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Thread: Naismith Factor

  1. #1

    Naismith Factor

    Just exploring an idea.

    People wonder how long a route is going to take them. If you've never done a given route, how long to expect it to take?

    I just calculate the percentage of the Naismith time for a range of routes I've run. That is, divide the mileage by 3, add the elevation divided by 2000 feet, and you get the time taken for a fast walker. Then divide the time you've taken on the route by the Naismith time. That gives you a rough idea of your Naismith factor.

    So I, as a beginner fell runner who's only been running for 3 years, and in my very late 40s, reckon on under 40% of the Naismith time if I'm racing an AM or AL, and more like 45-50% of Naismith time for a pleasure run of around 26 miles +3300ft.

    For example, I'm hoping to run the Ennerdale race this year, whose route's Naismith time is 11 hr 25. I've run a similar length route in 45% of Naismith time, so I'd expect to finish in around 5 hrs 15.

    I wondered if anyone else has used this rule of thumb when calculating route times. And whether they notice a clear trend in the data. I've plotted a graph of my own Naismith factor for various routes against the Naismith time for each route. I can upload it if I can work out how...

    I've found this pretty useful for forecasting times when I've gone out and done something for the first time - eg a Fairfield Horseshoe recce, or a couple of BGR stages. It's also a good objective measure of how I'm improving, giving a consistent measure to compare days out which have varied in length and elevation.

    Of course, Naismith is the subject of many a long debate, the ground and conditions will vary, and this will never be scientific. But in my limited experience I find it sticks pretty well even for routes which vary in ratio of distance and elevation.

    Do other people use a similar calculation? Interested in thoughts


  2. #2
    Master mr brightside's Avatar
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    Jul 2009
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    Never heard of it.
    Luke Appleyard (Wharfedale)- quick on the dissent

  3. #3
    Master Travs's Avatar
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    May 2015
    NE Lakes/Coventry
    First of all, if you go round Ennerdale in 5hrs15 as a "beginner" that is very impressive!!

    The first few years i was racing i had a little bit of a formula...

    I calculated a base time, 10 minutes per mile and 10mins per 1000ft.

    ie Fairfield Horseshoe at 9 miles/3000ft, would be a base time of 120mins = 2hrs.

    Then multiply that time between a factor of anywhere between about 0.75 and 1.25, depending on the severity of the race. Lake District races i'd usually score a factor of at least 1, but Fairfield being runnable i'd maybe go 0.9, which would be 1hr48..... this is very close to my pb of 1hr46.

    Obviously the multiplying factors can only come through doing a few races, and i had to reduce the factor as i improved, so it was still guesswork. And i must admit in the last couple of years i've binned this method, and just look at past results for the names of people i know i can compete with.
    Last edited by Travs; 31-01-2022 at 09:12 AM.

  4. #4
    Member ponte_ricky's Avatar
    Join Date
    Sep 2019
    Luddendenfoot, Calderdale
    I have a spreadsheet that i use which is based on naismiths rule that works well for me:

    so i start with estimated flat running pace for a given effort. so for me i'll usually work to about 5-6min/km depending on how long the route is and how fit i am at the time etc. i'll then use OSMAPS to measure the distance (km) and ascent or descent (m) between 2 points (i tend to work out climbs and descents separately). i divide the ascent/descent by 100 (cant remember why now, but its right haha) and then i have factors that i use:

    0.8 for climbs
    0.3 for descents
    (i may adjust these slightly depending on terrain)

    I multiply the ascent or descent by the factor and add the distance to get a grade adjusted distance which i then just multiply by the flat pace.

    I'll give you an example from a route i was doing last year. this is from the pennine way road crossing at ponden reservoir near haworth to the top of Little Wolfstones:

    so i set my flat pace at 6.5min/km
    the distance is 3.04km
    the climb is 211m
    divide by 100 gives 2.11
    multiply that by factor of 0.8 gives me 1.69
    add that to the distance (3.04+1.69) to get the grade adjusted distance which is 4.73km
    then multiply that by 6.5min/km and it comes out at 30.75 (which i just then tweak to 31 mins)

    I have a tendency to overcomplicate things, which i am sure i have done a lot here, but it works for me. i cant remember my actual split times on the day now but i was never too far off.

    worth noting i did this for ennerdale last year too, but i think i set it a little too fast and overbaked it early on and struggled in the 2nd half, although i think despite a bit of a bonk on pillar i only fell 20 mins behind in the end i think. i dont think i would do this kind of calculation for a race again but its incredibly useful for personal challenges i think.

