A good walk spoiled?

July 28, 2005 4:30 AM

Here's a physics/exercise question. If you walk over a closed course that varies in altitude over the course, is the energy expended the same going one way as the other?

This has a real-life application. In order to fight my middle-age spread, I'm taking a walk in the neighborhood regularly. The start and end are the same (my house), but if I go one way, I'm greeted with a big steep hill that I have to scale during the walk. If I go the other way, I go up and down some hills, and have a sustained climb, but don't go down the steep hill.

Do I expend the same energy going either way?

posted by jpburns to science & nature (18 comments total)

It is really hard to say. It depends on the relative size of the hills and the steepness as well as your pacing. E.g. going slowly over the lower hills might not be as challenging (and therefore calorie-consuming) as going slowly over the steep hill (energy released just due to changing altitude).

I would suggest you get one of those heart monitors or others like them. What you want is burn calories efficiently (scroll down in the FAQ list for more information). And then you can vary your routine by alternating walk directions every other day.
posted by carmina at 5:23 AM on July 28, 2005

In theory, if you walked at the same pace the whole time, they would be exactly the same.

In reality, if you're dragging yourself up that steep hill slowly, and then wandering the rest of the route slowly, as well, v. keeping up a brisk pace if you avoid it, then you'd be burning different calories for each.
posted by jacquilynne at 6:06 AM on July 28, 2005

A highly efficient machine would spend the same amount of electricity going in either direction, since the amount of energy required to go up and down hills *must*, by definition, be the same in both directions because the end point is at the same hieght.

The thing to consider, though, is that walking downhill for the human body is not significantly easier than walking on even ground, so the potential energy gained by walking up a slope is not returned to us by walking down the other side. Furhtermore, walking up an extended and steep incline will do a better job of raising the heart rate, so the excersive may be more effective on that route.

Because human locomotion is not particularly efficient - you won't expend the same energy in both directions. So, whichever leaves you more tired at the end, is probably the better workout.
posted by jaded at 6:10 AM on July 28, 2005

gravity is described by a conservative field - for any simple closed curve the line integral is zero. that means that from a very abstract physics point of view, you do no work against gravity (because coming back down you are "helped" as much as going up was harder).

clearly you do use energy when walking, so a pure physics argument doesn't help very much. in other words, this is going to depend on obscure details of how the body works.

in general, machines work best when they are operate within a "standard" range of parameters. if a machine heats up for some reason it's likely to become less efficient and heat up even more. so you might expect that a body would be similar, in which case the route that makes you most uncomfortable at some point is a good choice for burning calories (you want to be inefficient).
posted by andrew cooke at 6:45 AM on July 28, 2005

The thing to consider, though, is that walking downhill for the human body is not significantly easier than walking on even ground

I disagree. If you take a look at how your legs work when going downhill, particularly when you're tired, you'll notice you do a kind of "kick-fall". That is, you kick your leg out, then let gravity pull you down, then repeat for the other leg. This is significantly easier than pushing up your body mass against the force of gravity.

It is true that walking downhill can be taxing, and to different muscle groups that might not get a great deal of exercise under normal conditions, so this might contribute to feeling more "worn out" sooner.

To answer the initial question, on a closed-loop course, your rate of energy expenditure should be equal in either direction.
posted by Civil_Disobedient at 7:14 AM on July 28, 2005

Oh, I just noticed that you said downhill walking is not significantly easier than walking on even ground, not downhill, in which case I agree. My apologies, I think you are correct.
posted by Civil_Disobedient at 7:16 AM on July 28, 2005

downhill uphill. Sometimes I miss the old-style preview.
posted by Civil_Disobedient at 7:17 AM on July 28, 2005

maybe if you were on a bike.
posted by delmoi at 7:46 AM on July 28, 2005

you most likely expend more energy going up the steep hill. your heart rate stays elevated for quite some time after a hard bit of exercise. Going up the steep hill will probably have an overall increase of your heart rate during the walk than if you didn't - which means you'll burn more calories.
posted by escher at 7:56 AM on July 28, 2005

I'll tell you one thing from experience: walking up steep hills will cause some anaerobic effort and it's strength training - it will probably stimulate muscle growth - particularly in your calves. If you have tunnel vision about "losing weight" (rather than gaining fitness), this could frustrate you. And as others have said, your peak heart rate will be higher, and you're less efficient when you're "redlining."

