# Watts & HP - how puny are you? (perspective)

Discussion in 'Physics' started by strantor, Apr 27, 2012.

1. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,302
1,989
I've grown up around this term "horsepower" and I know what it means, but I guess I never really had a full grasp of what was going on around me. My thinking has always been that there's no way that 1 horsepower is equal to the amount of power that 1 horse can produce. I remember reading that the term origininated from observing how fast a horse could lift a weight, but what about my lawn mower? It's 5HP, does that really mean it's as powerful as 5 horses? No way, I thought. I've assumed for a long time that HP is just a measurement unit and shouldn't be thought of in terms of the power of horses, because there's just no way that a Kia Optima is as powerful as 200 horses.

Recently, I've become interested in how much power a human could produce on a treadmill or on a generator bike. I figured I could probably put out a couple of HP. Started looking around and found this (ignore the picture, there is good info on that page):
(watt-hours)

So, trained & determined athletes can generate about 500W max, and 300-400W per hour.
In my <athlete shape I now estimate I could put out half that, so 250W max and maybe 125W/hour. So I'm roughly 1/6HP at best. I think that sounds about right if you're looking at horsepower in terms of horses; Not hard to believe that a horse is 6X as powerful as me. But, when I consider my vacuum cleaner, it still sounds counterintuitive. My vacuum pulls 12A, says that right on the label. 12A on a 120V circuit is 1440W. so my vacuum is 11.5X as powerful as I am! does that sound right? Not to me, at first, but let's consider what it's doing:
• pulling a 16" long hair brush through the carpet at 150mph
• Drawing probably 5000X as much suction as I can with my lungs
• powering a bulb in the front (the bulb alone would probably be considerable strain for me to power)
• Driving it's own wheels a little bit
(and it's doing all this continuously)
So, maybe it is 11.5X as powerful as I am. I sure don't feel up to the job.

Another example; my oscillating room fan. It & myself are probably in the same weight class. It seems like a puny appliance to me, but then I consider that if I wanted to spin that blade as fast as the fan, I would need some up-gearing which would require a lot more torque from my arm. If I got the gearing right so I could keep up with the fan, it would definatel be a heck of a chore, and I would peter out long before the fan does.

This epiphany about power makes me even more determined to try out a concept I had before - A treadmill generator to power your TV. I was thinking that if you installed this device in your house, with no way to power your TV other than by building up sufficient charge by riding a bike or treadmill, then obesity would have a serious adversary. Now I'm just wondering how long you would have to ride or run to be able to watch a 30min program. You would pay a serious sweat premium for surround sound.

Imagine if people took a more active role in the production of their power. There would be a lot more awareness of energy waste, and therefore a lot less of it. We would strive for efficiency in every way.

DerStrom8 likes this.
2. ### praondevou AAC Fanatic!

Jul 9, 2011
2,936
489
Plus, we could continue eating the same amount of food (too much) and still be in a much better shape.
The only difficulty is how to efficiently capture this energy.

There are efforts being done to achieve exactly this , for example to charge cell phones via the energy released while simply walking. Energy harvesting.

3. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
In junior high we did a physics experiment where we went to a stair well that had a long straight flight of stairs. We each then ran up the stairs as fast as we could, any way that we could (two steps, pulling on the hand rail, anything was permitted) while being timed. We then calculated our average horsepower expenditure and mine came up to just over 1HP. The thing to keep in mind is that this was a full out effort for just a handful of seconds. Even the cyclists on a hard climb aren't going to be going all out because the race isn't over and they have to keep their expenditure at a sustainable level, which is well below the peak possible.

Even so, it is amazing how little power humans can produce, especially if we want to keep it up for any length of time.

Another thought that puts it in perspective is to consider the energy content of food.

I have long maintained that, while man is real good at making things that can only hold small amounts of energy but can release it really fast, nature is good at just the opposite -- making things that are real good at holding large amounts of energy but only capable of releasing it really slowly.

