# GB’s longest linear walk without crossing a road

Here at OS, we get asked some curiously specific questions by our Twitter followers. Our teams are always up for a challenge and, as this query required map exploration, who better to ask than our amazing Consultation and Technical Services (CaTS) team? Please see the query embedded below.

@OrdnanceSurvey Hello! An enquiry if I may…..what (and where) is the longest distance you can walk in a straight line in England/Wales/Scotland without crossing a road (defined as a paved surface for vehicular use)?? Planning a potential expedition. Ta!

— Roger Dalton (@100in7) November 15, 2018

Now, not only were our CaTS team able to identify the longest distance in Great Britain you can walk in a straight line without crossing a road (which consequently you may have read about in some newspaper articles), but as this was in Scotland, the team also decided to find the longest in both England and Wales too.

So for Great Britain, the longest straight line that you can walk without having to stop, look and listen is 71.5km or 44.43 miles (71500.817767m) and is unsurprisingly in Scotland. Crossing the Cairngorms, the distance goes from 262540, 778255 on the A9 and ends at 328042, 806921 south of the hamlet of Corgarff. The high point is on the summit of Beinn a’Bhuird at 1,179m (3,870ft).

While you have the right to roam in Scotland, it doesn’t mean it is advisable to roam. As quoted in The Times article, our CaTS member Eddie Bulpitt states “I wouldn’t recommend anyone do it unless they are very conversant with a map and compass. It is not following known tracks or paths, and it looks like there may well be several scrambles along the way too”. The relevant maps are below.

In Wales, the longest straight walk is 22.242 km (22242.534959m) and runs along the south of the Cambrian Mountains. Its northernmost point is located at 276605, 268059 on an unclassified minor road to the east of Ffair-Rhos, Ceredigion. Its southernmost point lies at 294252, 254502 on a classified unnumbered minor road approx. 5.25km (by road) NE of the village of Beulah, Powys.

Unlike Scotland, you do not have a right to roam and this route hasn’t taken trespassing in to consideration. Additionally this area will be remote and likely involves some water, so we do not recommend attempting it.

For England, the longest straight walk without encountering a road is in the North Pennines to the east of the Lake District. The straight line is 29.874km long (29874.438016m). The northernmost point of this line is at 369365, 543355 at a classified unnumbered minor road that comes off of the A686 and leads to Leadgate. The southernmost point is on the B6276 heading east from Market Brough/Brough, the coordinates being 381007, 515840.

Like Wales, trespassing is illegal in England, so permissions will need to be sought if crossing private land. Also, this straight line takes you right through the MOD Warcop Training Area so check this if you are thinking of exploring. This route is likely to involve water so please take this in to consideration!

**Summary of methodology**

Using OS MasterMap Highways road network, our CaTS team calculated the areas of all the polygons to identify the largest ones. This included all roads that are navigable by car, so the start and end points of the ‘straight walk’ start on vertices that are inherently within the OS MasterMap Highways road network. They then had to identify the longest straight line of sight that could be made between opposing vertex points that did not cross a road.

**Disclaimer**

Now in case you are eager to explore these areas, we must remind you that we do not condone trespassing and, as above, we cannot guarantee the routes avoid private property. Additionally, the bodies of water shown on the maps do not indicate depth as we do not have this data. Please take this in to account. If you are looking to explore these areas, make sure that you are prepared before venturing out. Finally, if you plan to investigate these areas, please do let us know via our Twitter or Facebook!

While I’m as much a stickler for accuracy as anyone, quoting the distances involved to one ten thousandth of a millimetre (71500.817767m) seems a tad extreme, being significantly less than the width of a hair.

Quite possibly Stuart, but we like to be precise! Thanks, Jocelyn

Jocelyn,

Since the accuracy of base information is no where near sub-millimeter, sub-meter at best, to quote a calculated distance and quote the result to that level of accuracy is flawed and plain silly.

The challenge and methodology was interesting enough.

Precise? May be. Accurate? Certainly not if quoting to a micron!!!

That’s a great challenge. I think I’ve found a couple of slightly longer routes on the other side of the A9. Starting on the A86 just outside of RoyBridge, head across the Monadhliath Mountains and land at the A9 just north of Carrbridge. Comes out at 74km. Alternatively, start from Roybridge and head straight past Kinveachy Lodge then the A9. Comes in at roughly 73.8km

Why are the polygons’ areas important? Theoretically, I can imagine a long, narrow (possibly non-convex) polygon with a long diameter but a small area. Do we know that this doesn’t happen for some other reason?

