Piotr on Młynarz 2172m, P118m, High Tatra, Slovakia - photo by the author 

How to estimate the time of an off-trail hike

A case based on the Tatra mountains in Slovakia and Poland

Many hikers know about the famous Naismith's rule, first published in the SMC (Scottish Mountaineering Club) Journal in 1892. It defines the time required for a mountain hike as 1 hour for every 3 miles, and an additional 1 hour for 2000 feet of ascent.

The present form of this rule – metric and recalibrated [i] – can be described in a following formula:

T = L/5 + H/500

where: T is time in hours, L is total distance in kilometres [ii], and H is total ascent in meters

The formula was used in Poland for awarding tourist badges (so called GOT, established by the Polish Tatra Association in 1935 in Stanisławów – now Ivano-Frankovsk in Ukraine). In a local version the formula equates to 1 km of a horizontal distance and 100 m of vertical distance. Each trip can be assessed with points calculated as follows:

P = L + H/100

The two key parameters of the rule are as follows: both 1 km of distance and 100 m of ascent take 1/5 of an hour, and the vertical effort is 10 times bigger than the horizontal one. Both figures are used to calibrate the model: 5 and 10 are benchmarks, but everyone can modify them if one does not agree with these parameters. On this basis, I have calculated a relative speed coefficient:

C = P/T

According to Naismith's and the ‘GOT rule’, C is always equal to 5 – you can substitute both formulas listed above and check that it works like that.

The problem is that C depends on the characteristics of a hike – is it on-trail or off-trail, and how rough is the terrain?

I have been calculating my ‘GOT points’ for each hiking day for 40 years now (I started as a kid). I have also been noting all the lap times for my trips. I therefore have a significant database of statistical evidence for my excursions (mostly in a hard-copy format). Just for the Tatra mountains it covers over 500 hiking days in various weather and terrain conditions. 80% of these trips were off-trail. These have proved to be crucial to my analysis.

I tried to apply the Naismith formula for my numerous hikes. In general, I seem to be slower than Naismith was.  Perhaps it is because I am rather a poor sportsman! However, I noticed a strict dependence to the type of terrain I walk through. The worse the terrain, the slower pace of my trip – this is obvious.

I checked my GPS for my local horizontal speed and its range is extremely wide. On a flat tarmac road with a backpack my maximum pace is 7 km/h. On very rough terrain it is 20 times slower- just 350 m/h. The most challenging types of terrain sections are: windfalls, scrub pine fields, thickets, deep snow and rocky exposed ridges. Going upward on a good trail you can manage each 100 meters of the ascent in just 10 minutes. Crawling in deep snow or scrambling on loose rock it can take even 4 times more – 40 minutes. The scope of divergence is huge.

Looking at a sample of the last 12 months, I see 50 trips and half of them were off-trail explorations. The average daily distance was 13 km and 700 m of ascent, done in 5 hours (the set also covers recreational family trips). Therefore the average C is equal to 4. The pace is 1 hour slower than the Naismith rule, so C is lower than the canonical 5. However, if we look just on the off-trails, the C drops to 3.5. This happens despite my competitive (non-recreational) attitude to this kind of the trip.

Looking at the most demanding trips in my 12-month set:

• 12.08:  the ridge of Młynarz (sumitting Młynarka), and

• 30.10:  Nowy Kopiniak (with Mniszek and caves). 

The first implies 30 km, with 1400 m ascent and 14.0 hours, the latter: 18 km, with 1300 m and 10.5 hours. Coefficient C for both cases is close to 3 and so is rather low.

Eventually the final formula to estimate the time of my trip is:

T = P/C, where C ϵ [2; 6]

I take 6 for marked trails and 2 for extreme off-trail exploration. The average C is close to 4 if the terrain is mixed.

The formula allows me to assess the minimum and maximum time consumption, depending on local conditions and my luck in finding the optimal way. The time-keeping takes into account short technical breaks that are natural in hill-walking, but excludes long bivouacs on the way.

The other issue is use of accelerators. There are basically two of them – bike and skis. A bike is useful on long tarmac approaches and ski-touring is advantageous in winter, making descents very fast. Such cases must be analysed on a case-by-case basis.

There is a separate problem in relation to pure climbing activity. It is usually much more vertical than horizontal (except ridge traverses), and time consumption depends on technical difficulties (i.e UIAA grade of the route), your rock climbing skills and usage of belays. The belay (and abseiling) is especially time consuming. I tend to use self-belay in the Tatra while descending P10m crags, due to exposure, unsafe grassy steps and loose holds.

It is easier to normalize the time of the ascent in speed climbing. We can analyse the average time reported by Grzegorz Folta, the top contemporary free-solo climber in the Tatra mountains. As an example, I took his 15-hour non-stop action in Batizovská Dolina in July 2020. It is described in detail (with heights of all crucial points and time laps). On the basis of this data, I estimated a C coefficient at the level of 2.0. It means that fast climbing generates a relative low C due to the difficulty of the terrain traversed. According to his data, the average speed on vertical faces with moderate rock-climbing difficulties (III-V) amounts to 20 minutes per 100 m of ascent. The pace upward is a bit better than the pace downward (as free-solo climbing descents are very demanding). The length of the climb ‘on Naismith basis’ can be zero meters on the map if a face is perfectly vertical. In practice, the slopes of the granite faces in the Tatra are between 45 and 90 degrees, so an average distance/ascent ratio is equal to 0.5.

A separate analysis should be done for winter-climbing. Here the C can be even lower than 2. This subject requires further research.

Notes

i.               One should notice that the original formula had slightly different coefficients – 4.8 for L and 610 for H. The contemporary formula is calibrated to suit the “GOT rule”.

ii.              The distance is calculated on the map as a flat surface. The real distance is longer due to the gradient of the slope. The difference is higher, the steeper the slope.