Measuring Lengths and Distances - UsingString

Length measurement of non-geometrical shapes using strings.

Written By: Kailash NR

Measuring Lengths and Distances - Using String Release: 1.2 [minor] 2018-04-24Guide ID: 309 -

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INTRODUCTION

Using a piece of string, we measure the length/perimeter of any oddly shaped track/object, e.g. thelength of India's coasts and/or borders.

TOOLS:Pencil or Pen (1)Ruler (1)

30 cm

PARTS:Cotton Thread (1)

Coloured1.5 meters

Map (1)With scale factor

Paper (1)

Measuring Lengths and Distances - Using String Release: 1.2 [minor] 2018-04-24Guide ID: 309 -

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— Precautions

Be careful when handling scissors, take care to avoid its pointed edges.

— Step 1 - Some Concepts

Distance refers to the actual length of the path traced by an object (in this case between A and B).

Displacement, on the other hand, is the shortest possible path from A to B. It is usually in theshape of a straight line.

When we deal with straight paths, often the distance and displacement is the same length, but asthe paths get more curved; this changes. It also becomes increasingly impractical to measure suchpaths with a ruler directly.

Start by making a mark on one end of the string either with a pen or pencil. This will help us markthe start position accurately.

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— Step 2 - Measuring a Curved Path

Now take the end of the string that you marked and place it on the glue-stick. With the string inbetween a thumb and the glue's surface, drag the thread through the glue-stick. This will make thestring sticky and will make it easier to trace the path.

Start placing the string along the path with the marked end at A.

As you place the string, keep tracing the string with a pen. The marks should cover both the paperand string. This will help in case the string falls away or moves before the complete trace isfinished.

Measuring Lengths and Distances - Using String Release: 1.2 [minor] 2018-04-24Guide ID: 309 -

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— Step 3 - Measuring a Curved Path II

Continue tracing with the string. Try to follow the path as accurately as possible, this will increasethe accuracy of the final measurement.

Once you have reached point B, make a mark on the string.

Cut the string at this mark. You now have a length of string that is as long as the path on thepaper.

Measuring Lengths and Distances - Using String Release: 1.2 [minor] 2018-04-24Guide ID: 309 -

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— Step 4 - Measuring the String

Remove the string from the paper and measure it with a ruler.

Be careful not to stretch the string too much while measuring it.

Make a note of the length you find. In this case we got 24.8 cm for the example path.

Measuring Lengths and Distances - Using String Release: 1.2 [minor] 2018-04-24Guide ID: 309 -

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— Step 5 - Scale Factor Concepts

This technique for measuring distances, though simple, is quite powerful. We are now going toestimate the perimeter of India using this technique.

A map with scale factor is required for this. This scale factor can vary from map to map. Itrepresents a ratio between the length on the map and the actual length of the area represented.For example here our scare factor is 1:16,700,000. This means one centimeter length on the maprepresents 16,700,000 cm or 167 kilometers.

Alternatively the map's scale factor could be represented graphically. With the length of the linesunder the distance number being the scale factor. To find the scale in this case, just measure theline using a ruler and the number of centimeters you get corresponds to the distance numberabove the line.

For example our line length is 1.5 cm. So, in this case 1.5 cm on the map represents 300kilometers. The line is also split into 3 equal parts. Therefore 0.5 cm length on the maprepresents an actual length of 100 km.

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— Step 6 - Measuring the Perimeter of India I

Start again by making a mark on one end of the string. If you are using a different piece of string,then pull it through the glue-stick again.

Start on any point along the perimeter and make a small line on the paper to mark the startposition.

Now continue along the perimeter, making marks periodically.

— Step 7 - Measuring the Perimeter of India II

Continue placing the string along the perimeter until you reach the point you stared from.

Now make a mark on the string where it intersects the initial end.

Using the final mark as reference cut the remaining string off.

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— Step 8 - Crunching the Numbers

Remove the string from the map andmeasure it. The string will be toolong to measure all at once, so usethe marks made in-between tomeasure in steps.

Once you have the total length ofthe string, multiply it with the scalefactor to get the actual length.

In this example we got a stringlength of 82.5 cm which whenmultiplied with 1,67,00,000 gives us1,37,77,50,000 cm or 13,777.5kilometers. The actual perimeter ofIndia is 15,106.7 kilometers, whichis an error of 8.7%.

This is an interesting point abouterror in measurement. Nomeasurement can be made withprefect accuracy. The actualperimeter of India has manycomplex curves made of yet smallercurves, measuring this in more detailwould require more and moreprecise measurements. Do you thinkthere is a limit to this detail?

— Troubleshooting

The stretching of the string can lead to measurement errors. Be sure not to extend the string toomuch while placing and measuring the string.

Measuring Lengths and Distances - Using String Release: 1.2 [minor] 2018-04-24Guide ID: 309 -

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