So I thought I would look up some examples that I've thought about from time to time and run some numbers.

A food calorie (Calorie or kcal) is 4184 J (joules) of energy. Thus, at an average of 9Cal/gm, fat stores approximately 38kJ/g or 38MJ/kg of energy.

A stick of dynamite is generally considered to contain 2.1MJ of energy with a density of about 7.5MJ/kg. Thus the energy density of fat is about five times that of dynamite. Notice that the energy equivalent of a stick of dynamite is almost exactly 500 Calories, which is about the same as a typical king size candy bar. For someone eating the FDA RDA of 2000 Cal/day, this means that they consume the energy equivalent of four sticks of dynamite a day.

Since fat is generally also considered to have 3500 Calories per lb, that means that a pound of fat is equivalent to 7 sticks of dynamite. For someone like me who has, sadly, something in the vicinity of 200lb of excess fat on him (not counting the fat I would still have at a healthy weight), that means that I am carrying around the equivalent of 1400 sticks of dynamite. Imagine if some suicide bomber ever did figure out how to release that energy quickly! And let's not bring this to the attention of DHS or TSA -- if you think the searches at airports were intrusive now!!

The TNT equivalent that we always hear with regards to really big booms is defined such that 1 ton of TNT is 4.184GJ or 1MCal. For someone eating the FDA RDA of 2000 Cal/day, this means that a ton of TNT has the same energy as what they consume in 500 days. But consider that the Hiroshima device (Little Boy) is generally considered to have yielded 15kt of TNT and that the population at the time was in the vicinity of 350,000. That means that the yield per person was about 0.04 tons of TNT, or about 20 days worth of food (on a contemporary American diet, not a wartime Japanese diet).

Thus, the total energy released over Hiroshima was something on the order of the energy released by it's population just in the food they consumed over the prior month.

The weight of Little Boy was just under 10,000 lb, meaning that it yielded about 1.5t of TNT per pound, or about 3.3t/kg, which is 13,800 MJ/kg, or about 363 times the energy density of fat. While, on the one hand, this indicates that man IS capable of cramming more accessible energy into a pound than mother nature, we had to resort to nuclear weapons to do it and, even then, only achieved a few hundred times the density. I wonder what the highest density is with modern weapons?

Now, the smallest nuke that I could find reference to has a yield of as low as 0.3kt of TNT, or about 300kCal, which is then about 85lb of fat. So I'm walking around with a couple of those! And, again, don't even THINK of mentioning this to the TSA! A kiloton of TNT has the same energy as about 285 pounds of fat, so there are definitely people out there walking around with a kiloton weapon on them.

Imagine that someone (perhaps an alien) develops a technology that allows them to irradiate (or use a beam) food in an area such that it releases its food energy on the same timescale as a conventional explosive. Such a beam, in theory, wouldn't require much energy itself since it is merely triggering the release of what is already there. That would make an interesting sci-fi tale. Perhaps it could be a sequel to Mars Attacks and the beam only works on dog biscuits, or tomatoes, or something like that (I don't know what might be a good tie to the movie, since it has to be food and not music recordings).

strantor likes this.
4. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,302
1,989
Wow wbahn, that started outside the box and made b-line for left field. That's some really interesting stuff to consider. Really glad you shared that. I will ponder this for at least a month and come back with another epiphany.

5. ### JDT Well-Known Member

Feb 12, 2009
658
85
Not very many years ago (~200) all the mechanical power we had at our disposal either came from human or animal muscles.

What is really amazing is how we are now used to using vast amounts of mechanical power without thinking about it.

6. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
That's a pretty big stretch. We've been using wind and water power for a pretty long time. Waterwheels have been in use for over 2200 years. But I agree with the main gist of your post, namely that mechanical power has only recently become easily and cheaply available. Even just 100 years ago, even though steam power was in wide use and many cities had electrical networks, most people still lived day-to-day lives that used nothing but animal muscle power (humans, included). In fact, I suspect that even today, worldwide, a sizeable fraction of the human population still lives this way (or very nearly so).

