Where is Scotland's pole of inaccessibility?

The first question you might be asking is 'what is a pole of inaccessibility'? Well, it typically refers to the furthest point from the coast - either at sea or on land. In this case, I've calculated Scotland's pole of inaccessibility using the coastline (Mean High Water mark) and arrived at a single, fairly accessible point a few miles from Braemar, in Glen Quoich. It's just over 41 miles from the sea and at an elevation of about 470 metres above sea level. It's almost slap bang in the middle of the Cairngorms National Park, as you can see below. This all began when Andy Arthur asked me an entirely different question on Twitter last night about dividing Scotland in two, but that's a different story with a different answer. 

UPDATE, 25 June 2020: a Braemar resident very kindly got in touch, went to the pole of inaccessibility (I provided accurate coordinates), and has taken some photos of it. Scroll to the bottom to see these.

Actually quite an accessible point, if you're keen

Where's the nearest coast to this point? Well, Dundee comes close and so does Montrose, but by my reckoning the nearest coast is just off Inverness (near the A96 and the big Tesco, since you asked). Nairn beach comes close as well though. In reality, as Colin Angus has pointed out, it's going to be more than one point but I chose Inverness because it's surely one of them, plus home town bias (EDIT: see bottom of post for the three closest points). From the centre of Braemar it's about three and a half miles to the point of inaccessibility. Here's how that looks on a national map (below) and some zoomed-in maps too. It should go without saying that this calculation is based only on what might be called 'mainland' Scotland for the purposes of this exercise - i.e. the calculation is based on the big landmass you see highlighted below in the first image.

The point furthest from the sea

Looks like you can walk pretty close to it

OS 20km tile N008, since you ask

To calculate this, all I did was load a detailed shapefile into QGIS, then I divided the Scotland file into separate polygons and extracted the 'mainland' polygon. Once I'd done that I just ran the 'Pole of inaccessibility' tool from the Processing toolbox and got the point you see here. I then did some buffering at single mile intervals to explore it a bit further, as you can see below - and above in the zoomed-in one.

The shading is 1 mile buffers - from the coast

The white lines are single mile buffers

By now, you might be thinking something like 'but how does this compare to the location of the geometric centroid of mainland Scotland'. Admit it, you definitely were thinking this. Well, the answer to that question is that it's just over 42 miles away to the south west, in between Loch Ericht and Blackwater Reservoir near Kinlochleven. See below for a couple of maps on this - and as always if you spot something iffy here or think this doesn't add up, feel free to get in touch. 

Amazing knowledge to impress your friends

The beating hearts of Scotland

I suppose the amazing thing about all this is that you didn't now how much you needed to know it until you knew it. I would say it's pointless information, but there are at least two points on the map above that provide evidence to the contrary. A little bit of map knowledge can't do us any harm, and you might even be able to use this to visit Scotland's pole of inaccessibility and then tell all your friends about it.

If you need a map of how to get there, see below.

There you have it - white lines are a mile apart

Addendum

A short addendum here because I couldn't leave this without knowing where the closest coastal points were, based on the Mean High Water definition. It turns out it's by Inverness, the tidal part of the Tay to the north of Perth Harbour, and the tidal parts of the South Esk just by Montrose Basin. The circle in the map below has a 41.25 mile radius from the pole of inaccessibility shown above.

Yes, Perth has a harbour

Obviously, this is 'coast' by the official definition

This is the most 'coasty' of the coastal points

I'd begin from Inverness if I were you

Technical post-script

Despite spending literally quite a few minutes on all this, I couldn't figure out a way to calculate a pole of accessibility for Scotland that didn't treat the border with England as coast. Not that this really matters anyway because you can eyeball it and see that it's not in the south. I also manually checked it. But, this does mean that the internal buffer map above should be read in this context - i.e. the buffers from the border are obviously not from the coast. In order to show a bit more of this, I've taken the circle in the maps above and centred it roughly where I think the pole of inaccessibility is in the south of Scotland - somewhere around Hawick I suspect. If I had spent a lot of time on this, I might have been able to solve it but for the time being a manual check on this is all I need.

The border is not the coast, obviously

Here are some photos of Scotland's 'pole of inaccessibility' - with a pole marking the spot!

As I said above, these were sent to me by a very kind local resident, so I didn't travel here to take them but I hope to do so one day in the future. The pole of inaccessibility is at the edge of the Glen Quoich Caledonian pinewoods and birchwoods, as you should be able to see from the photos. It is surrounded by expanding woodlands, so the view will be very different in a few decades' time! (words provided by our friendly on-the-ground Braemar resident who lives less than 5km away from this point).

Looking south to Morrone

Looking southwest to Creag Bhalg

Looking northwest

Small Scots Pine

Here's the pole - looking at Caledonian pinewoods

How long is the coastline of Great Britain?

This is a bit of a long read, so if you really want to know the answer to the question in the title of this post, it's very simple: it depends upon how you measure it. Or, you could say that the coastline of the island of Great Britain is infinitely long. But this doesn't really help anyone who wants to walk or kayak or swim round this island, so I'll attempt to answer the question here. Take a look at the image below and you'll see that I've calculated the distance of the coastline round the island of Great Britain as 11,023 miles. 

