Does weighted_grade work well for you in most areas as an approximation of grade? I am most worried about short edges in areas where elevation tends to be noisy. In those areas I suspect the grade approximation may be too high - though in these cases the edges are short so the impact may not be too great.

Does weighted_grade work well for you in most areas as an approximation of grade?

I don't know how to define work well in this context, but for us, the paths we have got with elevation data are consistent with what we would do in real life, so far so good.

In those areas I suspect the grade approximation may be too high

hmmm, that is an interesting angle and worth being looked into... in any case, it is baffling for us to see the speed factor drop under 1 even when we're on a mildly tilted and well-paved path...

You certainly are right, a mildly descending slope will not slow people down, rather do the opposite. Perhaps regardless of roughness of terrain, when compared to flat speed at same roughness. After all, walking is modelled as a kind of controlled falling, that is why it is so efficient. Only when terrain gets steeper than some limit, this fires backwards. From reading up on the literature, the limit is set somewhere between -6 and -12%.

The so-called DIN function looks to me a variation of https://en.wikipedia.org/wiki/Naismith%27s_rule - a rule of thumb to estimate ToA without a computer with pen and paper only. Unlike estimates from Naismith's rule the ones given by the DIN rule are easy to beat though. The Swiss have a more elaborate function, a polynomial with 15 degrees of freedom or so. They are nerds, and more sportive too!

When I pushed for the change, I feared that Valhalla results would get ridiculous, but they turned out rather fine. Maybe that was mostly due to the fact, that before the change, downhill speed did increase with no limit, so instead of walking you would be running? So in fact, what the change mostly did was smooth out noise in the elevation data?

Said all that, the turning point of where slowing starts rather be to the left of the zero degree mark. That for sure.

Any objections merging this @xlqian @hungerburg et al?

I'm ok with it

The changes to kGradeBasedSpeedFactor look sensible.