James’s route can be bettered slightly. Start near Carrbridge as he did, but head across the Monadhliath to just north of Stronaba on the A82 at around NN209847. Just over 78km.

For Wales, start near Tregaron and head in an easterly direction to near Newbridge on Wye, and you can clock up just over 30km. There’s some forestry towards the western end which needs to be negotiated.

There is no civil or criminal offence of trespassing in England or Wales. Any prosecution would have to be for damage, as in Scotland. Signs saying trespassers will be prosecuted mislead people on this point.

Interesting but did this really answer the question. I assumed the questioner actually wanted to attempt the route and wanted a linear/point to point rather than circular route. Not a perfectly straight line ignoring paths. So, what is the longest path that doesn’t cross roads?

These three answers are a huge disappointment. The person asking the question is planning an expedition, they are not interested in theoretical answers suitable only for wild animals.

Please answer the implied question “What is the permitted, walkable route that travels furthest in a straight line without crossing roads in each country within Great Britain?”

This is a fascinating exercise but unfortunately you haven’t answered the question, which defined roads as “paved”. Many of the tracks marked in blue on your map are not paved. If these were to be removed from the calculation I suspect we would get a different answer.

The map for the longest in England above shows another longer route. From just south of Melmerby in the north west (on the A686) south east to near Bowbank (on the B6276). This avoids the Cow Green reservoir. OK, so this crosses the road/track going up Great Dun Fell but the OS’s own route crosses a ‘road’ shared with the Pennine Way. Both appear on the OS with the same symbol so why is one allowed but perhaps not the other? Or are these tracks? Do the OS maps not show road classifications correctly then? When is a track a road?!

Thanks for your interest Tarun. The team have had a look and have said it comes down to the data that is used. The team included Restricted Local Access Roads from Ordnance Survey Highways data. These allow vehicular access and yes, by using this dataset, the line that you propose would have to cross some of these. They state that while some of these ‘roads’ might not necessarily subscribe to what people generally consider to be a road, they had to make a judgement call on what constituted a road and what didn’t, i.e. we decided that even if there was a very remote chance that we could meet a car on these roads then it would be precluded. We wanted to find a route where you didn’t have to stop, look and listen at all. We hope this helps, Jocelyn

Interesting, but rather pointless in my opinion. Also I would prefer to see more attention given to mileage conversions as well as kms. This is still the British Isles we are talking about, after all!

https://en.wikipedia.org/wiki/Metrication_in_the_United_Kingdom

Brilliant – a fascinating (if useless) bit of geography (plus geometry) that has clearly got us all staring at maps!

(I’ve ridden a bike along the gorgeous Claerwen reservoir near to the Welsh one, so that is currently my favourite 🙂

A fascinating journey into mathematical wilderness…

Any chance your team could find the longest bearing road to road in West Yorkshire by this method?

Which map/maps are needed for the new 44 mile Scottish walk, the one which doesn’t cross a road please?

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“So for Great Britain, the longest straight line that you can walk without having to stop, look and listen is 71.5km or 44.43 miles (71500.817767m) and is unsurprisingly in Scotland. Crossing the Cairngorms, the distance goes from 262540, 778255 on the A9 and ends at 328042, 806921”.

Calculated in the GRS80 ellipsoid (a = 6378137m, f = 1/298.25722210088271) using ETRS89 latitudes-longitudes a distance of 71516.149853m / 44.44 (44.438075298) miles.

Calculated in the Airy 1830 ellipsoid (a = 6377563.396m, f = 1/299.3249646) using OSGB36 latitudes-longitudes a distance of 71518.596612m / 44.44 (44.439595644) miles.

Used Charles Karney’s Online geodesic calculations using the GeodSolve utility, https://geographiclib.sourceforge.io/cgi-bin/GeodSolve: “GeodSolve is accurate to about 15 nanometers [0.000015 of a millimetre] (for the WGS84 ellipsoid)”. In emails to me from Charles Karney: “The accuracy of 15 nanometers that I quote is for paths up to half-way round the earth.” “The accuracy for the Airy ellipsoid will be (very nearly) the same as for the WGS84 ellipsoid (because the parameters are roughly the same).”

