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Let's assume that a person walks on a flat surface. Work performed by a human can be calculated by this equation: $W=F*s(1)$, where $F$ is a force and $s$ is a distance. I am curious how mobile applications are calculating burned calories? Google search on this topic bings results on this topic without explanation. For example, CNN article

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closed as off-topic by John Rennie, Jon Custer, sammy gerbil, Kyle Kanos, ZeroTheHero Apr 5 '18 at 7:42

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    $\begingroup$ This is much more an issue of body mechanics than physics. Different people burn differing amounts of calories doing the same exercise, and it's all down to how their body is built and the way their muscles utilize energy. It would be very difficult indeed to calculate calories burned starting from W=F*d. $\endgroup$ – enumaris Apr 2 '18 at 22:21
  • $\begingroup$ There are indeed complex metabolic models that can predict more accurately using for example the measured respiratory quotient; telling what type of fuel is burnt (fat or sugar). But the simple models used on mobile phones make many assumptions and base their estimate on the body weight entered and speed/distance traveled. And yes these are not physics models but rather biophysical models; perhaps even empirical. $\endgroup$ – docscience Apr 2 '18 at 22:35
  • $\begingroup$ I think that a human like a machine with coefficient of performance less than 100% where burned energy is more than physical work performed. So, by estimating physical work, we can estimate burned calories, can we? $\endgroup$ – yW0K5o Apr 2 '18 at 22:44
  • $\begingroup$ @yW0K5o Not with any reasonable degree of accuracy. Human bodies are much too complex to be modeled with a single efficiency measure like that. $\endgroup$ – J. Murray Apr 3 '18 at 0:45
  • $\begingroup$ Possible duplicate of Calories Burned While Hiking $\endgroup$ – sammy gerbil Apr 3 '18 at 17:26
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A pretty complete and systematic study of this was done by Minetti et al., with elite athletes on a treadmill, by measuring their oxygen consumption. The amount of energy consumed is proportional to:

  • body mass
  • distance traveled

It also depends on:

  • whether the gait is running or walking
  • slope
  • speed
  • athletic training

For walking on a level surface at the optimal speed, they find a cost of $1.6\pm 0.5\ \text{J}\cdot\text{kg}^{-1}\text{m}^{-1}$ (for these elite athletes).

On very steep uphill slopes, they found that the efficiency was approximately that of concentric muscle contraction. That is, if you hook a muscle up to an electrode and force it to contract while doing work, it does work $W$ while consuming chemical energy $W/\epsilon$ from muscle glycogen, where $\epsilon$ is the efficiency. When elite athletes walk or run up a steep hill, the work $W$ they do against gravity is found to relate in approximately the same way to the energy burned in glycogen, with approximately the same value of $\epsilon$. Of course this can't be true on all slopes. If it were true on downhills ($W<0$), then you could recharge your body's energy systems by walking downhill.

Your cell phone app may know your body mass (if you tell it) and also the distance traveled, slope, and speed. It may be able to guess based on your speed whether you're running or walking. There's no way it knows your level of athletic training, which probably introduces a possible systematic error that's on the order of a factor of 2. If the app is closed-source, then you have no way of knowing what model it's using. If you're interested in seeing figures from an algorithm that's open source, you can check out my app kcals. The way it works is that you save a GPS track and then upload the track, and the app analyzes it for you.

References

Minetti et al., "Energy cost of walking and running at extreme uphill and downhill slopes," J. App. Physiology, 2002, https://www.physiology.org/doi/full/10.1152/japplphysiol.01177.2001

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