  5. #5
    Thanks both for thoughts.

    Where I feel it is most useful is where there is a specific time goal - a BGR or a Joss Naylor challenge. Naismith factor (as described below) for a 24 hr BGR would be 0.66. For a 12 hour Joss (I'm 50 in the Autumn...) it is 0.487. When actually doing the route, a rolling Naismith Factor would be incredibly helpful to see whether you're on time (I realise pacers usually provide this service through their experience, and advise the runner on how far ahead or behind they are - perhaps I should just stick to using them!).

    A Garmin data screen could provide a rolling Naismith Factor throughout a run, using the formula:

    Elapsed time / ((miles run/3) + (feet climbed/2000))

    While there will be a lot of variation in pace with terrain, weather, quality of pacers' banter etc. And each individual's ascent/flat/descent pace will vary. But overall the maths is black and white: if your actual Naismith factor for the route is above your target factor by the time you finish, you're not going to finish in time.

    I'd love to hear if someone could tinker with the code for an open source Garmin app which would provide this.

    It is clearly a bit of a mathematical game - perhaps get Matthew Atkinson onto it!

    In the meantime, signed up for Duddon Long and Darren Holloway - sadly can't do the Ennerdale.


  6. #6
    Join Date
    Jun 2010
    Beverley, East Yorkshire
    I wonder if this helps.

    Two main calculation bases have now been established. The most used version can also be found in the DIN standard 33466 applied by the German Alpine Association (DAV) and states that a hiker travels 300 m uphill, 500 m downhill and about 4 km of horizontal difference per hour. The smaller value from the calculation of the vertical distances is then halved and added to the other two. The second formula comes from the Swiss Alpine Club (SAC) and assumes 400 m ascent and 800 m descent per hour and also 4 km of horizontal difference. So the Swiss are doing it a bit better. Our calculator is based on the DIN standard and therefore offers a small safety buffer for sporty hikers, which allows about 5 minutes break per hour.

    Guide values per hour of walking time
    Average (DAV standard) 300 500 4.0
    Trained (SAC standard) 400 800 4.0
    Professional 600 1000 6.0
    Average (ski tours) 300 1200 4.0
    A practical example: our tour has 1200 ascending and descending altitude meters and is 10 km long. According to the DIN formula, the total time for the tour is 7:40 hours, with 4:40 hours for the ascent and 3 hours for the descent.

    However, it should be noted that this is of course the pure walking time. All in all, there are no breaks at the cabin or for changing equipment (e.g. climbing harness or crampons) included. Climbing passages are not yet included either.

  7. #7
    Thanks Barry.

    I've dug out a paper which covers all this. There's more maths in it than I can handle, but there is basically one interesting conclusion I think, which is that Naismith's rule does indeed prove highly predictive of [male] race record time for a sample of 300 fell races. A plot of record time against Naismith equivalent distance (ie converting each vertical km to 7.92 horizontal kms) gives a near straight line (see chart hopefully attached).

    Scarf suggests that once a runner knows how their own race times relate to record times, the rule is pretty good at predicting their times for other courses. He also of course acknowledges some of the variability around descent times, ground, weather etc. But at the heart of it, Naismith is a really useful rule in its simple form. I've used it a lot for working out my own recce/race times and comparing performances across different days/routes, and it takes out a lot of the guesswork - but of course should never be used blindly.

    Screenshot 2022-06-06 at 20.31.20.png

    Abstract below; I can't upload the whole thing. Now for Ennerdale (back on for me!).

    Centre for OR and Applied Statistics, University of Salford, Salford, UK (Accepted 28 April 2006)
    In this paper, I consider decision making about routes in mountain navigation. In particular, I discuss Naismith’s rule, a method of calculating journey times in mountainous terrain, and its use for route choice. The rule is essentially concerned with the equivalence, in terms of time duration, between climb or ascent and distance travelled. Naismith himself described a rule that is purported to be based on trigonometry and simple assumptions about rate of ascent; his rule with regard to hill- walking implies that 1 m of ascent is equivalent to 7.92 m of horizontal travel (1:7.92). The analysis of data on fell running records presented here supports Naismith’s rule and it is recommended that male runners and walkers use a 1:8 equivalence ratio and females a 1:10 ratio. The present findings are contrasted with those based on the analysis of data relating to treadmill running experiments (1:3.3), and with those based on the analysis of times for a mountain road-relay (1:4.4). Analysis of cycling data suggests a similar rule (1:8.2) for cycling on mountainous roads and tracks.
    Last edited by Gordouli; 06-06-2022 at 08:43 PM.

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