Thursday, 18 June 2020

Guest Contributor – Eric Yeaman


This page heading on the Mapping Mountains site features articles from Guest Contributors, with the only stipulations being that the article has to be hill related and that I don’t end up in court through its publication!  Otherwise the choice of subject matter is down to the Guest Contributor.  For those wishing to submit an article please contact me via the email address given on the ‘About Me’ page heading.

Guest Contributor – Eric Yeaman

Eric Yeaman


In the beginning were the Scottish hills.  Then Sir Hugh Munro published his Tables giving all the Scottish Mountains exceeding 3000 feet in Height in the Scottish Mountaineering Club Journal in 1891.  After that, there were two kinds of Scottish hills – Munros (worth climbing) and others.  I didn’t know of any discrimination among the others until the early 70s, when the warden of the old SYHA hostel in Crianlarich told me of another elite species – a Corbett.

At that time, I was running hillwalking clubs for young people from my school and church.  Like everyone else, we ultimately aimed to conquer Munros, but twelve-year-olds need some outdoors experience first, so we started on the lower local hills.  From our bases in Arbroath and Broughty Ferry, my favourite hills were Deuchary Hill (behind Dunkeld) and Clachnaben (above the Cairn o’ Mount) – testing enough for the young people, but with variety all the way, and well-defined summits.  I was disappointed that no list existed of lower hills, and speculated on compiling one.

In spring 1972, I was notified of a meeting in Broughty Ferry YMCA of leaders who took young people to the hills.  I assume it was a consequence of the enquiry into the Cairngorm Disaster of November 1971, when five young people and one of their leaders lost their lives in a blizzard on the Cairngorm plateau.  I went along, to an attendance of three – two from the YMCA and me.  I was given a copy of the jury’s recommendations, and no doubt we discussed them, but the talk broadened, and I was given a formula for calculating the energy required for a hillwalk:

E = 100(R + 2C + 4H)

Where E is the energy in kilocalories, R is the road mileage, C is the cross-country mileage, and H is the height climbed in thousands of feet.

At the time, I had no idea of the origin of that formula, but I later found a similar one in early editions of Eric Langmuir’s Mountain Leadership:

E = 100 (10 + R + 2C + 4H)

This formula is credited to Waddell (1965).  In it, E is the energy expenditure over a 24-hour period, and I assume the 100 x 10 is the basic energy your body would use to maintain life, even if you never got out of bed.  The energy must depend on the size of the walker.  This is not specified, but the context suggests an adult male mountain-goer.

Since, as may be obvious, I like tinkering with numbers, I pounced on the formula.  For several years, I used it to assess walks I had done, and walks I proposed doing.  I found it consistent and useful.  For several years, my hillwalking club programme included the energy estimate for each walk.

I’d like to quote a date, and say, “On that day, I started writing the Handbook.”  But I have no record of that.  In the late 70s, however, I was keeping quite a full diary.  It was mainly intended as the Troubles of a Chess Teacher, but I made passing comments on my other activities.

At that time, the Ordnance Survey were replacing their one-inch-to-the-mile maps with the metric, 1:50 000 Landranger series, and my diary records buying these as I found them, e.g. 9 (Cape Wrath) on Saturday 9th December 1978, and 12 (Thurso and Wick) on Saturday 6th January 1979.  On that day, I also note: “During the week, I had the idea of writing an article for The Great Outdoors on calculations about hillwalks.  What I had in mind was metric versions of Naismith and Waddell’s formulae.  I would then go on to my application of the latter to grade walks according to difficulty.”

The following Wednesday, I give an attempt at a metric version of Waddell – inaccurate.  But, after a lot of wrestling, I finally converted the simpler formula to:

E = ¼R + ½C + 0.55H

Now E is in megajoules, R and C are in kilometres, and H is in hundreds of metres.

With a little practice, the mental arithmetic is not too hard.  Add H and H/10.  Halve the result.  Add ½C and ¼R, rounding nonchalantly.

The diary is silent on the subject for more than three months, but I assume I was gathering data for the article by calculating the energy required for various walks, including those to the tops of hills.

That would cause me to ponder – what is a hill?  It should be sufficiently separate from neighbouring hills.  Then: (a) it would have a view, and (b) you would feel you were on a distinct summit, not just a shoulder of something bigger.  What size of dip would give an adequate separation?

