first straight part of the road or curved line. Mark point B onto the strip at the beginning of it and make another mark (b) where the road starts to curve away from the paper strip. Step 2: Keeping the mark of (b) firmly fixed, rotate the straight edge of the paper strip until it follows the next straight part of the road. Now mark (c) where the road curves away again (up or down) from the paper strip. Step 3: Keep on rotating the paper strip and marking the parts on the strip, until the whole curved distance, from B to Namutoni, is marked onto the strip of paper. Step 4: Lay the paper strip against your ruler and read the distance from B to Namutoni as done below. Work out the real distance by using the map scales provided..

7 Calculating distance by using different scales If you know how to use map scales, you can easily work out the real distance between places. The map is provided with a ratio and a linear scale. To use the ratio scale, you must understand the following formula: Ratio scale =Map distance scale (if you convert from cm to km) Let us measure the distance the aeroplane travelled between Mogadishu in Somalia and Nairobi in Kenya by using our formula. Map distance = 1.5 cm map scale = 1.5 cm cm = cm (to convert to km) = 900 km

8 To use the linear scale, you must understand how to read the distance on this type of scale. It allows you to measure the real distance between places on a map. Use your ruler and measure the map distance from Windhoek to Luanda on the map of Africa (Figure 1.5). The distance is 2.7 cm. Now place your ruler on the linear scale so that the 2.7 cm mark on the ruler is directly below the km mark on the linear scale (between 2 cm and 3 cm). Now study Figure 1.6. Point A is Windhoek and B is Luanda. Point A lies somewhere in the secondary units on the left side of the 0 (zero). Take the reading from 0 on the linear scale to point B. Do the same from 0 on the linear scale to point A and add the two readings (distances). The answer will give you the distance in km (kilometres) between Windhoek and Luanda. From zero to B = 1200 km From zero to A = 450 km Windhoek to Luanda = 1650 km Lesson Summary Every map has a scale that shows the relation between a distance on the map and the same distance in real life. The three types of scales are: word scales, ratio scales and linear scales, and one scale can be converted to another one. Distance on a map can be measured in a straight line between two points or along a curved line, for example a road. The scale is then used to convert map distance to distance in reality in metres or kilometres.