Franco - in terms of energy used, it does not make a lot of difference whether you run or walk 100m. How tired you feel afterwards is a totally different question. That will depend on how much of the energy source is used (ATP, glucose, glycogen, or fatty acids), how well trained you are at a particular speed and a host of other factors.

There is an actual calculation that we can do in the lab that calculates something called running efficiency. Much of it is genetic, but it can be improved with training. Certain gait styles, shoes, ambient temps, etc can all alter running efficiency and this may be more to the point of your original question....

Short story - it's roughly the same if the only variable is speed. You can get as technical as you want, but the outcome won't change.

You use more fuel if you drive at 100mph than if you drive at 60mph. :-)

Depends on what the vehicle is geared for. You can gear for max efficiency at 60 or 100.

Same vehicle. :-)

Shifting from a three to a four hour run isn't going to change metabolism substantially, since either way, you aren't going to be finishing the run if you work much over your lactate threshold. Running 25% faster probably will play a big roll in how efficiently your digestive system works, so you may be running out of energy because you are using it up faster than your body can resupply the muscles. But that isn't using more energy, it is just using up a more limited energy supply.

Also, we have a running gate and a walking gate that is most energy efficient given our personal training and biomechanics. If we are running or walking either slower or faster than our most efficient gate, we are using more energy. Hiking with a hiker slower than me is exhausting, as is hiking with someone that walks or runs much faster.

Finally, more time standing is more energy used. So, if you spend four hours running vs. three hours running and one hour laying down, the overall energy usage would be closer than comparing the energy usage of only three vs. four hours of running time.

Okay, one more point . . . I don't think this is really an appropriate question for a physics expert, since physics actually has relatively little to do with it. It seems more appropriate for a physiologist. :)

"Also, we have a running gate and a walking gate"

No. How about gait?

--B.G.--

Haha. Thanks Bob.....

It is an interesting question for physics nerds (of which I am one...), but I agree that if you want a real answer it is actually a question for biomechanists and physiologists. What the OP asked boils down to running economy, fitness level, efficiency, etc.

Ever had a day when even though everything seems like it should be fine, you just don't have the legs? We call it an "off" day and they are quite common across all athletic pursuits, regardless of level. It is also a common maxim that it is MUCH harder to run a 6 hour marathon than a sub-three, but that 6-hour "runner" is incapable of actually performing at the level required to run a sub-three. He doesn't have the mechanics, the VO2 max, the gait, the stride, the percentage of fast vs slow twitch muscle fibers, etc. Yet the amount of damage to his body, the energy expended, etc is FAR greater for the poor slow poke the back (again...count me in!) than the elite guy at the front.

If we were to take only mechanics into consideration, none of this would be true. It works great for all those calculations of energy and work and mass and time etc, but unfortunately our bodies have a heck of a lot more going on than simple Newtonian physics. Well, actually it really is all just Newtonian physics...but a whole mess of it!!!!

Here is an article from the NY Times that is a good summary: http://www.nytimes.com/2007/10/11/fashion/11Best.html?pagewanted=all&_r=0
It does a good job of explaining all the variables to running efficiency: fitness, running economy etc.

This is a huge area of research right now for those of us who work with athletes.

"I don't think this is really an appropriate question for a physics expert, since physics actually has relatively little to do with it. It seems more appropriate for a physiologist"

The physics experts would be better at asking the question whether you'de get wetter, if it was raining, running faster or slower

"The physics experts would be better at asking the question whether you'd get wetter, if it was raining, running faster or slower."

Physicist Are good at asking questions...

And providing answers -

You'll get "less wet" by moving faster.

Edited by greg23 on 12/29/2012 21:39:05 MST.

You get less wet running faster.

well this is the typical area where I disagree regardless of how many experts come on board.
Here is why.
Go out when it rains really hard just wearing your standard running stuff.
After say 30 minutes max you will be completely wet regardless if you are walking or running.
Once you are fully soaked you can't get wetter than that...

