# Help with math - slope/elevation

With this I would definitely agree. And since the grade is usually given in rounded whole number increments, it’s even less important that someone do some sort of finicky calculation where the sine is used in combination with the inverse tangent to get an answer.

When it comes to trails that you hike, it might make a more significant difference. Some that I’ve hiked in the Sierra Nevada can be a bit steep in places. :eek:

Of course that might just be the average gradient. i.e. the length of the trail compared to the starting and end points. It doesn’t necessarily mean that there won’t be anything worse than 9%. Also, I walked plenty of paths that go up and down so that you may end up 300 metres higher than you started but have actually climbed more than 500

YM(literally)MV

Yes, but you could accomplish that with either standard (so long as it is in fact standard). Truckers would (in principle) have to learn a different set of numbers for what grade is safe at what speed and with what load, but that different set of numbers would be no harder to learn than the set of numbers they learn now.

All the responses seem to assume that the posted grade is the average grade over the whole trail. Is this really true?

This discussion has moved on a bit past the OP but out of interest I’ll clarify a bit more.

I measured a distance of the trail I hiked with a handheld GPS device. There was a sign posted a the trail head that gave the average slope (3%) and the steepest (9%) you could expect.

The first 3/4 mile was (consistently) the steepest. I’m pretty sure GPS measures distance as you would view it on a map. So Chronos provided the answer I was asking about - though I see now technically I might have been asking for the wrong thing. Noting however for my informal needs it works just fine.

Yes, true. But I thought we were discussing what actual existing road signs today measure, not what might be the case in some alternate universe. When you said “why wouldn’t the cartographers use the one that makes elevation calculations easier?” I assumed you were referring to what’s actually in use today.

GPS doesn’t actually measure distances at all. It computes your three-dimensional coordinates (though the vertical coordinate is less precise than the horizontal ones). An app can certainly use that data from the GPS to calculate distance, but it could calculate the distance in either way, and the distinction generally isn’t much publicized because it usually matters so little.

The distance & speed reported by GPS devices & apps are almost always horizontal. Because that’s what maps represent.

On Garmin devices, if you want to display the distance and speed along the slope, you need to select “3D speed” and “3D distance.”

But are there any false flats or dips in the trail? I’ve climbed many a hill or mountain on my bicycle where there were dips in the road. That could add to the total feet climbed. However if you are only worried about elevation change, it wouldn’t matter.

I’m putting together hiking trail information for people of varying degrees of fitness for an event. Flats or dips will be unimportant, they’ll use the information in a general way to determine the trails they feel comfortable attempting.

Average slopes do not tell you very much about how strenuous a hike is - it makes quite a difference whether a hight difference has to be surmounted in a small fraction of the overall distance travelled, or spread out over the entire length of the trip. (e.g. going over a mountain pass to the same elevation in the next valley vs. hiking around a lake. Good hiking guides here in Switzerland usually give you an elevation profile, e.gthis one

Why not just get the USGS quadrangle (or ordnance Survey, NTS or whatever) for the area and look directly? They’ll show the elevations and the steepness of the trail at every point.

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