The art and science of estimation

How long does a walk take?

So, you’ve designed your walk and you’re ready to publish it, but there’s one thing missing — an estimate of how long it’s going to take. Fair enough, let’s do it. But wait, there’s a problem, we all walk at different speeds and, even then, it depends on the situation. Clearly it’s not possible to take everything into consideration, nor is it possible to give a walk duration that will be accurate for everyone. Even so, a figure is expected, if only as a guide. The question is, how to obtain a reasonable estimate?

Doesn’t Naismith have a rule for that?

He does, indeed, but the trouble is he devised it way back in 1892 and a lot has changed since his day. In fact, people have been trying to revise and perfect his rule ever since, usually in the form of corrections. In addition to Tranter’s corrections, Aitken corrections, and Langmuir corrections, the internet is awash with all manner of formulas and calculators, each aimed at improving Naismith’s accuracy.

Do any of them work?

The answer to that depends largely on what margin of error you are prepared to accept, i.e. how closely does the estimated time match the actual time taken?

In my personal experience, the most commonly used formulas are too wide of the mark to be of any value.

Take, for example, my walk, Bridge Over the Tassonaro. This is 10.4km in length and has a total ascent of 580m. I put it to the test using two walking apps and an online hiking organisation. The first app gave an estimate of 4h 12m using Book Time. The other app estimated 3h 2m using a modified Naismith’s Rule. Finally, the hiking site’s online calculator estimated 3h 39m.

It was at this point that I began to wonder whether estimating walk durations might be an art rather than a science!

Ok, so how long did the Bridge Over the Tassonaro walk actually take? For me, it took 1h 45m.

That’s a world away! But why?

In a word — pace. We all walk at different speeds and I’m a fast walker. It goes without saying that our pace will change depending on any gradients we encounter along the way but, if we know what our average pace is when walking on the flat, then all we need is a reliable formula to convert the length of the walk and the total amount of ascent into an equivalent flat distance and we’re in business.

Does such a rule exist?

It certainly does and was published by Professor Philip Scarf in 2008 as Scarf’s equivalence between distance and climb. The formula is:

equivalent distance = 𝑥 + 𝛼⋅𝚢

where:
𝑥 = horizontal distance
𝚢 = vertical distance
𝛼 = 7.92 (a value calculated by dividing 3 miles by 2000ft). Scarf called this Naismith’s number.

I have tested this formula after every walk that I have done and found it to be remarkably reliable. Consequently, the estimated walk durations used on this site have all been calculated using pace multiplied by the flat distance equivalent with a rough average pace value of 12:00 (min./km) and rounded up to the nearest 15 minutes.

The table below illustrates why I chose 12 (min./km) as a rough average.

Average walking pace by age and gender

Age20-2930-3940-4950-5960-6970-7980-89
Female12.4412.4411.9912.7213.4414.7517.73
Male12.2511.6511.6511.6512.4413.2317.18

The unit of measure for pace shown is min./km. The lower the value the quicker the pace.

Logged in members will see that I have included the flat distance equivalent for each walk under the walk statistics table. If you know the pace of the slowest person in the group, then all you have to do is multiply that value by the flat distance equivalent to get a reliable estimate of walk duration (in minutes).

Nigel Fawcett

One of the many benefits of being retired is that I get to spend so much more time in the great outdoors, not only as a photographer but in exercising one of my other great passions — hill walking. This is a particularly good fit when one’s photography centres around nature and the landscape. There can be few better places to do that than here in the beautiful mountains of Tuscany.