Estimate the difficulty of a mountain route

[Adrianp]

TL;DR Summary

By the linear distance and vertical difference

Hello guys,

I am not into this field and finished my college long ago. I am trying to find a formula to estimate the difficulty of a mountain route.
The input is:
D = linear distance between start and destination (as given by Google Maps) in m, km, whatever. Both points are considered at the same level when this distance is shown.
H = the difference between the destination height and start height. Taken from Google Earth, usually in meters.

Others:

- I just want like a general index of the given mountain path, reflecting the energy consumed. Like twice the distance for the same angle will double the score (index).
- I have noticed that the real paths are usually 20-30% longer than the straight line, we will ignore this for the moment as it can be adjusted in the end.
- It should be a general formula independent of other factors like person weight, path difficulty (rocky etc), just the parameters mentioned.
- Steeper slopes are obviously harder to climb. You can walk 10km easily horizontally but climb extremely hard 20m vertically. However, if you walk more you consume more energy too.
- When you climb steeper, you obviously adjust the speed. However, you perceive the climbing more difficult too.

I cant even figure out right now if it about energy, power, mechanical energy or whatever....
It all started when I had to climb a route 2km long straight line and 600m vertical difference and I found it difficult.
I want to know is the same energy like for 4km distance and 300m vertical difference for example.
I've tried something like D(istance) * sin A = D * H / Sqrt(D pow 2 + H pow 2) but its obviously not accurate.

Thanks

 

[Adrianp]

 

[PeroK]

Check out Naismith's rule:

https://en.wikipedia.org/wiki/Naismith's_rule

 

[berkeman]

Check out Naismith's rule:

https://en.wikipedia.org/wiki/Naismith's_rule

The basic rule assumes hikers of reasonable fitness, on typical terrain, and under normal conditions. It does not account for delays, such as extended breaks for rest or sightseeing, or for navigational obstacles. For planning expeditions a team leader may use Naismith's rule in putting together a route card.[citation needed]

It is possible to apply adjustments or "corrections" for more challenging terrain, although it cannot be used for scrambling routes. In the grading system used in North America, Naismith's rule applies only to hikes rated Class 1 on the Yosemite Decimal System, and not to Class 2 or higher.[citation needed]

In practice, the results of Naismith's rule are usually considered the minimum time necessary to complete a route.[citation needed]

When walking in groups, the speed of the slowest person is calculated.[13]

@Adrianp -- can you say more about why you want this? As mentioned in the quote above, the calculated time is just the minimum time for easy hiking trails. In my experience, the trails I often hike on are more challenging because of all the rocks on the trail, and the need to zig-zag to find the smoothest way over everything...

The image below is the kind of trail I'm talking about. It shows a MTB on it, but I used to hike that trail most weekends when I was back in high school...

 

[Adrianp]

@Adrianp -- can you say more about why you want this? As mentioned in the quote above, the calculated time is just the minimum time for easy hiking trails. In my experience, the trails I often hike on are more challenging because of all the rocks on the trail, and the need to zig-zag to find the smoothest way over everything...

There are many routes to choose from. I want to check the distance and the vertical difference and estimate it as a score so to know if I will do it or not. My age and physical condition won't let me do 15km and 1200m up in one day...

 

[berkeman]

I want to check the distance and the vertical difference and estimate it as a score so to know if I will do it or not.

How does the Oat Hill Mine Trail look to you? It's only a few miles up and down, with a total vertical of maybe 1000', and the views of the upper Napa Valley are beautiful.

 

[Adrianp]

How does the Oat Hill Mine Trail look to you? It's only a few miles up and down, with a total vertical of maybe 1000', and the views of the upper Napa Valley are beautiful.

If I could climb that much I wouldn't need a score for a trail:)

Anyway, the Naismith rule is excellent.

 

[Adrianp]

Ok, I'll let you know what I did, it seems to work. Its the first raw version, it can be refined.

I made a function to get the horizontal effort like

HE = D + H * 8
(or HorizontalEffort = HorizontalDistance + VerticalDifference * 8)

I am using Scarf's equivalence adjusted with a higher importance of climbing. (https://en.wikipedia.org/wiki/Naismith's_rule)

Now, I set the Effort to 1 for my known limit which is like D = 2000m, H = 600m
HE = 6800

So the Trail Weight (score, index etc) is like (D + H * 8) / 6800. Everything above 1, like 1.22 etc may push my limits, everything under 1 is affordable.

Thanks a lot

 

[PeroK]

I made a function to get the horizontal effort like

HE = D + H * 8
(or HorizontalEffort = HorizontalDistance + VerticalDifference * 8)

I used to used $D + (H \times 10)$ as a measure of the difficulty of a day. This applied for $H \le 1000m$. For days where $H > 1000m$, I used $D + (1000 \times 10) + (H-1000) \times 15$. In other words, the second $1000m$ of ascent was 1.5 times harder than the first. And, for $H > 2000m$ I used a factor of 20 for every further $100m$ of ascent beyond $2000m$.

These days I rarely if ever get beyond $2000m$ of ascent. One further observation is that some people can just push on and slow down gradually; whereas, others suddenly grind to a halt. Someone I climb with in the Alps can do $1000m$ of ascent without real problems, but after that it's like he's hit the wall.

I am using Scarf's equivalence adjusted with a higher importance of climbing. (https://en.wikipedia.org/wiki/Naismith's_rule)

Now, I set the Effort to 1 for my known limit which is like D = 2000m, H = 600m
HE = 6800

That's very steep, given that the 2000m is up and down? I would normally associate 600m of ascent with a round trip of 6-10km.

So the Trail Weight (score, index etc) is like (D + H * 8) / 6800. Everything above 1, like 1.22 etc may push my limits, everything under 1 is affordable.

Thanks a lot

In the UK, we have several websites that give all the relevant details for each hillwalking route. For example, one of the best small mountains is Scotland is:

https://www.walkhighlands.co.uk/fionas/stac-pollaidh

The page with the route description gives 4.5km, 510m of ascent and a time of 2-4 hours. That said, the path to the true summit has one awkward rock-climbing move (harder on the way down) and is "out of reach for normal walkers".

https://www.walkhighlands.co.uk/ullapool/stacpollaidh.shtml

 

[PeroK]

Here are some photos from Stac Pollaidh (pronounced Stack Polly) last year:

 

[Adrianp]

I used to used $D + (H \times 10)$ as a measure of the difficulty of a day. This applied for $H \le 1000m$. For days where $H > 1000m$, I used $D + (1000 \times 10) + (H-1000) \times 15$. In other words, the second $1000m$ of ascent was 1.5 times harder than the first. And, for $H > 2000m$ I used a factor of 20 for every further $100m$ of ascent beyond $2000m$.

Good idea, I'll do the same.

That's very steep, given that the 2000m is up and down? I would normally associate 600m of ascent with a round trip of 6-10km.

Yep, it was steep and affected me for 3 days . That's how I've set my upper limits.
There are tons of awesome trails on high altitude, quite easy, with beautiful landscapes. I get as close is possible with my car, then I hike. I just don't want to get exhausted, after 4-5 hours of hiking I get back, make a fire, have fun etc.

The route rating on that site is quite nice and useful, I've also made my own website where you can upload routes as gpx files, the point was people will share routes like this... but I wasnt into it lately, there are more dedicated places.
https://www.obiective-turistice.com...caraiman-bucegi-platoul-bucegilor-transbucegi