The longest line (part 2)

In my last blog piece I wrote about my attempt to find a longer straight line in Great Britain that doesn't cross a public road than the one identified by Ordnance Survey in their 2019 blog. I did this using their OS Open Roads dataset, and I excluded public roads because that's what I think makes most sense. I found a longer line in a different area, though I definitely wouldn't recommend trying to walk it but I would recommend watching this video. I wasn't quite satisfied that my previous line was the definitive single longest line possible so I spent a bit more time on it and now I'm back to report my results. All of this was done in QGIS, using open data from Ordnance Survey - and just a bit of curiosity. The original OS piece was in response to a question on Twitter but I also found it very interesting from a methods point of view. And now here's a map of the single longest straight line I think you can possibly find between roads in Great Britain. I'll say a bit more about the method below, for the nerds. Here's the web map of the new longest line. And here's the Scottish Outdoor Access Code.

What I now believe is the definitive 'longest line'

Was I wrong at first? Well, no, in the sense that I was still correct in stating that I'd found a longer line - in a different area - than the original OS line, but I didn't quite find the single longest line possible. The line I have found is roughly in the same location though and this is all just a mix of curiosity, mathematical geometry and fun so there's no big issue here. Look for longest-line-new in this folder (gpkg, shp and geojson formats) if you want to load up the line in your GIS software.

But I would strongly suggest that if anyone wants to walk this route they should be extremely careful and only attempt in good weather, and if they are very experienced in Highland terrain (e.g. thigh-deep heather, nasty, tussocky, holey land, murderous midgies, etc). I know myself how hard it can be to walk over this terrain and how much pain it can cause. Many difficult walks over the years have proven this, including a particularly bad decision in Knoydart a few years ago where it took us about an hour to walk 500 metres over what looked like flat ground!

In doing all this I also found a much longer line in England than the one identified in the original OS piece - over 35km vs 29km. This was the case even if I used the file that has the restricted roads in it. I also found a longer one for Wales too but in both these cases there is no right to roam so I don't want to encourage trespassing.

You can read about the method below, but here are a few images from my map adventures.

All areas > 100 sq km between roads

Generating sets of 'longest line' candidates

I got to about 35km straight line in England

Yes, I got carried away with myself again

What about the distance over terrain? Well, that's important so I did the same as last time. I took the longest line, plonked it on top of the OS Terrain 50 digital elevation model and then generated a distance for the line. Obviously if I had even more accurate terrain data (Terrain 5 for example) then the distance would be a bit more.

So, a nice wee 50 mile stroll

This was an interesting methodological challenge and I think I've found the definitive longest line you can travel along a straight line without crossing any public roads in the UK. See my original blog post on this for more on the background.

A revised web map - I think this is the final answer

The method - let me know if you have a better, super-quick method :)

In theory the task is easy. Just draw a straight line inside the biggest gap in the road network, defined using the OS Open Roads dataset. It's quite easy just to eyeball the biggest gaps in the road network and come to a pretty good answer but this is not sufficient if you want to be systematic and definitive. I didn't just eyeball it the first time, there was more to it than that, but also I wasn't completely exhaustive either. So, here's what I did this time, in brief. Note that the data is just for Great Britain but the longest line is the longest in the UK because there are no gaps in the road network in Northern Ireland anywhere near this big.

I'm reporting my method for non-restricted roads, but I also did it with the entire OS Open Roads dataset, including restricted roads - just for fun.

1. Download the latest OS Open Roads dataset and add it to QGIS.
2. I decided to polygonize the entire OS Open Roads dataset because of a suggestion by John Murray, and this was pretty useful. This was also pretty quick and simple on my computer.
3. Then I decided to deal with the roads a bit differently, because they needed to be cut out of the 'between roads' polygons I made so that I could fit my lines entirely within the polygon geometry. But also because the OS Open Roads data is just centre lines and they have no thickness. So I approximated here and buffered the roads to 10 metre width, and dissolved the result. Then I ran a Difference on them to end up with a final set of polygons - lots of big 'no roads here' polygons. I only did this for areas of 100 sq km or more - for all road types this gave me 116 areas and when I removed restricted roads I ended up with 141 areas. 87 out of 141 are in Scotland.
4. Then I needed a simple way to identify the longest line within polygons. This is in theory very easy but also you could waste a lot of time computing vertex-vertex distances here that you don't need to - you're only really interested in the furthest vertices from each other that can be connected with a line entirely within the polygon. So for this I used the Python console in QGIS and a little snippet I found on StackExchange (of course). I've copied this below in case it ever disappears from there. With thousands of vertices this can take a long time so try it one shape at a time if you are doing it yourself. You could just draw a set of lines to/from selected vertices but this is also a bit of a pain, particularly because it won't avoid the roads.
5. How could I be sure which intra-road area contains the longest line? Well it's pretty easy to see visually but to be sure I created some minimum bounding circles and computed the radius and then the longest line was still clearly in my original Monadhliath Mountains area, so that was good. You can see a bit of this in one of the screenshots above.
6. Then it was a case of doing some checks, double checks and then writing this short note.

import itertools

layer = iface.activeLayer() #Click layer in tree

#Create empty line layer

vl = QgsVectorLayer("LineString?crs={}&index=yes".format(layer.crs().authid()), "Longest_line", "memory")

provider = vl.dataProvider()

