Wind power or energy waste?

I wrote already that the first message calculations were wrong since I've forgot about 3600 factor. So here are better ones (as I think):

Let's use 500KW windmill, since it's this kind of a mill weighs approximately 20 tonnes). Let's assume that capacity coefficient is 0.35 (i.e. the actual % of time blades will be turning at all). Since maximum power at low wind speeds can't be reached, it is hard to make up out of thin air coefficient accounting for the lower than maximum output let it be 0.1. 500,000*3600*24*0.35*0.1=552GJ/year; So it takes about 1 year of operation to smelt 20 tonnes of steel.

For more precise calculations, one needs to know windspeed distribution at a given location (i.e. # of hours/year the average windspeed is within certain limits) . Wind power density is a function of windspeed, semi-theoretical efficiency of a windmill -59%. Transform windspeed distribution into a powerdensity distribution. For crude approximation mutliply this distribution by 0.59*(bladecircle area)=maximum extractable power distribution. Integrate the area under distribution = maximum possible power extracted/year for a given windmill installed in this location.

I'll try to something like that in the future. If you see flaws in the last paragraph's outline let me know.

 

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I was watching "I want that", a show about cool, cutting edge products, and a guy had a small windmill on his roof that he claimed decreased his power bill to about two bucks a month. The thing cost like fifty grand, but it generated plenty of power.

 

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Here is an estimate of "roof power" from another website.


There are a few general rules.

1. The bigger the windmill, the more power you get. The power is proportional to the square of the radius of the windmill. Double the radius and you quadruple the power.

2. The faster the wind, the more power you get. The power is proportional to the cube of the wind velocity. Double the velocity, and you octuple the power. Approximately, the formula for wind power is given below for a nearly perfect windmill (and it is an overestimate)


That much in mind, do some figuring. If you had the world's best windmill, the amount of power (in watts) you could get would be just under the square of the radius (in meters) multiplied by the cube of the windspeed (in meters per second). (See Equation below)

P=1*R*R*v^3

(Note that it is the *radius* not the *diameter*). For example, the commercial unit I mentioned has an actual radius of 0.57 m. At 28 miles per hour (=12.5 m/s), it should produce (.57^2)*(12.5^3) = 634 watts. (Well, it produces only 400 W. As I said, the formula is an overestimate. The unit doesn't get up to 600 W until a speed of about 40 mph, 18 m/s.)


What does it mean 400W? That means this commercial unit(with blade 0.57m) will be able to power your PC (if you'll spend pretty penny on voltage regulators, accumulators) and not much more. Add there lights, fridge, conditioning, stove, water heater, washer .... That guy either makes a mistake or lying, because you cannot set up a monster blade mill on your house to power it. 1... 2m that's maximum blade length of a roof mill. Let's assume that the guy went berserk on the neighbors and his nerves and set up 2m blade-radius mill on his roof, that would give him roughly 1500W of power max. Hell, that's peanuts, the average daily use of electricity per household is 25KW=25000W. The only way guy wasn't lying, if he uses 10 times less electricity than average folks to begin with. Only then roof miracle would cut an electricity bill.

 

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Something that I learned from my dad - if it doesn't make logical sense you probably screwed up somewhere. If you could make $8.3m in little over 3 days there would be a lot more investment in wind power. Somehow I think you made a mistake.

 

You are correct on both points, but (you knew there would be a "but" didn't you)

The cost of the tower as function of blade radius in more than linear as is the cost of each blade. - That it should be at least linear is obvious. In fact it is also essentially quadratic as the blade root and tower base for twice as long blades are twice as big to support the at least doubled torques trying to snap off the blades or blow down the tower. As blades and tower have 2D cross- sections, this doubling of linear dimension is approximately increase the matterial requirements by the cube, but not really the cost by the cube, so you point (1) is basically "a wash." - I.e. if that is all there were to it, then two smaller wind generators of same total "sweepted area" would be as cost effective as one big one, if not more so because of ease of transport to site and twice the production volume etc..