“Should even millimetre accuracy not be sufficient for you, Charles Karney has improved on Vincenty’s method with a method which has errors in nanometers (and always converges on antipodal points) – Geodesics on an ellipsoid of revolution, 2011, Algorithms for geodesics, 2012 [2013]; though Karney’s method is a lot less straightforward (someday I may get around to an implementation).”

262540, 778255 = ETRS89 56° 52’ 30.885131” N, 4° 15’ 25.337349” W; OSGB36 56° 52’ 31.591259” N, 4° 15’ 20.589518” W (from OS Spreadsheet for coordinate calculations).

328042, 806921 = ETRS89 57° 08’ 50.992252” N, 3° 11’ 27.174061” W; OSGB36 57° 08’ 51.762367” N, 3° 11’ 21.845665” W.

Ordnance Survey: “Accurate distance calculations can be done using eastings and northings if line scale factor is taken into account. There is a sheet in our projection calculations spreadsheet that does this

Using OS Spreadsheet for coordinate calculations, the British National Grid distance (hypotenuse), mid point by BNG, and local scale factors with Simpson’s Rule:

Distance using National Grid references (hypotenuse) 71500.010909090076865410453403028m.

Line scale factor 0.99974013 = 71518.596447m / 44.44 (44.439595541) miles.

Line scale factor 0.99974012833333333333333333333333 = 71518.596566m / 44.44 (44.439595615) miles.

Ordnance Survey Blog “GB’s longest linear walk without crossing a road”, Jocelyn, 10 Jan 2019:

“In Wales, the longest straight walk is 22.242 km (22242.534959m)”. “Its northernmost point is located at 276605, 268059”. “Its southernmost point lies at 294252, 254502”.

Calculated in the GRS80 ellipsoid using ETRS89 latitudes-longitudes a distance of 22258.226110m / 13.830620495 miles.

Calculated in the Airy 1830 ellipsoid using OSGB36 latitudes-longitudes a distance of 22258.569383m / 13.830833795 miles.

276605, 268059 = ETRS89 52° 17’ 48.367671” N, 3° 48’ 39.167963” W; OSGB36 52° 17’ 47.002992” N, 3° 48’ 34.777132” W.

294252, 254502 = ETRS89 52° 10’ 43.005985” N, 3° 32’ 52.691537” W; OSGB36 52° 10’ 41.589897” N, 3° 32’ 48.210731” W.

Ordnance Survey: “Accurate distance calculations can be done using eastings and northings if line scale factor is taken into account. There is a sheet in our projection calculations spreadsheet that does this”.

Using OS Spreadsheet for coordinate calculations, the BNG distance (hypotenuse), mid point by BNG, and local scale factors with Simpson’s Rule:

Distance using National Grid references (hypotenuse) 22253.28870077409479704006125722m.

Line scale factor 0.99976276 = 22258.569324m / 13.830833758 miles.

Line scale factor 0.999762758333333333333333333333 = 22258.569361m / 13.830833781 miles.

Ordnance Survey Blog “GB’s longest linear walk without crossing a road”, Jocelyn, 10 Jan 2019:

“For England, the longest straight walk without encountering a road is in the North Pennines to the east of the Lake District. The straight line is 29.874km long (29874.438016m).” “The northernmost point of this line is at 369365, 543355”. “The southernmost point is on the B6276 heading east from Market Brough/Brough, the coordinates being 381007, 515840.”

Calculated in the GRS80 ellipsoid using ETRS89 latitudes-longitudes a distance of 29887.309262m / 18.571112989 miles.

Calculated in the Airy 1830 ellipsoid using OSGB36 latitudes-longitudes a distance of 29888.290061m / 18.571722429 miles.

369365, 543355 = ETRS89 54° 47’ 02.981573” N, 2° 28’ 40.335131” W; OSGB36 54° 47’ 02.627618” N, 2° 28’ 35.041448” W.

381007, 515840 = ETRS89 54° 32’ 14.915750” N, 2° 17’ 42.195479” W; OSGB36 54° 32’ 14.442107” N, 2° 17’ 36.860735” W.

Ordnance Survey: “Accurate distance calculations can be done using eastings and northings if line scale factor is taken into account. There is a sheet in our projection calculations spreadsheet that does this”.

Using OS Spreadsheet for coordinate calculations, the BNG distance (hypotenuse), mid point by BNG, and local scale factors with Simpson’s Rule:

Distance using National Grid references (hypotenuse) 29876.602701779866189351443167064m.