I also know that a closed loop can be dramatically different depending on which direction you traverse it when cycling - and there's no hard and fast rule to figure out which way is going to be the easier one. In the simple scenario where there's a short steep climb one way and a long gradual climb the other I will generally expect to finish faster if I ascend the steep side, despite what I said above.

My bottom line is that for your walk, the difference in energy expenditure is likely negligible, but it's the different effects of the two styles (high peaks efforts vs. a steadier, lower output) that you should be considering - even if they miraculously averaged out to exactly the same energy consumption.
posted by Wolfdog at 8:15 AM on July 28, 2005

The difference in direction is probably insignificant. To get the benefits of each, alternate directions.
posted by mischief at 9:17 AM on July 28, 2005

I say ignore physics and measure your heart rate. That will tell you which is causing you more exertion.
posted by Rhomboid at 9:30 AM on July 28, 2005

I'd agree with escher and Wolfdog.

Imagine a loop that has a long, gradual incline, followed by a steep downslope, bringing you back to your starting point. If you walk in this direction, your heart rate will be slightly elevated compared to walking on level ground, but not so much as you'd notice. You'll then have to walk down the steep slope, which might actually be more difficult.

Now go the other way. You climb the steep slope, cross your anaerobic threshold, get to the top winded, and then walk gradually downhill, recovering as you go. It's a completely different sort of workout.

Still, there's nothing like empirical results.
posted by adamrice at 11:09 AM on July 28, 2005

Correct me if I'm wrong, but if you go x distance, it doesn't matter how quickly you do it, you still expend the same amount of energy, don't you?

Energy = Force X Distance

Where Force is how much you weigh, right? So whether you do a 10km distance in 2 hours or 40 minutes, assuming the same weight, you are burning the same calories,right?

Now, I know, there are more benefits to going faster (increasing lung capacity, heart health, overall fitness, muscle conditioning, etc); but strictly talking about energy expended, it doesn't matter how quickly one covers the distance, right?
posted by eurasian at 2:41 PM on July 28, 2005

Take 10,000 steps on a flat treadmill then 10,000 steps on a steeply inclined treadmill and you'll quickly find that there is significant difference in the energy expended.

The uphill will expend more energy...but why bother, the fact that you are walking is good enough for now. Once your easy walk becomes too easy start mixing in the harder, uphill walk on occasion.
posted by m@ at 2:52 PM on July 28, 2005

Eurasian, you're wrong on several fundamental points.
Force is how much you weigh, right?
Only if jp were trying to lift himself vertically - generally not the case for runners. They're weird, but at least they usually move horizontally. So, as an exercise, think about what forces he's actually acting against when he runs.

So whether you do a 10km distance in 2 hours or 40 minutes, assuming the same weight, you are burning the same calories,right?
Now, that seems plausible from a Physics / Vector 101 standpoint but it's wrong in the real world. The guy who runs it in 40 minutes not only uses energy at a faster rate, he uses more total energy.

But from a health & fitness that's not the end of the story, because the guy who's burning energy at a high rate has to get a lot of his energy from - yes - rapid energy sources. And he only has so much of that stuff stored, so he has to keep replenishing as he goes. Whereas the more leisurely exerciser, if he has time at his disposal, can make use of slower-burning energy stores (like fats) and not have to take in as much while he's doing it. So for the guy who's specifically interested in weight-loss and has lots of time, a longer exercise routine at a lower intensity may be the better deal, contrary to expectations, even if it uses less total energy.
posted by Wolfdog at 3:48 PM on July 28, 2005

I've considered this when cycling and this is my maximally lazy solution. Go in the direction of the steep uphills. Because I'm a wimp who's afraid of speed, I don't get very much benefit (gravitationally, not exercise-wise) from going down steep hills, I ride my brakes. Descents that are long but not steep give me the most speed. I also prefer to have the steep parts at the beginning when I still have energy and finish with a downhill.

I imagine if you did the opposite of all those, you'd ideal workout.
posted by Octaviuz at 4:50 PM on July 28, 2005

Do I expend the same energy going either way? I don't think so. I live on top of a hill and my road is a five mile loop. If I take a left I go down a very steep hill for one mile, then walk on the flat for two miles, then two miles uphill. Same drop & raise in elevation. If I take a right (2 miles downhill, 2 miles on the flat and one mile hard hump uphill) it's ten minutes faster. Doesn't longer time=more work?
posted by Mack Twain at 12:37 AM on July 29, 2005