The real economic reason for big ones you did not mention so I will add fact number three for you:

(3) the speed of the wind as a funcion of altitude, is approximately a cubic increase with altitude in the near-ground region that wind machines can access. I have forgotten the power law, but 2.7 seems to come to mind. It is at least by the square and well known in the literature.

I am interested in various tethered wind-generator Kites for this reason. Some one might look into this and play around with a small one - probably not economic or practical, but interesting.

Perhaps tethered "BKlitES" - my just now invented word, which are nearly lighter than air (BlimpKiteEnergySources) up at a few hundred feet in a strong wind might be economically feasible? When wind dies down, the BKitE begins to slowly sink and is realed in to its tetherbase, landed (or placed on) a cart, which takes it some down-wind distance from the base for next launch (tether aiding initially, like pulling on a kite at launch to compensate for lower wind speed at ground level.)

BKiteS to the sea! - My new slogan as they can soft land without the cart etc.

 

A few tips for design of BkiteS (see my last post):

(1)The exterior is a right circular cylinder of strong light weight fabric with lead and final aluminum hoops to keep it circular. For initial testing rice paper, lightest sail clothe available, etc can be the fabric, but eventually this material is "hydrogen or helium tight" and so filled for lift, I think.
See (3) for the other enclosing surface.

(2)Approximatly central and approximate half the diameter is a third co-axial Al hoop. This hoop has many very fine wire* coils around it on the inner surface that the magnetic tips of two** wind turbine blades "just miss" - Probably the blade tips also have roller bearing and captivley*** run on this hoop with no axis bearings instead of a double tripods in the air flow channel to support the axis of the rotating parts. I think this a lighter and cleaner (less turbulence) design and the stationary light weight pick up coils are attractive instead of an axial generator to support and the problem of feeding the power out of the rotating parts.

(3)The inner surface of the wind channel is also light weight fabric, with "battens" (like in the sail of a sailboat) to maintain a smooth curve reducing the channel crosses section (approximately quadrupling the already high wind speed.) I.e. the BkiteS is a "ducted fan" design. Three battens are stronger than three light weight others as they hold the two larger hoops in place and keep the smaller one on axis.

(4) Solid state devices around the smaller hoop convert the pulses induced in the pickup coils to DC (it is initially a high peak voltage pulse). The aluminum "twin leads" (somewhat like the aluminum house wiring or TV cable used in the 1950s) brings the high voltage (low current, so not much weight in the aluminum "power wires" ) down to Earth. (DC can move more power over any given line than AC)

(5) Instead of one adjacent "twin lead" power cable, plus a separate support/ altitude control cable, two combination support tethers / power transmission cables should be considered. One attached to reinforced sections of the front hoop and the other to such a section of the back hoop. This provides the ability to get more lift in light winds at the expense of power generation by slight front-end-up-ward tilt of the cylinder axis.

Sounds like a fun project for some one to me. It is sort of like a round "box kite with fan in it. Try one about a yard in diameter at 100 feet up and see if it is feasible. (I am too old and busy for this nonsense, or I would do so.)
------------------------------------------
*Low duty cycle permits brief thermal overloading, but selection of wire size is complex as weight is not normally so strong a consideration.
**Two blades are more efficient than the three normally used (less air friction - one is even better, but not balanced). Three blades are normally required as when only two are vertical, the yawl moment of inertia is too small and a sudden gust of wind can twist the typical machine around so rapidly as to destroy the machine.
The wind at higher altitude is much more free of the usually ground-object-induced gusts and the "ducted fan" in right circular cylinder design should (I expect) permit only two blades (slightly more efficient and only 2/3 of the weight.), especially if the cable is as in (5) which I recommend. Also for any interested person, crazy enough to build small model, a two-blade prop is easier to buy from model airplane suppliers. - Some remote drones must use two blades of reasonable size for a serious model. - the availability of the "prop" should be used to set the scale of the entire test BkiteS.
*** Joined like the wheels & track of a loop-the loop roll-a-coster to avoid significant distortion of the circular inner hoop.

