How long is the coast of Great Britain? It depends how you measure it

How much of this is there? Cornwall enjoying the sun. Image: Getty.

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 on how you measure it.

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. When I calculated it again, I 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 per cent of these vertices are retained, so the geographical features you see below are represented 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.The coastline length is a function of 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 per cent of the vertices from my original Ordnance Survey map layer (I’ve explained the methodology in a note at the bottom of this artcile). I then created files with fewer and fewer vertices retained, all the way down to a nonsensical shape which retained hardly any of the original points.

This is what I got, at 2 seconds per frame. (Note the “percentage 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’ve 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 per cent 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 one 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 geographical information system (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. If you want to walk the coastline of Great Britain, then it's most likely going to be a bit more, or maybe a bit less (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.

Dr Alasdair Rae is a senior lecturer in the geography department of the University of Sheffield. 

This article was originally posted on his blog, and is reposted here with the author's permission.

 


Some notes on methodology: 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.

What are the 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.

All images in this post courtesy of the author.

 
 
 
 

Was the decline in Liverpool’s historic population really that unusual?

A view of Liverpool from Birkenhead. Image: Getty.

It is often reported that Liverpool’s population halved after the 1930s. But is this true? Or is it a myth?

Often, it’s simply assumed that it’s true. The end. Indeed, proud Londoner Lord Adonis – a leading proponent of the Liverpool-bypassing High Speed 2 railway, current chair of the National Infrastructure Commission, and generally a very influential person – stood on the stairs in Liverpool Town Hall in 2011 and said:

“The population of Liverpool has nearly halved in the last 50 years.”

This raises two questions. Firstly, did the population of the City of Liverpool really nearly halve in the 50 year period to 2011? That’s easy to check using this University of Portsmouth website – so I did just that (even though I knew he was wrong anyway). In 2011, the population of the City of Liverpool was 466,415. Fifty years earlier, in 1961, it was 737,637, which equates to a 37 per cent drop. Oops!

In fact, the City of Liverpool’s peak population was recorded in the 1931 Census as 846,302. Its lowest subsequent figure was recorded in the 2001 Census as 439,428 – which represents a 48 per cent decline from the peak population, over a 70 year period.

Compare this to the population figures for the similarly sized City of Manchester. Its peak population also recorded in the 1931 Census as 748,729, and its lowest subsequent figure was also recorded in the 2001 Census, as 392,830. This also represents a 48 per cent decline from the peak population, over the same 70 year period.

So, as can be seen here, Liverpool is not a special case at all. Which makes me wonder why it is often singled out or portrayed as exceptional in this regard, in the media and, indeed, by some badly briefed politicians. Even London has a similar story to tell, and it is told rather well in this recent article by a Londoner, for the Museum of London. (Editor’s note: It’s one of mine.)

This leads me onto the second question: where have all those people gone: London? The Moon? Mars?

Well, it turns out that the answer is bit boring and obvious actually: after World War 2, lots of people moved to the suburbs. You know: cars, commuter trains, slum clearance, the Blitz, all that stuff. In other words, Liverpool is just like many other places: after the war, this country experienced a depopulation bonanza.


So what form did this movement to the suburbs take, as far as Liverpool was concerned? Well, people moved and were moved to the suburbs of Greater Liverpool, in what are now the outer boroughs of the city region: Halton, Knowsley, St Helens, Sefton, Wirral. Others moved further, to Cheshire West & Chester, West Lancashire, Warrington, even nearby North Wales, as previously discussed here.

In common with many cities, indeed, Liverpool City Council actually built and owned large several ‘New Town’ council estates, to which they moved tens of thousands of people to from Liverpool’s inner districts: Winsford in Cheshire West (where comedian John Bishop grew up), Runcorn in Halton (where comedian John Bishop also grew up), Skelmersdale in West Lancashire, Kirkby in Knowsley. There is nothing unique or sinister here about Liverpool (apart from comedian John Bishop). This was common practice across the country – Indeed, it was central government policy – and resulted in about 160,000 people being ‘removed’ from the Liverpool local authority area.

Many other people also moved to the nearby suburbs of Greater Liverpool to private housing – another trend reflected across the country. It’s worth acknowledging, however, that cities across the world are subject to a level of ‘churn’ in population, whereby many people move out and many people move in, over time, too.

So how did those prominent images of derelict streets in the inner-city part of the City of Liverpool local authority area come about? For that, you have to blame the last Labour government’s over-zealous ‘Housing Market Renewal Initiative’ (HMRI) disaster – and the over enthusiastic participation of the then-Lib Dem controlled city council. On the promise of ‘free’ money from central government, the latter removed hundreds of people from their homes with a view to demolishing the Victorian terraces, and building new replacements. Many of these houses, in truth, were already fully modernised, owner-occupied houses within viable and longstanding communities, as can be seen here in Voelas Street, one of the famous Welsh Streets of Liverpool:

Voelas Street before HMRI implementation. Image: WelshStreets.co.uk.

The same picture after HMRI implementation Image: WelshStreets.co.uk. 

Nonetheless: the council bought the houses and ‘tinned them up’ ready for demolition. Then the coalition Conservative/Lib Dem government, elected in 2010, pulled the plug on the scheme. 

Fast forward to 2017 and many of the condemned houses have been renovated, in a process which is still ongoing. These are over-subscribed when they come to market, suggesting that the idea was never appropriate for Liverpool on that scale. 

At any rate, it turns out that the Liverpool metropolitan population is pretty much the same as it was at its peak in 1931 (depending where the local borough boundaries are arbitrarily drawn). It just begs the question: why are well educated and supposedly clever people misrepresenting the Liverpool metropolis, in particular, in this way so often? Surely they aren’t stupid are they?


And why are some people so determined to always isolate the City of Liverpool from its hinterland, while London is always described in terms of its whole urban area? It just confuses and undermines what would otherwise often be worthwhile comparisons and discussions. Or, to put it another way: “never, ever, compare apples with larger urban zones”.

In a recent Channel 4 documentary, for example, the well-known and respected journalist Michael Burke directly compared the forecast population growths, by 2039, of the City of Liverpool single local authority area against that of the combined 33 local authority areas of Greater London: 42,722 versus 2.187,708. I mean, what bizarre point is such an inappropriate comparison even trying to make? It is like comparing the projected growth of a normal sized-person’s head with the projected growth of the whole of an obese person, over a protracted period.

Having said all that, there is an important sensible conversation to be had as to why the populations of the Greater Liverpool metropolis and others haven’t grown as fast as maybe should have been the case, whilst, in recent times, the Greater London population has been burgeoning. But constantly pitching it as some sort of rare local apocalypse helps no one.

Dave Mail has declared himself CityMetric’s Liverpool City Region correspondent. He will be updating us on the brave new world of Liverpool City Region, mostly monthly, in ‘E-mail from Liverpool City Region’ and he is on twitter @davemail2017.