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Often when we go hiking, we encounter two kinds of paths whenever we have to cover elevation. We either go up via stairs or via walking up a ramp. Sometimes both are available side to side. And it's often got us wondering, what takes more energy?

I know that potential energy depends on the height alone. So, from potential Energy perspective, it's the same whether we ascend the same elevation via stairs or via a ramp.

But what other factors might affect the energy expended? Friction for example? Or energy used by muscles? Is it possible to say with certainty which path would expend less energy or there are too many factors to really compute it. I couldn't really find a solution using Google.

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  • $\begingroup$ You're correct that potential (not kinetic) energy difference is identical based on the height. Biomechanical effects might make one path or the other more efficient to climb. But that sort of takes it away from being a good physics question. $\endgroup$
    – BowlOfRed
    Commented Apr 24, 2023 at 23:44
  • $\begingroup$ Oops. facepalm moment >.< Thanks for the correction. How about the effects of friction at least? That should make it a physics question? $\endgroup$
    – Paagalpan
    Commented Apr 24, 2023 at 23:46
  • $\begingroup$ Nothing in the description suggests that there would be a difference due to friction. If one of them were steep and slippery and you couldn't keep your shoes on the path, that would be a source of energy loss. $\endgroup$
    – BowlOfRed
    Commented Apr 24, 2023 at 23:48
  • $\begingroup$ Are you asking about theory? or are you asking about biomechanics? In theory the lower bound on the amount of energy required depends only on the height difference. If some particular mechanical (or biomechanical) system uses more energy, then that would be a peculiarity of the system, and we would have to analyze in detail exactly how the system worked in order to understand it. $\endgroup$
    – Solomon Slow
    Commented Apr 24, 2023 at 23:51
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    $\begingroup$ It may even depend on the person. Some people will preffer the ramp, others the stairs. The shoes you wear may make a difference too. If you actually encounter these situations, why not try? $\endgroup$
    – nasu
    Commented Apr 25, 2023 at 1:10

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Another way to phrase this question is which gives the greater mechanical advantage (MA) a ramp or stairs where $$MA = \frac{L}{h}$$

Ramps are right triangles so L would be the distance of the distance of the hypotenuse.

For steps covering the same horizontal distance and height, L would be the horizontal distance traveled which is less than the hypotenuse distance for the ramp.

So a ramp gives a great mechanical advantage than stairs covering the same horizontal and vertical distances. Legs are given less of a mechanical advantage so stairs work the legs harder.

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    $\begingroup$ Do you really think that this is true for any inclination? Try to climb an incline at 60 degrees from horizontal and see how your legs feel. On the incline the foot is at an angle to the leg axis most of the time and this produces a stress on the ligaments and whatever else is there. The stairs allow to have your feet (soles) horizontal most of the time. I would preffer the stairs unless the slope is very small. $\endgroup$
    – nasu
    Commented Apr 25, 2023 at 1:17

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