 

2 megawatts. 5 cents per kilowatthour, which is less than the rate that appears on my electric bill. That's $100,000 per hour, and I just checked again. Sometimes if it doesn't make sense, it's because I didn't do the math before. You check the math, and I did give a low rate per kilowatthour.

When you're talking about tall towers, and a place like Kansas, the wind does blow pretty steadily, too.

I didn't make a mistake. It's just that even if the wind is not variable, the times that you can sell the power are and it is costly to integrate that power into the network. I don't know what the wholesale rates are, either. That was a retail rate.

One problem that can come up is that wind farms may not be able to produce as much power on the same land as a coal-fired or nuclear plant. One coal-fired power plant generates as much power as 500 of those wind turbines. A gigawatt of electricity is worth $50,000,000 per hour of full-power operation. Not being able to make some money is not as big a problem as not being able to gross 1.2 billion (American billion) dollars each day of full-power operation. It's harder to get a lot of investor interest in investments that are so much smaller than that, even if it's still a lot of money by human standards.

 

I notice that no one else caught my error when I charged 5 cents per watthour instead of per kilowatthour, so let's dispense with the "he messed up his math" jibes.

The number of joules involved was correct.

So a 2 megawatt generator produces 2000 kwh per hour or $100 per hour in energy. That does take some time to pay off the notes. It does take 500 of them to equal one billion watt coal-fired plant, which produces $50,000 worth of electricity per hour, 1.2 million a day, which is a pretty good amount of money, but investors are going to see it as a bit inadequate.

 

Good to see your are focusing on the economics as many advocates of alternate energies fail to realistically do this, however comparing wind and coal power is much more complex than you are indicating.

First the is the buying of the coal to consider (wind being "free") and then there is the advantage of wind displacing retail cost of KWh vs. income at whole sale to the coal plant. Then, of course, the wind system has zero (or much smaller) power losses and cost in transmission from source to end user. Even with all this one must still consider the cost of maintaince and useful life for depreciation differences.

Finally, and much more important than any of the above, and any of your considerations, there is the very important capital costs per KWh of generation capacity and the average capacity utilization factor to consider. By far the dominate cost reflected in your electric bill is this capital cost. (At least 80, often 90% of the bill the public service commission allows is due to the capital cost of the coal plant, the transformers and distribution lines etc.)

Summary you have considered such an insignificant part of the real economic analysis that if the remainder were done, the part you have considered could be neglected as "relatively unimportant."

Try again to make a reasonable comparison of total costs of wind power and coal power systems. One factory seldom mentioned (and not above either) is the health care costs. Advocates of wind power should make more use of this as coal has a lot of health care cost, especially when you start at the coal mine to add them up (black lung disease, rail workers injured, etc.) Wind is relatively free of these cost.

 

All that I was talking about was about how much product you can expect out of one installation and how much it would go for at retail. The rest is implied, but getting some idea of the gross income is a good first step. Then you factor in all the installed installations and who has to be paid what.

You can see that when you have all the middlemen and coupon cutters that the pool of money has to be quite large for anyone to want to invest in. Suppose I could make a million dollars selling widgets that cut household power consumption by half. Even the people who wanted to invest in something like it would consider it profitless. A million dollars is about a one-man fortune, but not worth much more than a new car to twenty investors. Even a billion dollars is beginning to look like chump change.

 

wind technology is very primitive,,,,
not much use for anything other than remote dwellings.

IMO the world needs to completely change its direction in energy production. We need common salt reactors and associated electricity storage systems, all powered by the perpetual and constant spin of the Earth..

Oil and coal should be totally banned as fuel sources.

 

Offshore:

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