Power output formula

[farazmasroor]

For the power output formula, Power= Cp * air density * swept area * speed ^3,
Is the power in Kilowatts/hour?
How much energy does an average house use?

[SparWeb]

Close.
(missed a factor of 1/2)

Power = 0.5 * (air density) * (wind speed)^3 * (swept area) * Cp

where:
   Power = Watts = rate of doing work
   air density = 1.225 kg per cubic meter at sea level
   wind speed = meter per second, to be consistent (must be measured at the tower height because it varies with elevation)
   swept area = square meters  (for a HAWT, area of the circle drawn by the tips, for a VAWT, area of the rectangle looking horizontally)
   Cp = Coefficient of Power = ratio of the power captured by the blades to the total power available in the movement of the wind (max 59.3%)

DO NOT confuse power with energy.  It is like confusing speed with distance. 

You can measure power in Watts or Horsepower
You can measure energy in Joules or BTU's

The relationship is that energy divided by time is power, so:

Joule / second = Watt
Watt x second = Joule

An average house in north america uses between 8 - 16 kiloWatt-hours of energy per year; has been this way for decades.
An average house in China uses between 1 - 2 kiloWatt-hours of energy per year; increasing rapidly

Just a broad hand-waving answer.  If you'd like something more specific, just ask a more specific question.

[rossw]

An average house in north america uses between 8 - 16 kiloWatt-hours of energy per year; has been this way for decades.
An average house in China uses between 1 - 2 kiloWatt-hours of energy per year; increasing rapidly

I think the average US household might use approximately 365 times more power than that, Spar

Those look like kWh/DAY to me, not per year.

[TomW]

An average house in north america uses between 8 - 16 kiloWatt-hours of energy per year; has been this way for decades.
An average house in China uses between 1 - 2 kiloWatt-hours of energy per year; increasing rapidly

Uh, we use 150 KWH of GRID power a month? Plus the RE.

Did you mean megawatt hours / year?

KWH per Month?


Tom

[ChrisOlson]

According to the U.S. Energy Information Association, the average American home uses 30.16 kWh/day.

Tennessee homes used the most at 42.69 and Maine homes used the least at 17.07

45% of the power generated in the US is generated with coal.  Approximately 4% with renewables.

Electricity consumption in the US was more than 13x greater in 2010 than in 1950.

Just some trivia:
http://www.eia.gov/electricity/
--
Chris

[joestue]

for a long time, residential energy consumption was 14% of the total electrical consumption, (the reason why they still don't care about residential power factor, it just doesn't matter.)

I looked up the numbers for Kentucky about a year back, 45% of their electrical consumption was still >100 hp electric motors, can't recall who said it but for a long time something like 60% of the electrical consumption for the entire country was electric motors over 100 hp.

As far as power in the wind, you'll have to do a site survey or look up the numbers for your area. 

[farazmasroor]

So, if my turbine, using the formula, generates 8 kwatts, then multiply by the time to see how useful it is for my home.

[SparWeb]

Oh No!  There's a whole lot of zeroes left out aren't there?  I'm very sorry!  (It's too late to go back and correct it on the first response)

I meant:

An average house in north america uses between 8 - 16 thousand kiloWatt-hours of energy per year; has been this way for decades.
An average house in China uses between 1 - 2 thousand kiloWatt-hours of energy per year; increasing rapidly

Moving on to your next question:

IF you put the turbine in a good spot, and IF it actually is rated for 8 kiloWatts, and IF it is reliable, and IF the balance of the system will accept the energy, then it may generate:

8 kWatts about 1% of the time,
4 kWatts about 5% of the time,
2 kWatts about 15% of the time,
1 kWatt about 25% of the time,
and less than that the rest of the time...

...except for the times when big storms blow in, and then it produces anywhere between 0% to 150% at any given second.


More broad generalizations, to prevent any hasty conclusions about what you can get out of a particular wind turbine.

[richhagen]

Just another method of explaining what has already been said:

An electricity generating wind turbine converts kinetic energy in the flow of air through its swept area and ultimately converts some of it into electrical energy.

The kinetic energy in the air is equivalent to one half times the mass of the air times the square of its velocity.  Now in the case of a wind turbine, which is generally fixed in location, the amount of air passing through its blades is also a linear function of the wind speed, and as a result the available kinetic energy to a wind turbine is related to the cube of the wind speed, such that if you double the wind speed, the available kinetic energy in the wind goes up by a factor of two cubed, or eight times as much energy is available. 

