How to get correct distances from the scale of a world map

 By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

22 July 2012

Anthony Kimemia asks two questions: first, “how is the scale of a world map determined? I ask because the Earth is round while the map is flat.” Second, “why are there two North Poles and two South Poles?”

Any world map drawn on a flat surface distorts the shapes of the continents and countries. There are several different ways of stretching out the spherical globe onto a piece of paper but the most common is one that presents longitudes and latitudes as straight lines.

In doing that, this type of map exaggerates distances near the poles while understating equatorial ones. Thus, one centimetre on the Equator will represent a much greater distance than 1cm on, say, the Arctic Circle. This is why Antarctica appears to traverse over the same distance as that from western America, through Africa to the far eastern Asia. In reality it is much smaller…and more circular.

There is a straightforward formula for determining the scale at any latitude, but it requires some basic knowledge of the geometry of triangles – trigonometry. To get the scale at a given latitude, you multiply the equatorial scale by the cosine of that latitude.

For example; the map in my desk diary has an equatorial scale of 1cm representing 1,500km. The width of Kenya is about 0.5cm. This translates to about 750km.

On the same map, Egypt has a width of 0.6cm at its centre – it actually appears wider than Kenya. But Egypt lies about 25 degrees from the Equator, therefore the scale at that location is 1,500 multiplied by the cosine of 25 degrees; that is 1,500 x 0.9 = 1,350.

In other words, at 25 degrees latitude, 1cm on my map represents 1,350km. Therefore the middle with of Egypt is about 800km – close to Kenya’s width.

On the second question, Anthony is correct; our planet has two sets of poles. The first and probably more common are the magnetic poles. These are defined by the Earths magnetic field.

The so-called magnetic north is actually the south pole of the planet’s internal magnet. But since it lies in the northern part of the globe, there is no need to cause confusion amongst the general public!

The above statement implies a fact that is not commonly appreciated: that the place called “North Pole” was given that name long before anyone realised that the Earth has a magnetic field.

To find the magnetic North, you would have to go with an ordinary navigation compass. When placed at the pole, the compass needle points vertically downwards.

The second set of poles is the geographic poles. They are the positions at which the Earth’s axis of rotation touches the surface. To establish their locations, you have to observe the stars in the sky.

When standing at a geographic pole, the stars will appear to be travelling in concentric circles centred directly above you. It’s not an easy thing to do!