In reality, highly accurate estimations are specific to the individual, but there are some basic properties to start with. So, we'll start laying at least a foundation now.

A paper from the Journal of Applied Physiology has looked at how energy expenditure is affected by the slope (grade) while walking (and running). You can read the full study with the link provided. Basically, they put people on a treadmill at different gradients and measure how much oxygen they are consuming. From that, they find an equation relating the relative work performed at a given grade relative to the work performed while walking on flat ground.

**Concept: Oxygen Consumed ~ Work ~ Calories Burned**

Given this relationship, if one know's how much work and oxygen they are consuming at any velocity and grade, one can estimate how many calories they are burning. The figure below (from the paper) shows how the relative work changes as a function of incline for both walking and running. The values of Cw are not intuitive, but how the numbers change relative to a 0 gradient may be. Given a certain velocity, positive grades increase energy expenditure, while slightly negative grades decrease expenditure. At about -10% grade, expenditure increases as the grade gets more negative.

*Minetti et al 2002*

So how well does this translate to outdoor hiking? There are plenty of other variables to consider such as terrain & altitude, but I think this will do a decent job estimating energy expenditure while going uphill. Downhill? I'm not as confident. I think the terrain will play a big part in make actual expenditure higher outdoors while hiking down steep trails.

You'll notice an equation deriving the energy relative to the treadmill grade:

With this equation, we can estimate the instantaneous energy expenditure at any given grade. If we have GPS data with information about the steepness as a function of distance along the trail, we can integrate and estimate the expenditure for the entire hike. Or more simply, use the average grade and distance values.

With this info, we will determine how many equivalent flat miles of walking the hike was worth. For example, I may estimate a hike up Mt Baldy (4 mile uphill, ~ 4000 ft gain) to be about the same as walking 12 flat miles (not in terms of time, but calories burned).

If we have a known quantity of energy expenditure and bodyweight for a given hike, we can make generalized estimates for other hikes and other bodyweights. For right now, the basic assumption is that calories burned is linearly related to bodyweight. So, a person weighing 100 lbs will burn 1/2 as many calories as someone weighing 200 lbs.

As I have measured my own caloric expenditure using indirect calorimetry, I use that as a basis to start with. The assumption of linear relationship between weight and calories burned will probably be improved, but we will start with that.

Also, I incorporated estimates for backpack weight, and a terrain "scaling" factor. The backpack weight inclusion will need improvement as it seems that there is a non-linear relationship between pack weight and calories burned.

So, here is the first version! Also place as a tab at the top.

I guess I needed to check my spelling before posting the comment. Sorry for looking like a buffoon.

ReplyDeleteSoCalMike

THis is a great post, Ze. I tried the calculaiotns with my morning walk with my wife today, and it was interesting to see. I can't wait to try it with a "real" hike. Great post, thanks.

ReplyDeleteSoCalMike

1 of 2:

ReplyDeleteThanks for much for researching and designing this very useful information! I've been interested in these calculations for a while now, and recently designed a spreadsheet based on exported data of a given hike route using only distance and elevation input variables. I have used your calculator as a base to judge whether or not my calculated values seem to carry any merit. After many hours and tweaks, I think I have assembled a very accurate spreadsheet. A few things to note:

Using exported data, this gives me detailed information at small increments of change in rise (height) and run (distance). Think about a 1000 data points for a 4-6 mile hike. This has allowed me to calculate slope based on each increment, which basically breaks down into about 10-100 ft distance segments. I calculated a theoretical hiking pace based on the slope, as well as METs based on these pace increments. As a result, my values have averaged around your website's calculated values, although they do vary quite a bit a times based on the hike data. This is due to a number of factors:

--You are calculating an average slope (and thereby unchanging slope value) from trail start to trail finish. This results in the same amount of calories being burned for any given distance increment from start to halfway. Same thing (although a lesser amount for assuming downhill) from half-way to finish.

--Using lots of data this doesn't always average out in terms of calories burned given that some slopes require MUCH more energy to traverse, (moreso, of course, uphill, but also downhill). If the trail involves lots of steep sections this can increase the final calorie-burned value by as much as 50-100%.

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ReplyDelete--It is also possible to have non-steep slopes that fall right into the ideal range when going downhill as to minimize energy used for increased pace/distance values (we move faster and use much less energy going downhill up to a point). A trail that has an average slope of around 2-8% for the downhill parts (whether a loop or out-and back trail) will actually decrease lower overall calorie-burn of around 25-100%.

--Also it should be noted by anyone who uses such a calculator that total accent is always more than lowest-point to highest-point elevation change. For example, a trailhead starting at 5000 ft that summits a 7000 ft mountain might be an overall gain of 2000 ft, but should also include every bit of accent in between that may follow a temporary descent on the way to the high point. This 2000ft average gain could (and often does) increase up to (and possibly even more than) 100%. Using the above example, it could very well occur that the trail starting at 5000 ft could go up to 5500, down to 4500 (the trail-head is not always the low-point), and then could continue like this all the way to the summit. This adds lots of uphill hiking both on the way to the summit and on the way back to the trail head.

--It is already known that your website's calculator averages out the entire trip, and of course assumes an out-and-back type trail. It must be noted, however, that for the case of loops, especially those that differ quite a bit for each half of those loops, these values can push or pull these extremes beyond the average even more. For example, a loop trail that goes uphill ever so gently (averaging about 2-4%, say) but returns back downhill slightly more steeply (4-8%) will burn MUCH less calories compared to a loop that involves a steeper (and therefore shorter) uphill and very gradual (longer) downhill can differ as much as (or possibly even more than) 400%. That's quite a variance.

In conclusion, while your website's calculator has indeed been very helpful for myself as well as hundreds if not thousands of others, variance can (and often will) exist to the point that a calculated calorie-burn on this website showing 1000 calories burned could in reality burn as little as around 500 (100% decrease) calories and as much as 2000+ (100% increase) calories... with a total potential variance of 400% from low to high.

A way to quick fix this calculation could very well be by adding a terrain steepness difficulty (in terms of sectional steepness as opposed to overall steepness) coefficient; also another coefficient could be used based on whether the trail is a loop or a one way out-and-back.. the one-way would require no coefficient, whereas the larger the difference/variance in loop sections (i.e., first half versus second half of loop) would play a role in either increasing or decreasing overall calorie burn.

Nonetheless, thanks again for creating a very useful tool that is otherwise very difficult to find anything else like it! :)