Does speed affect energy consumption over a certain distance?

[Norway]

Hi!

I just watched a video about cardio training, where it is claimed that the only thing that matters is the distance covered, and not the speed. "Four miles burns more calories than three miles." So, walking four miles burns more calories than sprinting three miles. (Click the link and watch one minute, if you have a minute to spare. Or watch it for 30 seconds in 2x speed, as I do!)
Part of the reasoning is that calories are just energy, which in turn is just work, and work just depends on the distance travelled, not the speed.

I remember that I once thought the same, but I was thoroughly put in place by a physics tutor many, many years ago. He said "Just imagine you're driving your car from A to B. You drive a set distance. Naturally, it will take more energy to go fast then to go slow."
I believed it immediately, and have thought so through all these years.

Now, I was about to correct this guy in the video. However, before I posted my comment, I wanted to verify this, but... I couldn't. There was a sudden doubt that came to mind. Yes, going faster takes more power, but you go for less time. So maybe they sum up to be the same energy, regardless of speed...?

I tried googling and reading my old physics books, but I didn't get any wiser.

My thoughts are...
Since W = F*s, then you will need more force (F) for the acceleration, and in the case of a car going fast, the air resistance will of course increase F a bit. On a treadmill without air resistance, however, and disregarding the few seconds of acceleration, as long as you go with constant speed, perhaps it doesn't matter if that speed is 5 km/h or 15 km/h...?
I'm really not sure!

Now I turn to you for help.

What is correct here?

Thank you very much in advance for replying!

 

[russ_watters]

You are 90% correct here. Small correction:

Since W = F*s, then you will need more force (F) for the acceleration, and in the case of a car going fast, the air resistance will of course increase F a bit.

Work is force times distance. Power is force times speed.

And:

On a treadmill without air resistance...

On a treadmill without air resistance, however, and disregarding the few seconds of acceleration, as long as you go with constant speed, perhaps it doesn't matter if that speed is 5 km/h or 15 km/h...?

Have you ever been on a treadmill...? Or run with a wind? I promise it is much harder to run fast than slow, unless there is an awkward gait for running slow, and regardless of wind.

Running requires pushing yourself up and forward, then catching yourself with an up and backwards force. The faster you run, the longer the stride and larger the force needs to be. Wind is not part of the issue.

 

[Norway]

You are 90% correct here. Small correction:

Work is force times distance. Power is force times speed.

Thank you for your reply!
I know, I just used the formula found on Wikipedia, which uses s as a symbol for displacement. I can absolutely see how that is ambigious!

Have you ever been on a treadmill...? Or with a wind? I promise it is much harder to run fast than slow, unless there is an awkward gait for running slow, and regardless of wind.

Running requires pushing yourself up and forward, then catching yourself with an up and backwards force. The faster you run, the longer the stride and larger the force needs to be. Wind is not part of the issue.

Haha, yes I have (and I hate it!) :-)
Of course I notice how every stride takes more power when I'm running compared to walking. However, the stride is also much longer, and because I haven't practiced technique, much of the force is also exerted upwards (compared to walking). A skilled runner who runs efficiently let's his/her body "glide", and exerts most of the force forwards, like walking.
Let's say I'm running 20 meters. That is perhaps 10 steps if I'm running fast, and 40 steps if I'm walking. So even though every step is harder when running fast, I use much, much fewer steps running. Perhaps they sum up to the same work over a distance of 20 meters? Or perhaps not? I'm not sure, and even thinking about my many hours on the treadmill couldn't give me the confidence to conclude. I was looking for a more solid proof rooted in the laws of physics. :-)

 

[russ_watters]

Thank you for your reply!
I know, I just used the formula found on Wikipedia, which uses s as a symbol for displacement. I can absolutely see how that is ambigious!

My mistake -- I'm an engineer, not a physicist!

A skilled runner who runs efficiently let's his/her body "glide", and exerts most of the force forwards, like walking.

While this is largely true, remember that how high you have to hop with each stride is dictated by the stride period. When you are in the air (given a certain upwards velocity), gravity alone dictates how long you are in the air. The only way to decrease the height is to decrease the time -- to increase your step frequency.

Let's say I'm running 20 meters. That is perhaps 10 steps if I'm running fast, and 40 steps if I'm walking. So even though every step is harder when running fast, I use much, much fewer steps running. Perhaps they sum up to the same work over a distance of 20 meters? Or perhaps not?

Well if we're comparing walking to running and not different running paces, then the key difference is that while walking you don't go airborne, so it takes much, much less energy per distance to walk.

 

[jbriggs444]

Moving the legs back and forth at high speed (high speed = high² acceleration = high² force) means more energy consumed doing nothing useful.

 

[Norway]

So...
In theory, if it was just a box, moving in vacuum, without friction, yadda-yadda, then it would actually take the exact same amount of calories to move from A to B, regardless of the speed it traveled with.

But because "the legs move more back and forth", in real life, you would spend more calories running than walking... have I understood you correctly?

 

[A.T.]

But because "the legs move more back and forth", in real life, you would spend more calories running than walking... have I understood you correctly?

There are multiple factors that increase energy / distance with increasing speed, because their energy requirement is non-linear to speed:

- Swinging the legs
- Braking in the early stance phase
- Air resistance

Even on wheels, you still would have the last factor, thus use more energy / distance at higher speeds. But for humans the first two dominate.

The key is: Muscles don't have regenerative braking. They use fuel (sugar) for doing negative work (absorbing mechanical energy). Both energy inputs are dissipated as heat. Only the tendons provide some limited regenerative energy storage.