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=The Difference Between Running and Walking=
Running and walking are two different forms of movement. In running you either have one foot on the ground or both feet in the air; both feet are never on the ground at the same time. In contrast, when walking you either have one or both feet on the ground and never have both feet in the air.
=The Effect of Incline=
It's intuitively obvious that running or walking uphill is harder than level ground. It's also reasonably obvious that modest downhill slopes are easier than level ground, but as the slope increases so the difficulty becomes greater. Scientific research has supported and quantified this<ref name="Minetti-2002"/>, showing that the energy cost of walking or running is to lowest at about 10% decline. There is some evidence that the slope of minimum energy is independent of pace<ref name=" Minetti 1994"/>. This slope of minimum energy requirement seems to corresponds with the slope that neither requires pushing back for forward movement nor energy dissipation for braking<ref name="SnyderKram2012"/>. The two graphs below show the relationship between slope and the cost of walking/running as measured by a number of studies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|- valign="top"
|[[File:Energy cost of running.jpg|none|thumb|300px|The energy cost of running for various slopes.]]
|[[File:Energy cost of walking.jpg|none|thumb|300px|The energy cost of walking for various slopes.]]
|}
There are a number of factors that could change these assumptions:
* A study looked at the energy cost of uphill, level, and downhill running before and after a 65Km mountainous ultramarathon<ref name="VernilloSavoldelli2015"/>. After the race, the energy cost of uphill running was unchanged, but both level and downhill running were significantly harder by 8% (level) and 13% (downhill). These differences were greatest for the slowest runners and at least for the fastest runners.
* A similar study of a rather more extreme 303 Km mountain ultramarathon found that the energy cost of uphill running and walking was lower after the race<ref name="VernilloSavoldelli2016"/>. This result is a little surprising, and it's unclear why runners would do better fatigued than fresh. (The study did not look at level or downhill running.)
* I've found no research on the effect of training on the energy cost of running uphill or downhill. I would expect that downhill training would reduce the energy cost of downhill running.
=The Transition Between Running and Walking=
The energy required to run a given distance is the roughly the same regardless of pace. This is different to walking, where the energy required to walk a given distance generally goes up with pace. This means that at slow speeds, it costs less energy to walk than run, but as you go faster it becomes easier to run. When people are put on a [[Treadmill|treadmill]] and the speed gradually increased, they will naturally transition from walking to running. This transition occurs at roughly the same speed for most people and is called the Preferred Transition Speed (PTS)<ref name="Rotstein-2005"/>. You can see this in the two graphs below. The graph on the left shows the energy expenditure over time, showing the energy required to walk goes up faster than for running. The graph on the right shows the cost per distance, with running staying constant and the cost of walking rising with pace. (It takes more energy to walk a distance very slowly, so the graph shows the low point which is the lowest energy cost to cover a distance.)
{| class="wikitable"
|- valign="top"
This table shows how the slope would change your pace if you keep the same effort (Calories per hour). The first column is the running pace on the flat, then each column shows the pace you would travel if you run or walk on various slopes.
<include_PHP file="CalorieInc_EvenEffort"/>
=Training Status Effects=
The graph on the below shows that there are slight, non-significant differences between runners and active non-runners. This indicates that training does not change the transition speed, though it’s it's worth noting that the actual transition speed is slower than would be expected from the energy costs<ref name="Rotstein-2005"/>. Also note that the actual cost of running is not quite constant with speed, but actually goes down as you go faster.
[[File:Transition Runners.jpg|none|thumb|500px|The energy cost for runners and non-runners, showing the Preferred Transition Speed (PTS) and the Energetically Optimal Transition Speed (ETOS).]]
=Formula=
for those who like to create their own tables, below are the underlying formulas that I'm using. The cost of running (Cr<sub>i</sub>) and walking (Cw<sub>i</sub>) on a slope is given by these equations:
Cr<sub>i</sub> = 155.4i<sup>5</sup> - 30.4i<sup>4</sup> - 43.3i<sup>3</sup> + 46.3i<sup>2</sup> + 19.5i + 3.6
Cw<sub>i</sub> = 280.5i<sup>5</sup> - 58.7i<sup>4</sup>- 76.8i<sup>3</sup>+ 51.9i<sup>2</sup>2+ 19.6i + 2.5
Where i is the slope and the result I in Jules per Kg per Meter.
=References=
<references>
<ref name="Minetti-2002"> AE. Minetti, C. Moia, GS. Roi, D. Susta, G. Ferretti, Energy cost of walking and running at extreme uphill and downhill slopes., J Appl Physiol, volume 93, issue 3, pages 1039-46, Sep 2002, doi [http://dx.doi.org/10.1152/japplphysiol.01177.2001 10.1152/japplphysiol.01177.2001], PMID [http://www.ncbi.nlm.nih.gov/pubmed/12183501 12183501]</ref>
<ref name="Rotstein-2005"> A. Rotstein, O. Inbar, T. Berginsky, Y. Meckel, Preferred transition speed between walking and running: effects of training status., Med Sci Sports Exerc, volume 37, issue 11, pages 1864-70, Nov 2005, PMID [http://www.ncbi.nlm.nih.gov/pubmed/16286854 16286854]</ref>
<ref name="VernilloSavoldelli2015">Gianluca Vernillo, Aldo Savoldelli, Andrea Zignoli, Spyros Skafidas, Alessandro Fornasiero, Antonio La Torre, Lorenzo Bortolan, Barbara Pellegrini, Federico Schena, Energy cost and kinematics of level, uphill and downhill running: fatigue-induced changes after a mountain ultramarathon, Journal of Sports Sciences, volume 33, issue 19, 2015, pages 1998–2005, ISSN [http://www.worldcat.org/issn/0264-0414 0264-0414], doi [http://dx.doi.org/10.1080/02640414.2015.1022870 10.1080/02640414.2015.1022870]</ref>
<ref name="VernilloSavoldelli2016">Gianluca Vernillo, Aldo Savoldelli, Spyros Skafidas, Andrea Zignoli, Antonio La Torre, Barbara Pellegrini, Guido Giardini, Pietro Trabucchi, Grégoire P. Millet, Federico Schena, An Extreme Mountain Ultra-Marathon Decreases the Cost of Uphill Walking and Running, Frontiers in Physiology, volume 7, 2016, ISSN [http://www.worldcat.org/issn/1664-042X 1664-042X], doi [http://dx.doi.org/10.3389/fphys.2016.00530 10.3389/fphys.2016.00530]</ref>
<ref name=" Minetti 1994">Minetti, A. E., L. P. Ardigo, and F. Saibene. "Mechanical determinants of the minimum energy cost of gradient running in humans." Journal of Experimental Biology 195.1 (1994): 211-225.</ref>
<ref name="SnyderKram2012">K. L. Snyder, R. Kram, J. S. Gottschall, The role of elastic energy storage and recovery in downhill and uphill running, Journal of Experimental Biology, volume 215, issue 13, 2012, pages 2283–2287, ISSN [http://www.worldcat.org/issn/0022-0949 0022-0949], doi [http://dx.doi.org/10.1242/jeb.066332 10.1242/jeb.066332]</ref>
</references>
[[Category:Science]]