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I want to find out how many calories are burned on any particular hike by any particular by using a formula. I figure it's probably a simple physics question, but since I never took physics, I don't know the math to do it.

My premise is that you will expend (A) energy (calories) when moving (B) weight (C) distance on a level path. And also (X) energy (calories) when moving (Y) weight (Z) distance when moving up against gravity.

The formulas I have found will add (A)+(X) to get the totals calories burned. Trouble is, the results vary greatly, and I have no way of judging which one is right.

Now, I know there lots of variables, but for this exercise, we'll skip the small ones. Here's what I'm thinking:

  1. Obviously there's resistance. At first I was dismissing resistance as being too minor when only traveling 2-4 MPH, but then I realized that without resistance, we'd just keep moving. Now, resistance will be based on the front profile size. Can we simplify things by saying X weight = Y profile?
  2. Assuming X weight = Y profile. A backpack would add weight, but not added profile. So we'll say no added weight for the formula.
  3. Up & down motion for each step. I figure that makes the formula a lot more complex because we have to deal with the height & stride of each person. So I guess we'll skip that.
  4. A fit person burns less calories (more efficient muscles) than an out of shape person doing the same hike. So we'll pick a good average.
  5. Downhill is considered the same exercise as level walking.
  6. Age & sex may be a factor, but I don't have those numbers, so can be ignored for now. I may later ask on a health forum for those factors.
  7. There's probably others I haven't thought about.

There are many sites on the internet that calculate this for you, but there's 2 problems with them.

  1. The majority want to ask you your hiking speed and time hiked. But most people don't their hiking speed, and some sites are vague with "brisk walk". Then all they do is convert speed with time to get distance.
  2. Even the ones that factor weight, distance, & elevation gain, I get widely different answers.

So, what I would like to get, if someone is in the mood to figure it out, is a formula for calculating calories burned.

Thanks

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closed as off-topic by Brandon Enright, John Rennie, Neuneck, Kyle Kanos, Carl Witthoft Sep 2 '14 at 11:47

  • This question does not appear to be about physics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Actually, this is a very complicated question, and it has at least as much to do with biology as with physics. So I'm not sure this is the right place for it. We'll see what the community thinks, but I would look to Physical Fitness or The Great Outdoors. They may already have questions like this. $\endgroup$ – David Z Sep 2 '14 at 5:15
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    $\begingroup$ This question appears to be off-topic because it is about biology and energy expenditure in the human body. Significant simplification and narrowing of the question is needed to make it on-topic here. $\endgroup$ – Brandon Enright Sep 2 '14 at 5:21
  • $\begingroup$ The question is definitely off topic. What you could ask would be a comparison between a physical model and, well, reality $\endgroup$ – Lord_Gestalter Sep 2 '14 at 6:36
  • $\begingroup$ I know that a question like this has been answered on The Great Outdoors! $\endgroup$ – Danu Sep 2 '14 at 7:17
  • $\begingroup$ It's been asked on The Great Outdoors more than once, but the only answer I could find was vaugue and pointed back this group. $\endgroup$ – Tom Collins Sep 2 '14 at 10:35
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The problem is that the main reason for the consumption of power is the inefficiency of human muscles. If I run a marathon on level ground then I shouldn't have used any energy at all because my potential energy hasn't changed (there will be some loss of energy to air resistance, but at the speed I run that's negligable). However experience suggests that running a marathon takes a huge amount of energy.

Faced with a situation like this we tend to defer to the engineers, and they will construct an empirical equation - that is they measure the energy consumption under lots of different conditions then work out an approximate equation that gives mostly right answers most of the time. The web sites you mention almost certainly use an equation of this sort.

So what you really want is to know what the empirical equation is so you can do your own calculations. But we can't answer that. You'll need to Google around in the hope you can find it.

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I spent some time pondering this question many years ago, when I had run up a pretty steep mountain and found that my Garmin gave me a very disappointing "calories burnt" result ("you didn't go very fast, so you didn't do a lot of work"...).

My reasoning went like this: if I climb a mountain, I will be doing work against gravity. Muscles are about 25% efficient (guesstimate), so conveniently I burn about 1 kCal (4200 J) for every kJ of work done. Going down hills, I don't get that energy back. For a mass m climbing h, the work done is $mgh$ (in J). For every 100 m climbed, this would be 1 kCal per kg body mass. A 100 kg guy climbing a 300 m hill burns about 300 kCal more than if he covered the same distance horizontally.

$$C = 0.01 m h$$

Where $C$ = (kilo)calories burned, $m$ = mass (in kg, including backpacks and gear), and $h$ is the total amount climbed (not net, but total - so if you climb 500 m, descend 300, climb another 200, then descend 400, your $h = 500 + 200 = 700$ and not $0$).

A bit of googling led me to a physiology paper that basically came to a very similar conclusion after putting people on treadmills and measuring their caloric output.

Back in 2010 I posted my thoughts at http://wishidknownthat.blogspot.com/2010/08/burning-calories-running-uphill.html . Right now I am in China, and apparently blogspot is not a sanctioned website - so I am writing this from memory. Please check that posting and see if it makes sense to you.

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