UKC

I am trying, in vain, to find a list of individual counties by length of coastline. Some counties e.g Devon and Cornwall, are easy to find, but a lot of the other ones don't seem to have this information.

The problem is that coastline length isn't possible to measure because coastlines are a) fractal and b) constantly changing.

So any numbers you do happen to come across are gross approximations.

Sorry to be the barer of bad news.

But some are well known to a high accuracy - Oxfordshire is exactly 0 km, 0 inches if you prefer Imperial units.

And Rutland is even less

Yes, but it increases to nearly double that length at low tide!

How big is your ruler? - https://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistic...

Then again other coasts have lots of islands...!

I'd ask the OS - they have measured this but their blog link has expired https://twitter.com/OrdnanceSurvey/status/828666341552959489?lang=en-GB

Can you even find a definitive list of counties? I needed to for work and quickly discovered that there are several contradictory definitions of what exactly constitutes a county.

Yes, but if you look at them with the same resolution, it is perfectly possible to make valid comparisons.

Sadly the way back machine / internet archive doesn't appear to have it (https://www.ordnancesurvey.co.uk/blog/english-county-longest-coastline) either

but I did find

https://diamondgeezer.blogspot.com/2020/10/which-county-has-longest-coastli...

I’ve got half a crown says this will be wittiest post of the week 

You might need to explain what half a crown is for some of the younger UKC crew - I presume there are some and that we're not all aging white men.

Indeed.  If you make more detailed studies you can determine their Hausdorff dimensions to enable comparisons at other scales.  Being fractal doesn’t mean the length is undefined or immeasurable, just that it comprises more information than a scale number.

Lazy pop sci nonsense to say you can’t measure the length of a coast because it’s a fractal. 

What about Rutland Water. That's quite a big lake.

My grandparents used to talk about crowns

Just over 2 bob

Can you explain this more?

I've always assumed measuring things like coastlines to be a complete nonsense, for the above reason. Are you saying there's a way to definitively say one coastline is longer than another, without having to specify at what scale you're viewing the two coastlines? 

It depends on the specific coastlines and the “Hausdorff dimension” of each, which says how their measured length scales with ruler size.

If both have the same characteristics ie the same Haussdorf dimension - meaning their measured length increases by the same fraction when you, say, halve the length of the measuring ruler, then if one is longer then the other for one particular measurement size, it’s definitively longer for all measurement scales.

If they scale differently - for example a coast made of straightish cliffs like near Saltburn vs the complex marshes of Foulness island, then there may be a critical ruler length for which one coast is longer for rulers smaller than the critical scale, and the other is longer for longer rulers.

For coastal counties in some given geographic region the way length scales with measure size is going to be pretty similar meaning that a ranking of coast lengths is going to be invariant over a wide range of measurement scales, so long as you take a fixed view on the inclusion or exclusion of tidal river sections across those scales.

Now you're just being silly

Whilst I know it’s not a county, but when Blackburn joined up with Darwen, to create Blackburn with Darwen, they effectively lost coastline due to each of them loosing a boundary.  
Edit: you know, the boundary that has gone. It’s quite hard to explain. 

If you're using the ceremonial counties, there aren't that many for England. For UK it does add a lot more.

But when you do look up each individually you'll need to be sure they're measured similarly - are they including islands off the coast which makes a huge diffence to the number, especially for Scotland.

For Great Britain mainland, once we have a complete coastal path, you'll be able to just walk round and count steps.

But then of course you'll have to be sure that all your steps are the same length - I would recommend tying your legs with a length of thin static rope which will stop you overstriding - you'll have to be very disciplined to make sure every step fully stretches the rope.

Also, you'll need to measure any height difference for each step, a bit of simple trigonometry will then sort out the horizontal map distance.

Any volunteers?

I know I'm just being silly with my previous post but it does help illustrate the problem, especially as soon as you start to think "the path cuts across the tip of that headland, should I add on something for that?", etc.

Coastline length does not have an absolute answer, totally dependent on ruler length.

It would however be interesting to see the answer to the OP with different ruler lengths, say 1km, 500m, 200m, 100m, 50m. All of those should be doable for Great Britain mainland with standard 1:25,000 OS maps.

Question: could the starting position make a significant difference? (e.g. 1km ruler starting a 0, at +200m, +400m, etc)

For a fixed ruler length, then yes.

As an example, consider a river with a meter wide and 5 km long tidal section.  If you start measuring from a point adjacent to the river mouth with a 5.1 km long ruler, you’re going to miss it entirely.  If you start around 0.1 km down coast from the mouth, you’re going to include it.

There’s massive potential for aliasing effects based on where you start.

As long as your ruler length wasn't significant compared to the coastline being measured, I'd say the starting position could make a significant difference (as in Wintertree's extreme example) but the likelyhood of that happening and not being swamped or negated by other measurement variation (i.e. noise) wouldn't be significant.

This is the key to the inner scale of the question!

I was pondering if you can measure below a meter or so in scale?  No two tides are perfectly alike, the water level between any two waves or ripples is not alike, atmospheric pressure fluctuations change the sea’s position, small rocks, pebbles and grains of sand at the waterline are constantly shifting.

Somewhere not far below a meter in scale, the temporal noise explodes and the somewhat fractal nature is meaningless against the frothing noise.  When was the last time you saw someone out there measuring a coastline with a 30 cm ruler?  

Every county in England's coastline is 550km* long.

* measured to an accuracy of plus or minus 550km.

Three Scottish counties (not council areas) are entirely islands.

Shetland, Orkney and somewhere in the Outer Hebrides?

There's a UKC member called Slartibartfast - best ask them directly

Bute - somewhat forgotten.   Arran, Cumbraes and some other island  what was it now?

Careful.. you’ll be forced to mention Kolmogorov before you know it!