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## Hiking Speed and Trail Steepness

### Hiking Speed and Trail Steepness

For anyone interested in a little GPS analysis, I did a little study on the relationship between trail steepness and hiking speed.

Ze

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### the pleasure of Science...

Your graphing was very impressive, and although it confirms what we know fromt our own experience, it is interesting to see a large accumulation of data graphed, and converted to a visual interpretation.

robertjoy

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Interesting stuff.

90% of the hiking I do is on approach to climbs, so I am carrying at least a moderate load and not running.

A few years ago I started wearing a heart rate monitor on these approaches out of curiousity. I learned quickly that I was over exerting on the uphills and slacking on the more level terrain. Balancing this out improved my overall speed in most cases and especially on longer hikes.

My downhill speed is pretty much determined by the ruggedness of the terrain. For example I will move much more quickly up class III than down it.

On a groomed trail I'll probably produce a pretty symetrical curve like your graphs but not over rugged ground.

ksolem

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### Re: Hiking Speed and Trail Steepness

Ze wrote:For anyone interested in a little GPS analysis, I did a little study on the relationship between trail steepness and hiking speed.

Nice, but to believe your conclusions (i.e, that they are significantly more precise than the well known rules of thumb) I would like to see some measurement of energy expenditure per time, e.g. heart rate, to show that that is really constant during the measurement. From my own experience I would suspect that for most people power output changes with terrain angle, i.e. one tends to exert oneself more on steeper terrain if not actively pacing oneself using a heart monitor.

Anyway, apologies for being too critical, I should be trying to make a scientific paper referee proof rather than doing SP research. So, back to work....

Christian

cb294

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Really cool plots and analysis!

I created a scatter plot like these for a bicycle ride once. As opposed to hiking, leg movement and muscle use while biking do not vary depending on grade (if you're big like me and remain seated on inclines), so it's maybe less complicated to keep the energy output somewhat constant, provided the proper gears are available for low and high speeds.

One more-complicated part is that now there is big wind friction to affect the results. For example, taking two data points on exactly the same percent grade, a different wind direction or speed will significantly affect the biker's speed. Also, there is the kinetic-energy factor that one does not really get with hiking. So on a bike, your speed on a level grade (for example) immediately following a big downhill is going to be much faster than that on a level grade elsewhere.

Anyway, for the hiking analysis, I wonder if some would argue that it makes a difference if you're ascending and the hill is stationary, or if you're stationary and the hill is descending! http://www.summitpost.org/phpBB2/viewtopic.php?t=51786&postdays=0&postorder=asc&start=30

Day Hiker

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Excellent topic. Also, you could probably put the graph on canvas, add a frame, and sell it as art. Very interesting visual.

Grampahawk

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Thanks for the feedback. Of course these are somewhat generic and there are many instances / variables which will affect the relationship - and I'm planning on analyzing in the near future.

ksolem wrote:A few years ago I started wearing a heart rate monitor on these approaches out of curiousity. I learned quickly that I was over exerting on the uphills and slacking on the more level terrain. Balancing this out improved my overall speed in most cases and especially on longer hikes.

My downhill speed is pretty much determined by the ruggedness of the terrain. For example I will move much more quickly up class III than down it.

Yes I agree. And the downhill is very interesting stuff, like you state the terrain will be a large factor. I'm trying to save downhill for later b/c its more complicated!

cb294 wrote:Nice, but to believe your conclusions (i.e, that they are significantly more precise than the well known rules of thumb) I would like to see some measurement of energy expenditure per time, e.g. heart rate, to show that that is really constant during the measurement. From my own experience I would suspect that for most people power output changes with terrain angle, i.e. one tends to exert oneself more on steeper terrain if not actively pacing oneself using a heart monitor.

Anyway, apologies for being too critical, I should be trying to make a scientific paper referee proof rather than doing SP research. So, back to work....

No worries that's great feedback, and I totally agree. I have a heart rate monitor, unfortunately I would need to get one that samples data at a high frequency (i see a polar one I could get for \$200 bucks, hmm...) and add that. It is a big piece to the puzzle.

As for this data, I specifically picked these two tracks based on my consistent exertion in each, both for about the same pace (a bit under a marathon). My top speed on flat (8.5 mph) makes sense for how long it would take me to do a flat marathon, so I feel the data is decent, but you are right heart rate would make it a lot better.

In theory, if I had a heartrate with all these, I could create a nice surface plot with all the isoEnergy curves based on heartrate. That would be really cool.

Day Hiker wrote:Really cool plots and analysis!

