SI Units Explained with Worked Examples

 

 

 

 

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  Length

How long would it take to walk around planet Earth? To answer this question we need to consider distance, or put another way the length of the path we need to take. There have been many units used for length throughout history and some of them are still in use today, but here we consider the SI unit of the metre, with the symbol m.
 

How long would it take to walk around the Earth?

Firstly, a quick comment on the unit name. Strictly speaking it is spelled metre, but in many English speaking countries meter is used instead and widely accepted. Now, on with the question...

One of the earliest known units of length was the cubit. This was defined as the length of the arm from the elbow to the tip of the finger. This was further split into smaller units and even today we still use the "hand" to measure the height of horses. The obvious problem with the cubit is that it varies depending on the size of the person making the measurement. Other units where also based on arbitrary measurements with a notable example being King Henry I (1068 - 1135) decreeing that a yard was the distance from the tip of his nose to the end of his outstretched thumb. What's perhaps surprising is that the SI unit of the metre was also initially based on an arbitrary measurement, namely the circumference of the Earth.

In 1791 the French Academy of Sciences decided to adopt a new unit of measurement, called the metre, based on 1/10,000,000th of the distance from Earth's equator to the North Pole. This was certainly a step forward from nose-to-thumb length, but it also had its problems such as the fact that the Earth constantly changes shape a little due to gravitational forces and other factors. For this reason the metre was slightly changed in length and based on something much more stable. It is now defined as "the length of the path traveled by light in a vacuum during a time interval of 1/299,792,458th of a second". Not quite as handy as the cubit, but a lot more precise.

The metre, then, is the SI unit of measurement. It is further split into 100 centimetres, or 1000 millimetres. For long distances it sometimes makes sense to talk in thousands of metres. One thousand metres is one kilometre, with the units km. For comparison, 1 metre is close to 3.28 feet (about a yard) and 1 kilometre is about 0.62 miles.

Now back to our original question of how long it would take to walk around the Earth. At its equator the Earth's circumference is 40,075 km (24,901 miles). The average walking speed, depending on age, is about 5 kilometres per hour (km/h), so in 12 hours a distance of 5 km/h x 12 hours = 60 km is covered.

So to work out how long it would take to walk around the Earth at 5 km/h for 12 hours a day we simply divide the Earth's circumference by the distance walked in a day:

40,075 km / 60 km = 668 days

This is about 1 year and 10 months. But what if we could drive around the Earth at 100 km/h (about 60 miles per hour)? Now we cover 100 km/h x 12 hours = 1200 km in a day, so:

40,075 km / 1200 km = 33.4 days.

In other words, even if a car is used it would still take about a month to travel all of the way around the Earth. With the Internet and other forms of global communication, as well as fast jet transport, we tend to think of the world as quite a small place, but when we think about walking or driving around it we soon realize that it's actually quite big.

Finally, for most of human history we have thought of distance as being absolute  - one mile is one mile and one metre is one metre. Einstein, in his theory of relativity, demonstrated that in reality distances shrink when we move at very high speeds. If we travel at about 90% of the speed of light distances, in other words lengths, shrink by about 50%. You can read more about this, together with worked examples, by clicking here or on the picture of Einstein:

Click for Einstein's Relativity

 
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