Oct 2, 2009
12,652
3,460
8. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
I'm gonna cry SNAKE OIL!!!!

Interesting idea (and nothing new, conceptually), but let's look at the numbers the maker is throwing out.

He says that:

• The material compresses 5mm when stepped on.
• The average person takes 150 million steps in their lifetime.
• A single step provides sufficient power to run an LED street lamp for 30 seconds.
• 250,000 foot steps is sufficient to charge 10,000 mobile phones.

It's hard to quantify these claims, because, for instance, he doesn't say what kind of LED street lamp he is talking about and they vary all over the place. Similarly, he doesn't say what kind of phone he's talking about. But let's do what we can.

The claim is that 250,000 steps is sufficient to charge 10,000 mobile phones. This means that it only takes 25 steps to charge a cell phone! I've found numbers on the internet ranging from 10kJ to 50kJ per charge, so let's use 10kJ/charge. That, in turn, means that the person is delivering 400J/step to the cell phone, or right at 0.1Cal. To walk a mile, a person with a 24" stride has to take 2,640 steps and would thus need to deliver over 250Cal/mile to the phone. Yet most tables for Calories burned from walking put it in the vicinty of 100Cal/mile, and keep in mind that by far the largest fraction of that is consumed by the muscles and metabolic processes and released as heat from the body. So this claim would appear to be patently absurd.

Now let's turn out attention on the street lamp. If a single step can power an LED street lamp for 30 seconds, then conceivably a person walking at a pace of 3mi/hr could keep 66 such lamps operating continuously. The smallest lights I've been able to find are 20W. There are probably smaller, so let's be generous and cut this in half to 10W. So the claim then requires that this person is delivering 660W of power to the tiles, which is well over 500Cal/hr. So this is even more absurd than the prior claim.

Now let's consider the stated compression of 5mm. As the material is compressed, the amount of work done on it is the integral of the force times the distance. Using an average force over the distance, it is Fd where F is the force and d is the distance of 5mm. So what does F need to be in order to get 100J/step (let along the 400 to 800 J/step the two claims above would require). Well, 100J is 100Nm and so a force of 20,000N is required, or 4500lb. And, remember, that's for 100J per step. The stated claims would require between 18,000lb and 36,000lb per step!

To put some bounds on things, let's assume that our "average" person consumes the good 'ole FDA recommended 2000Cal diet and weighs the FAA standard 170lb. A 2000Cal diet works out to an average energy consumption of 96W. A large fraction of that is consumed just keeping the body alive and is dissipated as heat. A good fraction of the rest goes to performing mechanical work and the conversion factor is not too great (meaning more energy dissipated as heat). So it's pretty safe to say that the amount of energy given up by the body with each step is, at best, a tiny fraction of the total body energy budget. But, hey, let's be generous and assume an average consumption of 100W and that every joule is dissipated in our footsteps and is captured, without loss, by these tiles.

The claim that the average person takes 150 million steps in their life, assuming a 75 year life expectancy, works out to 2 million steps per year, or about 5500 steps per day. Assuming a 24" step, this works out to a bit over ten miles of walking per day. Note that most of those steps are probably constrained to something like a 50 year period, which would require the average daily walking journey to be more than 15 miles, or about five hours per day of walking around. Somehow I doubt that more than a small fraction of people achieve anything approaching this on a day-in, day-out basis. But, for the sake of argument, let's grant the guy his claim of something between 5000 and 8000 steps per day.

So, with the fantasticly optimistic assumptions thus far, we are saying that our average person is dumping 2400Wh into 5000 steps, or about 0.5Wh/step. This is 1800J/step. While this would seem to compare favorably with the 400 to 800 J/s needed to make the claims work, keep in mind that we are assuming that every joule of energy consumed by someone, throughout the entire day, is delivered to the tiles when they walk. There is no way that more than a fraction of a percent would actually do so and, assuming 1% makes it would mean less than 20J/step, or, looked at another way, to make the street light example work, despite the favorable assumptions made, would require that nearly half of what a person consumes is dissipated in their footsteps.