Quite a lot of coastline for a small island

But hold on a minute, I also calculated it again and got an answer of 3,876 miles, as you can see below. What's going on here? Well, the first image is an extremely detailed digitised representation of the coastline of Great Britain and surrounding islands (bearing in mind 'detailed' is a relative concept). This first map is represented by 2,282,000 individual vertices which create the polygons you see in the image above. 

In the second map, only 0.1% of these vertices are retained, so the geographical features you see below are represnted by 2,282 individual vertices. You can't see much different between the two at the scale you view them at here but if you were trying to navigate your way into a harbour or sea loch on the west coast of Scotland, for example, it would make a big difference. Click the first image to enlarge it and then compare it to the next one and you will see some differences, but nothing too drastic.

The coastline length is a function of how you measure it

At this point, you might be thinking 'hasn't this got something to do with fractals and Benoit Mandelbrot?' - and you'd be right. He wrote a very famous paper in Science in 1967 on exactly this topic, entitled 'How long is the coast of Britain'. The answer is that there really is no definitive answer - it's all about how you measure it. But let's say you want to swim or kayak around the coastline of Great Britain and nearby islands. How far would you have to travel? I tried to calculate this based on a 1km distance from the shoreline and concluded that it could be done by covering fewer than 2,000 miles - even though the coastline seems to be a lot longer. After all, you wouldn't want to go in and out of every little cove and estuary.

Be my guest

I created a little gif based on different ways of measuring the British coastline, starting off with a file that included 100% of the vertices from my original Ordnance Survey map layer (see notes below for more on this). I then created files with fewer and fewer vertices retained, all the way down to a non-sensical shape which retained hardly any of the original points. This is what I got - at 2 seconds per frame (note '% of vertices retained' figure in each image):

Coastline length at different measurement scales

It's a bit difficult to see the difference between some of these images at this scale, so I also zoomed in to the west coast of Scotland to produce another little animation. This time, you can really see more of the difference between the layers I produced. The figures on the graphics indicate what percentage of the original vertices were retained in each case. Below, this, I have also provided a still image with different versions of the coast overlaid on top of each other, just to demonstrate the impact of reducing the number of vertices on the representation of the coastline, and hence its length.

This shows Morar, Mallaig and Loch Nevis 

Each line represents a different level of generalisation

I then decided to take a smaller island and extract the individual vertices (also known as nodes) that make up the shapes you see in the maps above. For this, I chose the Isle of Skye because it's one of the biggest British islands and the coast is highly irregular and indented. Using the version of the original shapefile where I retained 1% of the original vertices, Skye is represented by 772 individual nodes joined together to make a single polygon, as you can see below.

This produces a pretty good approximation of the coastline of Skye for most purposes. At this resolution, the coastline of Skye comes in at 330 miles (530km), compared to 456 miles (733km) at the original resolution. But of course we need to remember that if we had digitised around every single rock around the coastline the length would be nearly infinite. If you measured the coastline with a matchstick, for example, you'll get an extremely high value (and a sore back).

Skye represented with a polygon comprised of 772 vertices

Here's what this looks like when you show them one by one, in an animated gif - just to give you an idea of how it is plotted spatially. This is shown at 15ms per frame, so the dot fairly zooms around the coastline. All of this also gives you a little insight into how a GIS deals with geometry and what goes into the shapes that you see on your screen. It also helps explain why the very detailed, highly accurate spatial data files we can download from Ordnance Survey aren't always the most appropriate ones to use in small scale mapping. Or, maybe I just wanted to make another geogif, but either way I think I learned something.

A dot going round the Isle of Skye at 99,000 mph (forever)

So, how long is the coastline of Great Britain? Well, if you want to swim or kayak around all islands then you should think about training for a distance of around 2,000 miles and if you want to walk the coastline of Great Britain only then it's most likely going to be a bit more, or maybe a bit less - but that depends upon how you plan your route. Despite all the uncertainty, however, I think we can all agree that you'll need to go more than 1,024 miles.

Yes, this is Britain (kind of)

Last of all, I also did a little gif showing the 174 vertices of Great Britain when the file is massively reduced - so I'll end with this.

Another one, just for fun

Notes: I used the OS OpenData Boundary Line product for the coastline. This was a polyline file so I converted it to a polygon and then generalised it several times using the Visvalingam algorithm in mapshaper. Contains OS data © Crown copyright and database right 2015. You'll see if you search online that my measurements are close to those of others - so I'm at least as right or wrong as some people. If you're interested, you might want to look up the coastline paradox as well and, of course, Lewis Fry Richardson. Other big British islands? After the island of Great Britain, it's Lewis and Harris at 741 miles of coastline (1,193km), the mainland of Shetland at 692 miles (1,113km), Skye at 456 miles (733km) and North Uist at 334 miles (537km). Remember that this refers to coastline length and not land area.