# Calculating the force required to generate 100 kilowatt per hour

1. May 11, 2013

### Jaxodius

Hello to everyone,

I am trying to calculate how much physical force is needed at point B (imagine a person pushing on a bar attached to point A) to generate 100 kw per hour where the radius is 50 meter. If you imagine that at point A there is a system of gears attached to an alternator/generator which transforms 1 rpm from point B into 3600 rpm at point A(4 gears with a gear ration of 15:1 between them), how much force would be needed to generate 100 kilowatts per hour? I understand there will be friction, but at the moment i am just trying conceptualize how much physical work is needed to generate that amount of power.

This is the first time i am trying something like this so if i have made any wrong assumptions, please correct me.

2. May 12, 2013

### Andrew Mason

Power is work done per unit time. So 100 KW is 100 KJ per second = 100,000 Nm/sec.

In order to determine how much force is required to generate such power, you have to tell us how fast you want to make the bar rotate. For example, if you want to generate 100 KW at a rotation rate of 1 revolution/second (ie. B moves 2∏R = 314 m. in one second) then you would need a force of 100,000/314 = 318 N.

AM

3. May 12, 2013

### Jaxodius

Thank you Andrew. you raise a very good question:

[1] i am not sure weather to generate 60 kilowatts per hour ( i am simplifying the numbers so i can understand easier but my actual project is for 100 kilowatts per hour ), if one needs to generate 60 kw per second or 1 kw per minute?

[2] Also, the way i visualize it in my mind, is that a person will have to be applying 318 newtons per meter for 314 meters to make 1 revolution. is this correct? if so, do i use the 60kw/sec or 1kw/min to calculate the force i would need.

4. May 12, 2013

### Staff: Mentor

You are confusing yourself by talking about "kilowatts/sec" and "kilowatts/min"; those terms make no more sense than something like "miles per hour per day". Power, measured in watts, is not an amount of work but the rate at which that work is delivered: one Joule of work per second is one watt.

Your problem is asking for 100 kw, meaning that it will deliver 100,000 Joules/sec for as long as it is operating, and it will take some force in Newtons to do this. Obviously the longer it operates the more total joules it will deliver, but the force in newtons will be the same; it'll just be operating for a longer time.

5. May 12, 2013

### Jaxodius

Thank you Nugatory. I think i really am confusing myself more. let me explain what it is i want to do. i have an oven that is rated at 100 kWh and it need to run for 3 hours. I am trying to determine how much force would be needed to provide 100 kWh to that oven using the set-up i mentioned in my first post ( 4 gears with 15:1 gear ratio attached to a bar with the length of 50 m ).

Clearly i cannot do 314 m in 1 second so i was thinking what if i added more gears so that instead of providing the 318 N force per 1 revolution of point B, i provide it over 1/60 of that one revolution. Therefore :

3600 rpm * 60 = 216000 rpm . If i used 6 gears with ratio of 15:1 between 5 of them and 5:1 between 1 of them making it a total of 253125:1 and then proceeded to make 1 revolution from point , will i be providing the same power every second of that revolution? I know i cannot do 314 meters in 1 minute either lol but am i thinking about this the right way? or is there another way to spread that much force and still provide 100 kw/s?

6. May 12, 2013

### Staff: Mentor

You're still confusing power (watts) and energy (joules) here. 100 kWh is a measure of energy. It's the amount of energy a 100 kw power source delivers in one hour, or a 10 kW source delivers in 10 hours, or a 1 kW source delivers in 100 hours. If you remember that there are 3600 seconds in an hour, and one watt is one joule per second, you'll see that all of the above combinations come out to the same amount of energy, 3.6x108 joules, whether it's a little power delivered over a long time or a lot of power delivered over a short time.

(100 kW is also a LOT of power... It's about 130 horsepower, and I suspect that you're misreading the specs of your oven).

Yes, you're thinking about it the right way now: as long as you're maintaining a constant speed and force you're delivering a constant power. But notice that this doesn't change if you play with the gearing or the length of the lever arm; all that does is make it so you're applying the same force over a different distance and (because your speed is constant) a different time, so applying the same amount of power for a longer time and doing more total work.

You're also quite right that you can't do 314 meters in one second - as I said above, 100 kW is a lot of power.

7. May 12, 2013

### Jaxodius

Thank you both for your help. I consider this problem solved.

8. May 12, 2013

### sophiecentaur

I'm afraid the problem will not be solved until you understand what the real units of power and energy are. Under even the mildest of scrutiny, what you are writing makes no sense. It would not take too much of your time to learn how to use the appropriate units and it would help so much more for your credibility.
It really does matter.

9. May 12, 2013

### Staff: Mentor

Just for emphasis:
There is no such unit as "kw per hour" or "kw per second". I don't believe you understand that yet either, so I'm relatively certain you have not calculated anything of value yet.

10. May 13, 2013

### Jaxodius

Sophie please let me know if my understanding of power and energy is still wrong:

Example: when i use a 1kw AA cell in my phone that has the ability to use either 1 watt or 1000 watts every second it is turned on, the 1kw AA cell will either last 1000 seconds or 1 second depending on the amount of energy it draws. So the power in the 1kw AA cell can last depending if the energy drawn by my phone is 1 watt / sec or 1kw/sec.

