Wednesday, 6 February 2013

Coastwalk distances

On his website, Tommy B. claims that his walk around the coastline of Britain will be 7,000 miles. To me, that sounds on the long side.

So how long is the coastline? The first paper on fractals, a massively useful branch of mathematics, was entitled 'How long is the coastline of Britain?'. In the paper, BenoƮt Mandelbrot states that the length of the coast increases to infinity the closer you examine the detail. Measure it on a roadmap, and it would be shorter than if measured on a 1:50,000 map, which in turn is shorter than on a 1:25,000 map. On the ground, it would involve measuring around every pebble and rock; a near infinite length. The picture of Loch Ewe below shows the problem - the coast is never straight.

The Ordnance Survey claim that the length of the mainland (excluding islands) is 11,075 miles; the British Cartographic Survey come up with a similar figure, with more details. As it is often impossible to walk along the Mean High Water, what distance can we expect to walk?

Most people who have walked the coast have taken ferries, and that makes a journey of about 4,500 miles. This can be reduced by taking a few more ferries (for instance Ardrossan to Brodick, then Lochranza to Claonaig), but 4,500 seems the norm. Without taking ferries, and leaving out islands, it seems to be about 6,000 miles. I got up to near 6,300 miles only be doing a couple of island (Anglesey, Arran) and walking some tidal rivers further than the first crossing point.

In the book about his 1978 walk, John Merrill claims he walked 6,824 miles, measured using a pedometer. Whilst I was on my walk, I got a phone call from one of the other walkers that year, Graham. He had been using his GPS to measure distances, and noted that the distances in Merrill's book were large overestimates. I did the same test with my GPS, and came to the same conclusion.

Since then, I have done several walks with both pedometer and satellite navigation to see how they match up. Whilst on the level both correspond remarkably well with the distance measured on a map, whereas on hilly terrain the pedometer generally overestimates compared to the GPS and map.

The reason for the difference is simple: a pedometer relies on the concept of an average stride length. It is easy to maintain a similar stride length on the flat, but it is harder to do this on hills, where strides tend to shorten. Although a small effect, it adds up considerably over the course of a day, week or year,

Since my return, I measured my route electronically on the map, and think the figure of 6,200 to 6,300 miles is realistic for my route.

At the end of the day, the distance walked is somewhat irrelevant. Bragging about distance or speed is not the point of the walk: just achieving the feat should be enough. After all, under forty people have done the walk in one go; less people than have made it to the top of Everest in one day.

You are only competing against yourself, not others.


Alan Sloman said...

I've only just caught his blog - he started yesterday, but it should be a good one to follow.

bernieT36 said...

Perhaps there is also discrepancy due to vertical distances travelled? If you are measuring distance on a 2D map you are unlikely to take into account the vertical distance travelled. Perhaps the same is true with the GPS measurements. Using the pedometer you are measuring the horizontal and vertical distance walked. If you think of the slope up a hill or mountain as a triangle, the distance walked during the ascent is the hypotenuse, whereas the distance walked on a 2D map is the bottom side of the triangle, which is shorter.

David Cotton said...

Alan: indeed. I quite like the way he writes, and I think he's going to have a riotous time as he travels around.

David Cotton said...


For various reasons, I don't think the vertical distance goes anywhere near accounting for the difference - there just isn't enough ascent. But it's a good question, and probably worth a blog post all of its own.