One more-complicated part is that now there is big wind friction to affect the results. For example, taking two data points on exactly the same percent grade, a different wind direction or speed will significantly affect the biker's speed. Also, there is the kinetic-energy factor that one does not really get with hiking. So on a bike, your speed on a level grade (for example) immediately following a big downhill is going to be much faster than that on a level grade elsewhere.

Anyway, for the hiking analysis, I wonder if some would argue that it makes a difference if you're ascending and the hill is stationary, or if you're stationary and the hill is descending! http://www.summitpost.org/phpBB2/viewtopic.php?t=51786&postdays=0&postorder=asc&start=30

Good stuff on the biking. Definitely different variables to consider there. Once I do a few more cycling bouts, I'd like to compare the two to find which grade do I go the same speed on the bike and walking!

Don't get me started on the moving hill

Also it will probably be more interesting to see the vertical ascent rate, which I have but put in the next post.

Ze

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Day Hiker wrote:Anyway, for the hiking analysis, I wonder if some would argue that it makes a difference if you're ascending and the hill is stationary, or if you're stationary and the hill is descending! http://www.summitpost.org/phpBB2/viewtopic.php?t=51786&postdays=0&postorder=asc&start=30

As long as the hill is not accelerating, the results should be the same. You can verify this by walking up and down a ramp in an elevator, while carrying an accelerometer.

MoapaPk

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MoapaPk wrote:
Day Hiker wrote:Anyway, for the hiking analysis, I wonder if some would argue that it makes a difference if you're ascending and the hill is stationary, or if you're stationary and the hill is descending! http://www.summitpost.org/phpBB2/viewtopic.php?t=51786&postdays=0&postorder=asc&start=30

As long as the hill is not accelerating, the results should be the same. You can verify this by walking up and down a ramp in an elevator, while carrying an accelerometer.

Yes. And your elevator example is a good example for trying to understand the correct analysis of the stairs in the other thread. As long as the elevator is traveling at a constant velocity, a person placed inside, with no view of the outside, has no way to detect its movement, and, relevant to the debate, the person would have to exert exactly the same forces while stepping onto a step inside the elevator, regardless of how fast the elevator is moving and regardless of whether the elevator's motion is up, down, sideways, or whatever.

Day Hiker

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I've been on a hillside that was accelerating under gravity, but didn't think to keep an accurate GPS record at the time.

MoapaPk

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FortMental wrote:use the basic work equations and you'll see why, as well (at least for the uphill).

If we're talking about the same thing, basic work equations would only consider the potential energy changes in relation to the terrain, so they would not explain the non-zero power required to move on a level trail.

As a first-level guess at a more accurate function, I would suspect there is a certain amount of energy required in moving the legs (etc.) per given trail distance. This energy per distance could be assumed to be constant for level and moderate slopes. Add to this the calculated change in potential energy to obtain the total formula in terms of energy versus distance.

This is for non-negative slopes only.

Day Hiker

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FortMental wrote:This is pretty-looking data, but all you can say with it is: As angle increases/decreases, I slow down; which is a perfectly reasonable conclusion, given the data. Your "isoenergy" curve and conclusion is baloney. Use a heart rate monitor and you'll see why ... use the basic work equations and you'll see why, as well (at least for the uphill). Incidentally, what is the limiting factor that makes the left side look like the right side?

As I stated before I agree that a heart rate monitor would help validate that assumption I made. However, knowing my body from much training (and using a heartrate monitor all the time) I am pretty confident that these values are similar in energy exertion. The curve itself may change slightly, but the general trend and principles derived from it (shifting of the curve) would be the same.

Work equations are not enough, they don't incorporate the biomechanics of the body. Heart rate and "perceived exertion" do, in a black box sort of way.

Limiting factor on the downhill? I dunno, very interesting stuff to ponder, huh? Something to do with impact generation, balance control, and eccentric muscle contraction I suppose...

Ze

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Ze wrote:Limiting factor on the downhill? I dunno, very interesting stuff to ponder, huh? Something to do with impact generation, balance control, and eccentric muscle contraction I suppose...

When not injured (which is infrequent these days) I typically jog down trails, mainly to avoid excessive boredom. Braking on turns, to avoid breaking, is tiring.

MoapaPk

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Interesting symmetry to the Iron Mtn graph.

The right side (uphill) of the graph make perfect sense to me (steeper = slower), but I’m surprised that you don’t have more scatter on the left side (downhill).

I know Iron Mtn has some steep and rugged downhill sections (maybe class 2) that require some slow and careful foot work. But there are also clean downhill sections that you can really motor down and would expect to be at least as fast as on level terrain; hence a lot more variability to the left side of the graph (downhill). Am I missing something?

Do you have a sore knee, ankle, etc. that slows you down on the descents?

graham

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