#For each polygon find the longest line that is within the polygon

for feat in layer.getFeatures():

    verts = [v for v in feat.geometry().vertices()] #List all vertices

    all_lines = []

    for p1,p2 in itertools.combinations(verts, 2): #For every combination of two vertices

        all_lines.append(QgsGeometry.fromPolyline([p1,p2])) #Create a line

    all_lines = [line for line in all_lines if line.within(feat.geometry())] #Check if line is within polygon

    if len(all_lines)>0:

        longest_line = max(all_lines, key=lambda x: x.length()) #Find longest line

        #Create a line feature from the longest line within polygon

        f = QgsFeature()

        f.setGeometry(longest_line)

        provider.addFeature(f)

QgsProject.instance().addMapLayer(vl)

Population Density Comparisons

I grew up in the Highlands of Scotland - well kind of. Perhaps the New York of the Highlands is more accurate (Inverness, obviously). But I am also partly of crofting stock so spent a lot of time in very sparsely populated areas. I lived in Liverpool for 5 years and now live in Sheffield and visit London a lot, and I also like looking at maps and making maps. That's why I was particuarly interested in Steven Kay's population comparison map which compared circular areas centred on London to the populations of Scotland, and also Scotland plus Wales and Northern Ireland.

You can see the original map here

Steven has lots of really interesting, clever maps on his website, many of which do this kind of thing. I also really like his Edinburgh comparison with less populated European nations, as you can see below.

Edinburgh - population about 495,000

Obviously, at one level, such graphics don't really tell us that much beyond the fact that some places are really densely populated, and some aren't - and we all know that. But their power lies in the cognitive trick of the simple spatial overlay. By putting them in the same place and simplifying the shapes to roughly circular ones it makes the comparison more powerful and immediate. And this is why it's both easy to understand and quick to digest. It's also what makes me like it as a simple comparison. There are lots of other examples of this kind of thing online, including one I did in the past looking at the Highland local authority area vs Greater London (which is 32+1 authorities, but also a single political space).

Most definitely not a town planning policy suggestion for Nicola Sturgeon

Talking of the Highlands, the other Steven Kay piece I really liked was his analysis of which parts of Britain and Ireland are closer to Westminster, Dublin, Stavanger, and Oslo respectively. My part of the Highlands is, of course, closer to Stavanger than Westminster. But again, this is just a geographical curiosity and not a reason to suggest we be governed from there! Mind you, their sovereign wealth fund would be nice (current value and nice video - click here).

So, where were we - ah yes... These maps are interesting geographical artifacts but they often have a kind of power that connects with people at different levels - including the emotional. But that's a whole other topic.

For the time being, it's interesting to note the different responses to my tweet of Steven's map. I only noticed it because I went back into the Flickr QGIS feed the other day to change my password after the Yahoo! hack. I liked his map because it made an interesting comparison and even though I know London has 'lots of people' and a good few million more than Scotland, seeing it in this way was quite shocking. For some, that might feel threatening (see notes below) but for others - including me - it's just a comparison which captured my attention as a data/map buff.

Notes: for map nerds, Alan MacEachren's 1995 'How Maps Work' has some good stuff on how maps are imbued with meaning - Part II from p. 213. The section on map connotation (p. 336 onwards) is quite relevant here. For some, the London/Scotland comparison is immediately annoying because of the nation/city comparison (I have a little sympathy here) and for others there is something of an 'incitive connotation' because of the current state of UK politics and particularly the push for Scottish indepdenence vs continued Westminster governance. While I'm on a roll, I'll add that Norway has about £56bn invested in the UK, including ownership of 50% of Meadowhall in Sheffield and 25% of Regent Street in London. So, if you are ever at a loss for words, impress your friends with this knowledge. Tenous links here are that I live in Sheffield and Scotland and Norway have similar populations.

The Road to Applecross

The road to Applecross, known as Bealach na Bà in Gaelic (the Pass of the Cattle), is a narrow, winding, single-track road in the west Highlands of Scotland. It's quite famous among cyclists, bikers and drivers - and notoriously snowy in winter. It's also not for the faint-hearted. It even has its own Tripadvisor page. As a Highlander in exile, I dream of remote, snowy places but don't get to go there much so of course I turned to Google Streetview to refresh my memory. As it happens, the Streetview car went on this route on a remarkably nice day. So I made a little time-lapse video, which you can see below, in addition to a map of the route.

Here's the warning sign before you hit the road...

Source: Neil G Hamilton, Flickr (CC BY 2.0)

This is the exact same route I used in the video.

This road is also part of the route of the north of Scotland's 'North Coast 500' which has recently become really popular among cyclists and other people who love driving rain and extreme pain. But, the scenery is amazing and there are plenty of good places to stop off on the route. Billed as 'Scotland's answer to Route 66' it also has an incredibly positive Tripadvisor page. This has inadvertently turned into a marketing piece for the Highland Tourist Board when all it was supposed to be was a bit of holiday blogging on a great Highland road, so I'll end here.

Further information: I used Brian Folts' brilliant Streetview Player to generate the frames and then just made an mp4 file on my own.