Local Scale factor 0.99960897 = 29888.289920m / 18.5717223415 miles.

Local Scale factor 0.99960896833333333333333333333333 = 29888.289970m /

18.571722373 miles.

The most accurate method for calculating geographical distance, ignoring changes in elevation, is using ellipsoidal-surface formulae. “An ellipsoid approximates the surface of the earth much better than a sphere or a flat surface does. The shortest distance along the surface of an ellipsoid between two points on the surface is along the geodesic.”

Hi Thomas. The route was created in response to a tweet that we received and was devised using technology and software that would be available to most people at home sitting at their laptops. The accuracy of the length of this route reflects this which would be accurate enough for anyone planning on (carefully!) hiking the route. Hope this helps, Jocelyn

Hi Jocelyn. What are the start and finish grid ref and can you order a custom map to attempt this route. Thanks

Hi Dan. The grid references are listed in the blog and yes, it would be possible to create a relevant custom map. While we appreciate your enthusiasm, we’d like to take this opportunity to remind you this route is not for the faint-hearted and preparation is vital. Many thanks, Jocelyn

Please correct the decimals on your metre measure. The founders of the os would be horrified.

Great work you guys. Having had a good look at the Scottish route I’m going to attempt it next week. The main difficulty is actually getting to Cock Bridge. It involves taking the bus to Aberdeen (from Glasgow), bus to Aboyne, staying overnight there, bus to Ballater and finally taxi to Cock Bridge. The walk is over 100km and it does not appear t have any difficult sections apart from going up and over Ben MacDui (care needed in poor visibility) – the proviso is that you are an experienced hill walker. There are only two possible bothies and so carrying a tent is essential. I’m planning on going up this Tuesday and completing the walk the following Tuesday at Dalwhinnie (only a slight change in destination) where I’ll get the train.

No phone signal and next to no people – nice and quiet:)

Let us know how you get on, Ian Logan!

Well I’ve now done the walk and I’m retracting my comment about “it does not appear to have any difficult sections”! The amount of rain meant that there were lots of river crossings, with the River Feshie being a serious one. There was also a 2km section where there were seedlings e.g. silver birch, planted all along the path! Ben MacDui was also not on due to the wind and the amount of snow on the ground (which was not soft but actually quite hard).

If you want to read my report then you can see it on my web site: http://www.stevensonway.org.uk/index.php/your-walks/87-stevensonway/167-cock-bridge-to-dalwhinnie

I’ve also created route maps for each day using the OS’s premium subscription. Links to them are on the above web site.

Hi Jocelyn. Thanks for your reply to my post of 21 March, 2019 at 20:47.

Sorry, my reply is late.

Jocelyn, 9 April, 2019: “The route was created in response to a tweet that we received and was devised using technology and software that would be available to most people at home sitting at their laptops. The accuracy of the length of this route reflects this”.

However, the tools I used are all easily available:

Ordnance Survey Coordinate transformation tool https://www.ordnancesurvey.co.uk/gps/transformation/

Ordnance Survey Spreadsheet for coordinate calculations https://www.ordnancesurvey.co.uk/business-and-government/help-and-support/navigation-technology/os-net/coordinate-spreadsheet.html

Charles Karney’s Online geodesic calculations using the GeodSolve utility, https://geographiclib.sourceforge.io/cgi-bin/GeodSolve

If only WGS84 / GRS80 (ETRS89) ellipsoidal distances are required, then the Ordnance Survey Spreadsheet for coordinate calculations is useless for this purpose.

If only Airy 1830 (OSGB36) ellipsoidal distances are required, then only the Ordnance Survey Spreadsheet for coordinate calculations is needed, and the Ordnance Survey Coordinate transformation tool is useless for this purpose.

On my post of 21 March, 2019 at 20:47:

Jocelyn, 10 Jan 2019: “For England, the longest straight walk without encountering a road is in the North Pennines to the east of the Lake District.”

My work: “Distance using National Grid references (hypotenuse) 29876.602701779866189351443167064m. Local Scale factor 0.99960897 = 29888.289920m / 18.5717223415 miles. Local Scale factor 0.99960896833333333333333333333333 = 29888.289970m / 18.571722373 miles.”

“Local Scale factor”, of course should be Line Scale factor.

