It's easy to take GPS and modern technology for granted when it comes to mapping, but plenty of surveys are created using old-fashioned ways and good old trigonometry.
Sure, cutting-edge tech like LiDAR is necessary when it comes to things like autonomous cars and HD mapping, but some maps are still built for humans, and there’s still plenty of scope for more traditional methods.
There are three relatively low-tech ways of measuring distances for surveys and maps, known as triangulation, trilateration and traversing. They've been used for decades, but although technology and the mapping world has changed beyond recognition since the 1950s, they're still a tried, trusted and reliable means of accurately measuring distances. So what's it all about?
Triangulation makes it possible to calculate the distances between different places, by picking three locations set out in a triangle, and making a series of measurements. You'll need to know the actual distance between two of those three points, which is known as a baseline, and you'll also need to measure the angles of the triangle, which can be done with a tool called a theodolite, but once you know that you'll be able to use basic trigonometry to calculate the distances involved for the other two sides of the triangle.
Triangulation can then be used on a far wider scale, as you'll be able to use the calculated distances as virtual baselines for other triangles, setting up a much larger triangulation network. With up to and over 50 kilometres between triangulation positions, calculations also need to incorporate calculations to accommodate the curvature of the Earth, but aside from that it's not actually too dissimilar a process to trigonometry questions asked in schools.
Triangulation is incredibly useful, but you'll still need to work out the baseline distance before you can get started, and with such large distances involved that's not exactly an easy task. That's where Trilateration comes in, this time making it easy to accurately work out any of the distances in a triangle, and also to calculate the angles themselves.
To measure a distance, trilateration uses the known speed of light (299,792.458 km per second) and times how long it takes for either a wave of light or a microwave to return from set locations. Along with being a quick and incredibly accurate way of measuring distances, it's also possible to work out the angles if you know how far both other locations are from your own position. It's then easy to create a network of triangles as you would with triangulation.
Both triangulation and trilateration face a problem where there's a lack of hills though, and it may not be physically possible to see between two different locations in a triangle. Traversing is the solution, using the same measurement devices as trilateration but this time measuring the distances and angles between successive survey control points. Unlike triangulation and trilateration, there's no requirement to end up at the same starting point, although the use of more locations does mean it's possible to loop round to the start again.
Traversing may be more flexible when it comes to tricky conditions, but adding more control points to the mix, along with different shapes or even open-ended traverses means it's also impossible to use trigonometry to double check angles, and it's slightly easier to make mistakes without noticing.