The Cp referred to is the fractional efficiency of the wind turbines ability to convert this kinetic energy into electrical energy.  A fellow by the name of Betz figured out that you can not capture more than sixteen twenty sevenths of the available power (because the more you slow the air the less can move past the blades), and actual wind turbines are generally significantly lower than that in efficiency because of friction, electrical resistance and other factors.  Additionally this coefficient of efficiency is itself a function of the wind speed for a particular wind turbine. 

Now in your case I am guessing that you are asking about an 8kw rated turbine.  The rating probably means that the manufacturer is stating that at some given wind speed the turbine will generate 8000 Watts.  Since we do not know what that wind speed is we can not even give a rough estimate of the annual power production for this turbine.  It would also depend upon the distribution of wind speeds over time.  Just because the turbine is rated at 8000 Watts does not mean that you are going to see 8000 Watts for very much time.  Additionally there will be times when it is very windy and the turbine may produce more power than your house is consuming, as well as times when it will be calm when the turbine will produce less power than the house would consume.  To figure this all out for purposes of determining what percentage of the homes energy consumption you could expect, in addition to knowing the homes actual power consumption over time, you would need to know the turbines power curve, which the curve representing the amount of power generated as a function of the wind speed, as well as the overall wind speed distribution for the location and height at which the wind turbine is to be mounted. This would also enable you to estimate the size of battery bank required to provide power for a certain percentage of the time for an off grid home.

For an off grid situation, where the home is not connected to an electric utility, this usually means charging stationary batteries with the energy generated by the turbine and using the energy from the batteries to supply household power.  In the case of a grid connected home, generally with approval of the electric utility, it is more economical to use the power grid as a pseudo-battery, sending any surplus power in excess of what is being consumed at that instant by the home to the grid, and when the power demand of the house exceeds what can be supplied by the turbine, drawing power from the grid to supply the difference.  With net metering offered by many electric utilities the home owner then only pays for the net power used from the power grid, or in some cases where the turbines energy generation exceeds the homes consumption, receives compensation for the net power sent to the utility.

Don't know how much this helps you, as I realize it is a bit broad, but the questions have to contain all of the specific relative facts to get specific answers.  Rich

[hothead]

so how much kw/h can you get out of homemade wind generator for a month. lets say i now use 44 kw/h for one month, can i get the same out of a homemade wind generator and even  more.
sorry for asking dumd questions i am new and want to make a microwave magnet one just want some answer and encouragement before i start thank you

[CaptainPatent]

@ Hothead - If you actually use only 44KwH / month, it may be easy to make a generator to offset your demand, but as discussed, the KwH numbers in this thread were a bit off. The average I'll go through some quick math:

First off, 44KwH / month is only around 500KwH per year which means you use less than half of the electricity of an average Chinese household. If that's true, you could easily offset your electricity demand, but I'm suspicious it is.

Remember, the average energy consumption of a Chinese household is around 1-2 THOUSAND KwHs or 1-2 MwHs per year.
US and Europe are between 8-16 MwHs.

Let's say you build a 10 foot turbine (each blade is 5 feet long) that is of average efficiency (35%) and sees an average of 7.5mph winds (reasonable if you exclude unusable dump-load gusts) the output power you're going to see is around 34 watts. Over a day, it will generate just under one KwH, and over a month, that's around 25KwH which is enough for about a third of a small, average Chinese home.

If you increase to a 20 foot machine (10 foot blade) that is of the same efficiency and sees an average of 7.5mph wind speeds again, you can see around 140 watts of power - so every day you will generate an average of 3.4KwHs or around 100KwHs per month. This is enough for about an eighth of a small European or North American home or one Chinese home.

The most important factor is average wind speed though. Let's say you have a godly 12.5mph average and after dumpload gusts, your machine can handle an average of 11 of that, With the same machine above, you suddenly produce 440 watts average for 10KwHs a day and over 300 per month.

A 20 foot machine is no small or inexpensive task though. The tower needs to be tall enough to clear the treeline to prevent wear, you need a nice storage system in order to handle spikes in power creation AND consumption, and everything needs to be well maintained if you want anything to be even somewhat cost-effective (if that's what you're after)

[hothead]

CaptainPatent thank you (your info worth a million kwh to me  ) thank you...
can i squeeze in one more question. Can i use ferrite magnet and get a close amount a kwh a month

[ChrisOlson]

can't recall who said it but for a long time something like 60% of the electrical consumption for the entire country was electric motors over 100 hp.

I always thought 60% of the total electrical consumption for the entire country was women.  Better hope they never get organized and form a revolt.  If they all turned on their hair dryers at the same time it would overload the grid and the entire country would go dark   
--
Chris