And also on my post of 21 March, 2019 at 20:47:

“The most accurate method for calculating geographical distance, ignoring changes in elevation, is using ellipsoidal-surface formulae.”

Better is: The most accurate methods for calculating geographical distance, ignoring changes in elevation / height, are ellipsoidal-surface formulae.

To add:

“So for Great Britain, the longest straight line that you can walk without having to stop, look and listen is 71.5km or 44.43 miles (71500.817767m) and is unsurprisingly in Scotland. Crossing the Cairngorms, the distance goes from 262540, 778255 on the A9 and ends at 328042, 806921”.

Using the Ordnance Survey Spreadsheet for coordinate calculations “True Azimuth [Bearing] from eastings and northings” is 64° 28’ 20.471699” or 64.472353250°. The Ordnance Survey Spreadsheet for coordinate calculations, calculates in the Airy 1830 ellipsoid.

Using Charles Karney’s Online geodesic calculations using the GeodSolve utility: Using the GRS80 ellipsoid with the ETRS89 latitudes-longitudes, forward Geodetic Azimuth is 64° 28’ 14.9175164553” or 64.47081042123759° “clockwise from north”.

Azimuths from 262540, 778255 to 328042, 806921.

“In Wales, the longest straight walk is 22.242 km (22242.534959m)”. “Its northernmost point is located at 276605, 268059”. “Its southernmost point lies at 294252, 254502”

Using the Ordnance Survey Spreadsheet for coordinate calculations “True Azimuth [Bearing] from eastings and northings” is 126° 6’ 6.510805” or 126.101808557°. The Ordnance Survey Spreadsheet for coordinate calculations calculates in the Airy 1830 ellipsoid.

Using Charles Karney’s Online geodesic calculations using the GeodSolve utility: Using the GRS80 ellipsoid with the ETRS89 latitudes-longitudes, forward Geodetic Azimuth is 126° 6’ 3.9799425073” or 126.10110553958536° “clockwise from north”.

Azimuths from 276605, 268059 to 294252, 254502.

“For England, the longest straight walk without encountering a road is in the North Pennines to the east of the Lake District. The straight line is 29.874km long (29874.438016m).” “The northernmost point of this line is at 369365, 543355”. “The southernmost point is on the B6276 heading east from Market Brough/Brough, the coordinates being 381007, 515840.”

Using the Ordnance Survey Spreadsheet for coordinate calculations “True Azimuth [Bearing] from eastings and northings” is 156° 40’ 38.526441” or 156.677368456°. The Ordnance Survey Spreadsheet for coordinate calculations, calculates in the Airy 1830 ellipsoid.

Using Charles Karney’s Online geodesic calculations using the GeodSolve utility: Using the GRS80 ellipsoid with the ETRS89 latitudes-longitudes, forward Geodetic Azimuth is 156° 40′ 32.7377236166” or 156.67576047878239° “clockwise from north”.

Azimuths from 369365, 543355 to 381007, 515840.

Stuart Anderton “While I’m as much a stickler for accuracy as anyone, quoting the distances involved to one ten thousandth of a millimetre (71500.817767m) seems a tad extreme, being significantly less than the width of a hair.”

10 January, 2019 at 18:42

Actually, to one thousandth of a millimetre.

“So for Great Britain, the longest straight line that you can walk without having to stop, look and listen is 71.5km or 44.43 miles (71500.817767m) and is unsurprisingly in Scotland. Crossing the Cairngorms, the distance goes from 262540, 778255 on the A9 and ends at 328042, 806921 south of the hamlet of Corgarff. The high point is on the summit of Beinn a’Bhuird at 1,179m (3,870ft).”

However, 1,179m equals precisely 3,868.1102362204724409448818897638…..ft or rounded to the nearest whole number foot, 3,868ft (1,179m ÷ 0.3048). An international foot equals precisely 0.3048 of a metre. Furthermore, this is the South Top. The highest point of Beinn a’Bhuird is North Top 1,197m (3,927ft).

Incidentally, how were the distances calculated?

Thomas, the length of the line was calculated in ArcMap by adding a new attribute field and calculating the length from this based on the line’s geometry and CRS. Elevation models were not taken in to account. We appreciate your interest in this, but I would like to reiterate that this project was solely as a response to a tweet as opposed to academia and as a result, software that a lot of people might have access to was used. Hope this helps, Jocelyn