# Tobler's hiking function: resulting walking speed in KmH or m/s?

I was reading some literature dealing with least-cost path calculation and accumulate cost-surface generation using the Tobler's hiking function. I was reading this literature since I am trying to implement in R the generation of isochrones around a starting location (Integrating use of surface distance when calculating cumulative cost-surface based on walking pace?).

I can't understand what seems to me quite odd: some sources (e.g., Wikipedia) indicate that the speed predicted by the function is in KmH, while the author of the `gdistance` R package (see this PDF at page 14) indicates that the off-path speed would be in meter-per-second (he actually indicates m/s).

I am having hard time in understanding which is correct. This is not a trivial issue since different results are bound to crop out using Kmh vs. m/s.

The formulae in wikipedia and the R doc are identical, lets see what they say walking speed is on flat ground:

``````> tobr = function(m){6 * exp(-3.5*abs(m+0.05))}
> tobr(0)
[1] 5.036742
``````

About 5 units. Is that km/h or m/s?

If it was 5 m/s that would be 5 * 3600/1000 = 18 km/h. That's a pretty quick running pace, never mind walking.

So I think `gdistance` is wrong, and you should perhaps contact the maintainer. I don't think it affects the construction of the path in the R package vignette, and I don't think the travel time is quoted in that example so the units of speed don't make a difference.

• Hello. Thanks for your reply, which clarifies things. Yes, I believe that in the 'gdistance' PDF there is a typo: m/s would indeed be kmh. I agree with you that that does not make any difference for least-cost path calculation, but I think it would indeed change things for the calculation of isochrones (walking-time areas) around a start location. Thanks again for replying and for the elucidation. – NewAtGis Jun 19 '18 at 6:51
• I've just posted a friendly email to the maintainer, and pointed him here. – Spacedman Jun 19 '18 at 12:39

This is indeed incorrect. The original article by Tobler has km/h. Note, however, that Tobler's Hiking Function is just there for illustration and should probably not used at all in research about human mobility.

• Being a hiker myself, I can attest to the function's overall robustness. There are variations between individuals (my cruising speed on flat open ground is about 6km/h and I can maintain 4km/h on a +15° slope if the surface is regular), but it's a very good model. I review my hiking data after each outing, which is close to 600 tracks now, and the numbers are pretty close. – Gabriel C. Jun 19 '18 at 12:54
• @Jacob van Etten: thank you for your feedback. I did not mean to criticize, just trying to wrap my head around that discrepancy. – NewAtGis Jun 19 '18 at 14:20
• @Gabriel C.: yes, indeed I came across some literature in which (more recent) empirical measurements seem to confirm the broad validity of the Tobler's equation. – NewAtGis Jun 19 '18 at 14:21