9. ### THE_RB AAC Fanatic!

Feb 11, 2008
5,435
1,305
You got that right! Walking is very energy efficient, if cycling with both legs at peak heartrate can be 200W or so casual walking is at least 20 times less exertion for the person. So that's maybe 10W continuous.

So at 2 steps/second that "one footstep" only cost the person 10W for 0.5 second or less. The efficiency of that 10W will be incredibly low as casual walking is very horizontal and the least energy possible spent on pushing the ground down, that's what makes walking so casual compared to jogging.

So that's maybe 1W downward for 0.5 second?

The efficiency of converting that downward force to electricity has got to be low. To be generous aybe 50%?

So it's 0.5w of electircal power over 0.5 seconds. How many watts does an LED streetlamp need?

10. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,302
1,989
Are you saying that walking is more efficient than biking? I don't have any numbers, but off the top of my head that sounds counterintuitive. Walking may burn less calories over time, but when you look at calories burned over distance (which is what I would consider to be the measure of efficiency), I have a strong feeling that the bike would be more efficient.

11. ### Brownout Well-Known Member

Jan 10, 2012
2,375
998
If a 150 pound person lifted himself 5mm, then he would provide .2in*150lb=30in*lbs of energy, or 2.5lb*ft. A joule is = .738 ft lbs, so that gives 2.5/.738= 3.39J. An LED consuming 20mW could be lighted for 3.39/.02=170s. 250,000 steps could make nearly 850Kj. Theoretically, of course.

Last edited: May 2, 2012
12. ### Markd77 Senior Member

Sep 7, 2009
2,803
594
I think Brownout has the best method of calculating it. I imagine it would be annoying to walk on, probably quite tiring if they paved a large area, and I bet wheelchair users would hate it.
It reminds me of the stupid idea of putting wind turbines on motorways to harvest the air movement that traffic makes.

13. ### MrChips Moderator

Oct 2, 2009
12,652
3,460
Can be done. I sailed with a friend on a lake in the centre of city. When there was no wind we got sailing by the draft created by the cars going by.

14. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
One of the problems is that when a person steps, they are not pushing down with just their weight. The force is significantly more -- many times more -- (otherwise they wouldn't stop, they would keep going down at the same speed. If you new the effective downward velocity of their center of mass then you could calculate their kinetic energy and use that as a good measure of the energy expended with each step.

Keeping an LED that is consuming 20mW going for a minute and a half is a far, far cry from keeping a street light going for half a minute. Even for the smallest streetlight I could find, we are talking about a factor of over about 350.

15. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
4,302
1,989
good point. It's not like the sidewalk is capturing "wasted" energy. It's actually robbing you of energy as you walk. Imagine walking for a mile across a line of plush couch cushions. That would really take it out of you.

16. ### Markd77 Senior Member

Sep 7, 2009
2,803
594
My problem with it is that cars also save energy because of the draft, so anything that slows the draft down wastes petrol.

17. ### Brownout Well-Known Member

Jan 10, 2012
2,375
998
That's why I used 'stepping up' energy, which is conserved. The energy going up is the same as going down.

Perhaps, but a sidewalk light made from 5 such LED's could, in theory, be lighted for 30s.

18. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
Same issue. When you are standing on the tile, you are pushing down on the tile with your weight (let's use the moment when you are on one foot, having just barely transferred the weight off the other foot and getting ready to lift it to start the step). In order to start your center of mass moving upward, you have to exert a force greater than your weight on the tile.

19. ### Brownout Well-Known Member

Jan 10, 2012
2,375
998
The energy of shifting your weight would be far less than the upward energy of stepping up. That's most of the energy being converted.

20. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
Agreed, which is why I am neglecting the energy owing to shifting your weight.