So , it depends....


anyway going back to calories here is a bit from this article :

http://www.runnersworld.com/weight-loss/how-many-calories-are-you-really-burning-0?page=single

I was still gathering my resources for a retort when a new article crossed my desk, and changed my cosmos. In "Energy Expenditure of Walking and Running," published last December in Medicine & Science in Sports & Exercise, a group of Syracuse University researchers measured the actual calorie burn of 12 men and 12 women while running and walking 1,600 meters (roughly a mile) on a treadmill. Result: The men burned an average of 124 calories while running, and just 88 while walking; the women burned 105 and 74. (The men burned more than the women because they weighed more.)

than goes on to talk about Net Calorie Burn :


Thanks to the Syracuse researchers, we now know the relative NCB of running a mile in 9:30 versus walking the same mile in 19:00. Their male subjects burned 105 calories running, 52 walking; the women, 91 and 43. That is, running burns twice as many net calories per mile as walking. And since you can run two miles in the time it takes to walk one mile, running burns four times as many net calories per hour as walking.

Edited by Franco on 12/29/2012 23:12:43 MST.

I think there is room for both physicists and physiologists in my original question.

As the OP, I posted it to physicists first because I wanted to make sure what the answer was "holding everything but time constant".

this answer seems to be that doing the run in 3 or 4 hours would use the same energy.

Now its up to the physiologists to bring in all the inefficiencies that prove in a real world situation that one or the other is more efficient (most likely the slower time).
some points have already been mentioned.
but there are so many variables here ...

Edited by asandh on 12/30/2012 08:46:58 MST.

As Jen and others who are thinking that PHYS in this case has to include both physics and physiology, this is all about efficiency.  A few good freely available references are at http://www.ncbi.nlm.nih.gov/pubmed/17766303
and http://www.clinicalgaitanalysis.com/history/Ralston_IZAP.pdf

N.b., slower is more efficient only to a point. There's an optimal gait and speed even on level ground, but think, too, about going downhill. If you go very, very slowly, holding back on every step down, you're going to burn a ton of extra energy (think weight-lifting or pushups done in slow mo).

Cheers,

Bill

Note that the calorie calculator at the bottom of the runnersworld link above has

Total calorie burn per mile (running) = 0.75 x weight (lbs)

This is almost exactly the same as the equation I posted on the previous page

Total calorie burn per km (running) = weight in kg

I'm with Jen on this. An engineer /physics person is going to tell you the human body has done zero net work on this journey. You really need a human body expert like a physiologist who can tell you the differences in efficiencies of the human body at different speeds, on average.

"An engineer/physics person is going to tell you the human body has done zero net work on this journey."

NO engineer/physicist will tell you the Work walking around a closed loop is zero. As posted above, that is only for the specialized cases involving conservative force fields in scenarios that a hiker will not encounter.

Edited by greg23 on 12/30/2012 11:04:22 MST.

I am no expert.

But if an elite runner ran a 10K in 40 minutes, then later in the day ran a 28 minute 10K he would burn a lot more energy during the 2nd run.

As humans don't have much in the way of regenerative braking, I've set out the following scenario for two speeds. Please let me know if I've made any errors in the calculations!

The setting: a 75kg person, traveling 100m. Assume 2 seconds are used accelerating to either 1.5m/s or 3m/s.

F=ma, W=Fd, and d=0.5at^2 so:

F₁ = 75kg * (1.5m/2s^2);
F₁ = 56.25N
d₁ = 0.5 * (1.5m/2s^2) * (2s)^2
d₁ = 1.5m (He will travel 1.5m in this time.)
W₁ = 56.25N * 1.5m
W₁ = 84.375 J

F₂ = 75kg * (3m/2s^2);
F₂ = 112.5N
d₂ = 0.5 * (3m/2s^2) * (2s)^2
d₂ = 3m (He will travel 3m in this time.)
W₂ = 112.5N * 3m
W₂ = 337.5 J

Disregarding friction, we can assume that person then coasts at this speed until near arrival at destination, at which point he digs his heels into the ground to stop.

Now, the equation for net work is:
W_net = 0.5mv_final^2 - 0.5mv_initial^2

Obviously starting, traveling, and stopping would give a net work value of 0, but I think one must consider the energy flow. The initial acceleration has v_initial = 0m/s and v_final = 1.5 or 3m/s, and represents chemical energy being converted to kinetic energy. The second "acceleration" has v_initial = 1.5 or 3m/s and v_final = 0m/s, and represents kinetic energy being converted to heat (friction braking). Thus, the caloric cost is mirrored by W₁ and W₂ above, i.e. roughly quadruple for the faster speed. So, what am I missing?

Edit: added final W₁ and W₂ values, changed "double" to "quadruple".

Edited by requiem on 01/01/2013 23:51:44 MST.

"So, what am I missing?"


Uh, plain English?

;)