The new metric maps suggested a possible criterion – a drop of 100 m all round.  After a bit of work on the maps, I reckoned that might be a suitable basic condition.

But a hill with a lesser drop could be on the end of a ridge, far from anything higher.  So I added an auxiliary criterion – a summit would also qualify as a hill if it was at least 5 km (walking distance) from any higher point.

That ‘(walking distance)’ was an attempt to clarify what I meant.  Clarify?  It certainly didn’t do that.  By ‘walking distance’, I meant along the watershed.  That’s obvious on a ridge but, if a hill has two parallel ridges, I would usually walk round, rather than down into the dip, then up the other side.  After thirty-one years, I’m glad to clear that up.

Using various Landranger maps, I tested the criteria to make sure they identified hills which seemed distinct.  I visited some borderline local ones.

On Tuesday 24th April 1979, the diary records: “I looked for hills on the Glen Carron map.  I hope they’re not all as messy as this one!”

The ‘Glen Carron map’ is Landranger 25.  And a comment the following Tuesday is enlightening: “I also did a bit more hill-spotting on the interminable Map 25 for my book.”

That’s the first reference to my intention to produce the book.  One more trial is recorded.  On Wednesday 2nd May: “I spent much of the evening cataloguing hills.  Today was a successful session during which I polished off all of Skye except the main Cuillin Ridge, where contours are indistinguishable under the black mass of rock symbols.”

One more reference, mentioned later, indicates that I was still working intermittently on the project, but I didn’t buckle down to it for another sixteen months.  On Tuesday 30th September 1980, the diary includes.  “I spent the bulk of the day in Caithness, on the Catalogue of the Scottish Hills.”

Throughout October, comments take me down through Sutherland to Torridon.  By the middle of November, I reached an obvious boundary, the Caledonian Canal.  On Wednesday 26th November, I noted Ben Nevis.

Two days later:  “Home from school to the maps, trying to decipher the wandering contours over the hills of Moray and Banff.”

I hit my local Perthshire hills in early December, then, on Sunday 28th: “broke all records with 118!”  No location is given, but Tuesday 30th says,  “A day on the hills – a dreary bunch of Borders ones – probably nice if you got there, but difficult to sort out.”

Much of that difficulty was due to the new maps.  I had great trouble in determining the heights of the cols.  Many of the First Series of Landranger maps were more metric in spirit than in fact.  They were photo-enlargements of the most recent one-inch-to-the-mile maps, with imperial heights converted to metric.

That included the contours.  The 50-foot contour remained – now (sometimes) relabelled 15.  The 100, 150, 200, 250 and 300 contours became respectively 31, 46, 61, 76 and 91.

That didn’t matter to me if a quick inspection showed a mass of contour lines around a summit, but it was a nightmare on bumpy ridges, especially when the contour lines were sparsely numbered.  I soon learned the values for the heavier contours (every 250 ft) – 76, 152, 229, 305, 381, 457, 533 etc.  Not very memorable.

This wasn’t a minor problem.  It applied to the first Landranger maps of Orkney, the Moray coast, and all from 45 (Stonehaven) south.  A total of 50 out of the 85 maps that covered Scotland.  Another 19 had metric contours obtained by interpolation from the 25-feet contours of the six-inch map.

Throughout the 80s, those maps were updated to fully metric, and I visited the bookshop regularly to obtain the new versions.  At one Christmas season I took my Sunday School class to the pictures in Dundee, leaving the wee souls outside the bookshop en route while I went in to check the maps.  I remember the occasion because I was delighted to find the updated maps of the Perthshire hills.

I spent Monday 5th and Tuesday 6th January 1981 over the 1:25 000 Pathfinder maps in the University of Dundee Geography Department, trying to sort out heights and cols which were indefinite on the Landrangers.

Wednesday 14th January records:  “an epoch-making evening, for I finished the mainland, and have only assorted islands to complete – Jura, Colonsay, Coll, Tiree and the Small Isles.”  Then, next evening, “I finished the Scottish hills!”

For each hill, I used a 5x3-inch file card with a ruler-wide column for data down the right.  The illustration shows a few examples:

File card

In the wide, left-hand column, I recorded:

(1)  the name of the hill, plus code letters for details.

