AN ON-LINE GEODATA COLLECTION ACTIVITY TO BE HOSTED BY THE SOCIETY OF AFRICAN EARTH SCIENTISTS 0N 20TH MARCH 2013 AS PART OF DAY OF EARTH SCIENCES IN AFRICA
The Society of African Earth Scientists (SAES) will on the 20th March be participating in “Day of Earth Sciences in Africa “ as part of the Association of African Women in the Geosciences-led, “Day of Earth Sciences in Africa and the Middle East”. The Society, as a partner in the event, will be hosting an on-line geodata collection activity involving the measurement of the length of Africa’s coastline and the area of Africa’s landmass. All participants are invited to post their results on the SAES facebook page on the 20th March or email their results to email@example.com.
To measure the area and coastline of Africa’s landmass in square km and km respectively, using Google earth software. Google earth software is downloadable free from the Internet.
The SAES hosted activity will
- encourage African scientists and interested public to become familiar with a potential earth science tool that is freely available
- enable appreciation of the true size of the African continent, until recently unknown.
The advent of satellite technology and the Internet has liberated the African scientist from having to accept, based on faith, statistics of his/her own continent as measured by others. Until 2010, the size of the African Continent appearing on most maps, made Africa 14 times smaller than its actual size! This is because the Mercator Projection ( published by Gerardus Mercator in 1569) on which most maps are based till this day, failed to correctly allow for the curvature of the Earth, thereby distorting true values of African continental size on earlier maps. In 2010 the computer graphics expert Kai Krause published a map of Africa which showed other countries crammed into its outline. It gave, at a glance, an appreciation of the true size of Africa, which is able to encompass the United States, Mexico, Japan, China, Iberia peninsula, India and western Europe including the UK .
Detailed Description of the Activity
The Society of African Earth Scientists’ Earth Science Day activity invites us to measure two very important quantities: the area and the coastline of the African continental landmass. The tool we recommend for this exercise is Google earth. Google earth can be freely downloaded from the internet, and measures distances on the surface of the earth. Google earth (assuming we do not have Google earth Pro, which measures areas directly) allows us to measure Africa’s coastline very easily; whilst we need to work a bit harder to get an estimate of area by measuring only distances.
Ideally, we could get a very good estimate of Africa’s area by supposing that the shape of Africa is made up of an array of very thin rectangles of equal width, d, (see fig. 1 above). This fine estimate can in theory be made easily as it is easy to measure the lengths of each rectangle drawn within the shape of the continent. Since each rectangle is of width d, and the area of a rectangle is its length multiplied by its width, the area of the continent is thus given by the sum of the lengths of all the constituent rectangles multiplied by their common width, d. The smaller the value of d, the more accurate is the estimate. Theoretically, if the width d is infinitely small, the estimate is exact.
In practice, it is very time consuming to measure area by making the width, d, so fine as to require the use of many rectangles to fill up the shape of Africa approximately. Also it is not easy to ensure the measurement of lengths which are perfectly equidistant as in the case of the idealised rectangles.
A quicker method which still gives us an acceptable accuracy within 5% is to approximate the shape of the continent as closely as possible using an arrangement of rectangles and triangles to occupy the space inside the outline as closely as we see fit. We then determine the areas of these rectangles and triangles in the usual way (i.e., the area of a triangle is ½ x base x height; whilst that of a rectangle is width x length), and we sum all the areas to obtain the estimate of the area of Africa’s landmass. We note that making use of respectively thinner and smaller (and therefore more numerous) rectangles and triangles will improve the accuracy of our estimate; but will be more time consuming. We must balance the benefits of one against the other, accuracy against labour saving, depending on the level of accuracy we need to achieve.
Having appreciated the method by which we approach our task we proceed to the measurement of distances in Google earth. In the tool bar at the top of the google earth screen, there is a symbol of a ruler. There is also the symbol of dots connected by a line. These icons are a clue as to how we are to use Google earth to measure distances.
i) Measurement of the African coastline using Google earth
To measure the distance around the outline of the African continent, we click on the icon showing dots connected by a line. Hovering over the icon reveals the label “add path “over the icon. A window will appear with various tabs, including one labelled “measurements”. Click on the “measurements” tab and a “new path” window will appear with a space for the display of length. At this point you may choose from a drop down list in this space to display these distances in units of your choice. For this exercise, we choose kilometres (km).
We then use the mouse cursor to trace a path around the outline of Africa. When we have completely traced the coastline as closely as possible, the window gives us the distance (length) in kilometres. Your answer should be close to 26,000 km.
ii) Measurement of the Area of Africa’s Landmass
ii) Measurement of the Area of Africa’s Landmass
As described above, we begin by sketching an arrangement of rectangles and triangles to fit inside the outline of the African continent as closely as possible (see fig 2 ). We then use this sketch as a guide for the distances we are going to measure using Google earth’s ruler facility. We proceed to measure the required distances. We will not trace as we did in the last activity, but instead at each step measure the distance between two points.
We begin with the first rectangle side (or triangle side, depending on our arrangement). We click on the ruler icon in the top tool bar. A window appears with two tabs (“line and “path”) and we choose the tab labelled “line”. This time we click on the upper point of a vertical rectangle side (for instance) on Africa’s north coast, the length of which we intend to measure. Then we click on the lower point at the bottom end of this vertical side. A line appears joining the two points and the window shows the length of the line in kilometres. We write down the length of this line on our outline sketch of Africa (as shown in Fig. 2). We continue in this fashion until all the lengths of rectangle and triangle sides in Fig. 2 have been measured. We then proceed to determine the areas of the rectangles and triangle shapes composing the shape of Africa and sum them up to arrive at our total continental land area as described previously.
 This is the principle behind estimation of geometric areas and other quantities in mathematics by means of the operation known as “integration”