Power= 1 Kw and Energy= 1kw/s or 1w/s

I spoke to nugatory in pm after his last message because i was getting embarrassed and wanted a clarification. it was after his reply in pm, which clarified things a bit more, that i made my last post.

Russ_watters you wrote:

I want to quote you something from http://physics.nist.gov/cuu/pdf/sp811.pdf page 24 which reads:

So are you wrong or are you talking about something other than what is mentioned on that page? because when i use the term kwh, i mean x kw per hour. please clarify.

As for not calculating anything of value, i was able to calculate how many people i would require to use x amount of force over x amount of distance to make the whole thing realistic. so for me, it was very valuable.

11. May 13, 2013

### QuantumPion

Replace every instance of watt with joule and it is mostly correct.

Understand that kW*hr (kilowatt-hours) is not the same as kW/hr (kilowatt PER hour). One kilowatt-hour is a unit of energy, and is equal to 3600 kilojoules (1 kW * 1 hr = 1 kW*hr). Kilowatt/hour represents something entirely different. Physically, a kilowatt per hour would be a rate of change of power, for example the ramp rate of a nuclear reactor (which typically have limits on how fast they are allowed to change the power level due to material constraints).

Last edited: May 13, 2013
12. May 13, 2013

### willem2

The unit of power is indeed Watt (W), or kW = 1000 Watt.
The units of energy is Joule or Watt-second and NOT Watt per second.

A You gett one Watt-second by producing one watt for a second. (or 2 watts for a half second etc.)
You have energy = power * time, E = P T here, and because the units of power is watt, the unit of time is seconds, the unit of energy must be watt second.

You use "per second" in a unit for a rate of change, for example speed,
wich has unit meters per second. you have speed = distance/time, we divide here instead of multiplying, and thats why you have m/s or meters per second, and NOT meter-second.

The capacity of batteries is usually given in Ampere-hour, If you multiply this by the voltage you get watt-hours. You're talking about a 1 kW AA cell as if this is the capacity of the battery, but kW is a unit of power. 1 kW would drive a vacuum cleaner, and is a few hunded times the maximum power a phone would use, or that an AA battery could deliver.

13. May 13, 2013

### sophiecentaur

I think it would help if, instead of hanging on to your particular version of this, you started way back at the beginning and stuck with the definition of Energy and Power that everyone uses. Some of the figures you are calculating are correct (by chance, because some errors are sort-of cancelling out) but your thesis is just flawed. If you cannot see what you are doing wrong then you have to believe that you are wrong and find out, for yourself, what the problem is.

Start with the definition that Energy is Power TIMES time and that Power is Energy PER unit time.

14. May 13, 2013

### Staff: Mentor

Jax, a kWh is kw TIMES hours, not divided by hours. So you actually have two errors here, not one:
1. You don't know what a kWh is.
2. You shouldn't be using it anyway.

Just about everything you've posted should be about power, not energy. kW - just kW - not kWh, not kw per hour, not kWh per hour. Just kW.

Now perhaps you got lucky and your errors cancelled each other out, but it is more likely you got the wrong answer.

15. May 14, 2013

### CWatters

Just for info... What will be applying force on the bar?

i believe a fit human can generate about 1/3rd of a horsepower (eg 250W) for sustained periods. If you need 100kW thats quite a team of people you will need (400 people).

I read somewhere that to produce one horsepower (750W) you actually need 1.5 real horses (so 200 needed). I've no idea if they can keep that up for three hours though.

PS: Insulate the oven better. They will thank you for it.

16. May 14, 2013

### Jaxodius

Thank you sophie, i will keep that in mind.

CWatters i was planning on hiring people to do it because it will only be for 3 hours. and you are right it will be about 400 people. I was thinking that maybe i can divide them into groups and 1 group takes over another.

Honestly, hiring people is not a problem. i am more concerned about the 6 gears with a ratio of 15:1 between them. is a gear system like this even realistic? what kind of problem can arise?

17. May 14, 2013

What is the purpose of your giant human-powered generator? Hiring 400 people for 3 hours at $10/hr would cost$12,000. I did some googling and found that you could rent a 100 kW generator for a day for $500. 18. May 14, 2013 ### Jaxodius It does not take$10/hr to hire someone in china or india :)

Do you think the gears will hold up?

19. May 14, 2013

### jeffrey c mc.

Jaxodus;

From just a mechanical perspective. A 50 meter lever seems somewhat excessive. And your discussion of running an oven, and then running a cell phone with a 1kw AA battery does not add to the clarity at all. Besides it would be more instructive if you first told us about the generator, and the rating of same. Irregardless of the gears and the lever used to drive the generator, the power availability would depend on the capabilities of the generator itself. Whether or not the lever and gears can deliver the necessary torque to the generator does not depend on the weather. Sorry, as I have been taken to task for my language and use of same, I may as well make my own observations. Nothing personal!

20. May 14, 2013

### Jaxodius

Thank you jeffery. and please do not hesitate to point out any wrong assumptions i have made (as i said in my first post ). this will be my first attempt at anything like this and i would like to get it right. and to clarify, the project is for 100 kw-second ( thank you willem2 for clarifying this ) but i gave the example of the cell phone just for sophie. i know there is no 1kw AA battery lol

This is the item i had in mind to attach the gear to at point A ( diagram in the first post ). only instead of using fuel, i wanted to calculate the force required to do it manually: