why is it more difficult to run at an incline on a treadmill when you aren’t actually climbing higher, (g potential energy not increasing)?

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why is it more difficult to run at an incline on a treadmill when you aren’t actually climbing higher, (g potential energy not increasing)?

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The fact your feet are at an angle stretches out your tendons and makes your muscles work differently than they’re used to.

You are gaining potential energy with every step, just losing it again as the belt accelerates your leg back down. Then you have to apply force again to change your velocity upwards, etc…

You are climbing higher, but the treadmill is moving you back down at the same time. For the legs it feels the same.

It’s probably a bit easier to visualize if you imagine walking up an escalator that is moving down at the same time. You stay in one place, but it’s equally as hard as walking up regular stairs.

The escalator is taking potential energy away from you by moving you down and you need to use your muscles to regain that potential energy. In this case you’re actually helping out the motor of the escalator, so that’s where the energy is going.

Even if your upper body stays in one place, the escalator is stealing potential energy because the leg that’s on the steps is being moved down, and you counteract it by lifting the other leg up to the next step.

**ELI5**: Because every step you take your foot is going *down* as the treadmill rolls backward and down the slope. It takes energy to stop your body *also* going down.

**ELI15**: It’s easier to start from standing still (Physicists would call this “the static case”). When you’re standing still, you’re actually holding your weight up against gravity. This basically only takes energy due to the fact that your muscles aren’t 100% efficient and because you put effort into balancing, a chair could do the same job without needing *any* energy. The slope of the treadmill is irrelevant.

Next, let’s look at walking (physicists would call this the “quasi-static case” because the you can ignore momentum)

While you’re taking a step, you’re still doing the same thing, but because you’re moving, there are extra ways your body needs to spend energy (it takes energy to move your muscles at all and your body does have some internal friction, for example) The faster you move, the worse these extra energy costs get.

When your foot is going down the slope, however, you’re also spending energy due to the change in distance from your foot to your centre of mass. The energy needed to push with a force in the direction of movement (e.g. pushing something across a desk, or lifting something) is given by W = F×D – Work done is Force multiplied by Distance travelled (in the direction of the force), and in this case the force is basically your weight and the distance is how far the treadmill lowers your foot while you’re taking the step.

The energy it takes to push with the force of your weight against the treadmill while it lowers your foot by a distance D is what makes it more tiring. It’s actually the same force and therefore the same effort as if the treadmill was level but you were *lifting* your body by the same amount. It takes the same force, and the distance is the same, so the energy taken is the same.

[[EDIT: to extend the “chair” comparison from the “standing still” case, you could replace your legs with wheels. A wheel doesn’t use up energy to just hold the weight (well, friction is still a thing) but it *would* require energy to stop the wheels rolling backward down the slope – you’d need to push *forwards*. If you tied yourself to the wall, you wouldn’t be putting any energy in, but the *treadmill* would have to push harder to keep rolling, so the energy would come from there instead.]]

When you’re running, the difference is a little more because you’re working your body harder and it gets a little less efficient, but most of the difference between a flat and an inclined treadmill is basically the same.

**ELINerd**: To extend it to running (physicists would call this “the dynamic case”), you get secondary effects like the fact that your centre of mass is actually accelerating up and down during each step cycle, so the force between your foot and the treadmill isn’t constant (and indeed is zero while both feet are in the air between steps) but the average is the same as in the dynamic case.

The inefficiencies of your body and the chemistry it’s based on aren’t linear, though, so it ends up taking more energy than walking.

In this region, the *physics* doesn’t actually change much – if we look at the averages over a full cycle of steps the numbers are the same, but your body’s ability to perform work gets less efficient the harder you push it.

Your muscles and joints have more internal friction as movement speed increases (and there’s air resistance, too) The chemical processes used to convert your body’s energy stores into movement are less efficient because the supply of chemicals is thinned out. Your heart has to pump blood around your body faster to keep your muscles supplied with those chemicals. Your lungs have to work harder to keep up with the oxygen demand (and the level of oxygen in your blood might dip a bit under the strain again reducing the efficiency of the chemical reactions). Heat needs to be dissipated, so you spend energy on that.

If you keep working hard enough for long enough, your body actually starts running out of its primary sources of energy (ATP & glucose) and has to use progressively less easily accessible forms of energy to replenish them (all the way up to stored body fat, which is probably why you’re on the treadmill in the first place :-P) Every step further away from the ATP that your muscles actually contract involves another chemical process that again loses some energy and is less efficient the more of your body’s capacity you use.

Of course, if you keep up the exercise on a longer time scale (over days / weeks / months, rather than a single gym session) then your body starts adapting various things to make their capacity larger, meaning you can do the same work with less need for the secondary sources of energy.

Adaptations include how/where your body stores its energy, increasing the size of your muscles (including your heart), increasing the number of mitochondria in cells (they’re involved in the conversions between energy-storing chemicals “mitochondria are the powerhouse of the cell!”), increasing the number of red blood cells to increase oxygen transport in the blood, and probably 1001 others that I’m not really qualified to talk about (your liver is heavily involved in the chemical conversions, for example, and I imagine it adapts in its own way if increased capacity is needed)