(2)  the bearing and distance of the hill from one of a series of places around Scotland.

(3)  B: the boundary of the hill, starting at the north and going clockwise.

(4)  I: a brief description of the hill – its shape, and the position and shape of any ridges and shoulders.

The data column had:

(5)  the height (in metres, of course).

(6)  the number of the Landranger map/s the hill is on.

(7)  the map reference for the summit of the hill.

(8)  the region and district of the hill.  Two letters, the first indicating the region, the second the district, of the local authorities of the time.

(9)  the number in the data column, under the district code, was part of an early attempt to group the hills.  My diary records several unsuccessful attempts to divide the country into suitable regions.  11th September 1979, for instance, records ‘version n’ with the comment: “I think I might have something there.”  But none of the attempts, based on topography or the national grid, satisfied me.

It finally occurred to me that such groupings may be less helpful to anyone looking for a hill to climb.  But sensible hill-goers – locals or visitors – would buy the relevant Landranger before going out.  With the hills listed by map, users could consult the corresponding page of the Catalogue to find a suitable hill.

(10)  the distance in kilometres along roads and paths; the distance in kilometres cross-country; and the height to climb, in hundreds of metres; to reach the top of the hill from the most convenient place of public access – usually a metalled road, but occasionally a railway station or hypothetical landing place on an uninhabited island.

To measure the distances, I ran my map measurer over the map, following the route I would have expected to take.  I avoided obvious obstacles such as lochs and wide rivers.  But, to the calculated value, I added code letters indicating possible problems shown on the map – “c” for cliffs; “f” for forest; “r” for river, and “b” for bridge – which might have fallen since the map was published.  These warnings didn’t survive into the Handbook.

The listed height to climb is the total, taking into account any dips in the route.  Example: the route starts at 200 m, climbs to 370 m, drops to a col at 310 m, then climbs to the summit at 500 m.  Then the height to climb would be (370 – 200) + (500 – 310) = 170 + 190 = 360 m.  On a bumpy ridge, it’s often easier to subtract the starting height from the final height, then add downhill parts:  (500 – 200) + (370 – 310) = 300 + 60 = 360 m.

The distances and height were the raw data for calculating the next two figures.

(11)  the energy to climb the hill, calculated by the adapted Waddell formula.

(12)  the time for the trip.  I calculated this using Naismith’s Rule (1892).  As originally formulated, it gives the time for a hill excursion as 3 miles per hour, plus ½ hour for every 1000 feet climbed, i.e.

T = D/3 + H/2

where T is the time taken in hours, D is the distance walked in miles, and H is the height climbed in thousands of feet.

The metric equivalent is:

T = D/5 + H/6

Now D is in kilometres, and H is in hundreds of metres.  Some sources quote D/4, and that’s the value I give in the Handbook (page 43).

Naismith’s Rule makes no allowance for terrain.  But I had a little information about that – the road/path distance and the cross-country distance.  Hoping it would be helpful to use them, I arbitrarily adapted the rule, using:

T = R/6 + C/4 + H/6

When I prepared the book for publication, I had to limit the data I could include.  It occurred to me that the time taken on a hill would be roughly related to the energy required to reach the top.  By the simple process of comparing the energies and times for a number of hills, I reckoned the simplest approximation was to allow 25 minutes per megajoule.  For the book, I rounded that to half an hour.

(13)  the final entry, at the bottom of the data column, is the six-figure map reference for the starting place.  If there seemed two possible starting places, I calculated the energy for both and gave the lower in the Handbook.

The numbers in square brackets under the place names, and in the data columns, were added after the Handbook was published.  I was groping towards a hierarchy of the hills.  Others have since done this with more persistence.

During the next eight years, the Catalogue transmuted into Handbook of the Scottish Hills.  But that’s another story!

Eric Yeaman

Handbook of the Scottish Hills (published in 1989 by Wafaida)

Ups and Downs - The Story of Handbook of the Scottish Hills (published in 2020 by Mapping Mountains Publications and Smashwords)

UKHillwalking article - critique of Handbook and details of Ups and Downs - The Story of Handbook of the Scottish Hills

Grough article - critique of Handbook and details of Ups and Downs - The Story of Handbook of the Scottish Hills

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