ABSTRACT:
Wind power, commercial jets, and politics.
And almost no humor this time...
A couple of weeks ago, maybe 3~4 days after posting the little thingy about Solar energy, two things happened.
- I was a guest at an eminent solar scientist BBQ lunch, and we had a little chat about what I wrote.
He said he'd send me a paper he wrote, so I could avoid making the same mistakes as everybody, and go on to make some mistakes of my own... :)
I promise when I finish reading it, I'll atone for my sins, stop eating meat, cease all gasoline use and switch over to the green side. Well no. but I will try to rework my logic and share my thoughts to the extent possible, since it is article material and I don't want this blog to jump the gun on hard work, not my own.
- I came across this nice video :
Now, a word of caution, this video is very political, and actually, the field of environmental science is highly political in nature, which by the way brings the question whether Thomas Kuhn's largely misinterpreted view on science is actually correct - i.e. science is as politicized as everything and social trends actually effect scientific truth.
Kuhn probably never intended to say or write that, but that's a different story altogether.
Anyway my only intention here is to derive the part of how much energy an electro-windmill can produce.
After digging a bit, I found several sources, but I'm going to be extremely optimistic and take the average wind velocity, averaged over the globe over a period of about 50 years to be about 7.5 m/s.
So, the energy is given by \(\frac{1}{2}mv^2\) but we need a way to evaluate the total mass of the moving gas that comprises the wind right?
Let's do that real quick shall we?
the volume of air passing through an incident area \(A\) in one second is basically given by \(A\cdot v\), thus the wind power that goes through a windmill with incident area \(A\) is simply:
\[P=\frac{1}{2}\rho_{air}Av^3\]
with \(\rho_{air}\) being roughly \(1.25 kg\cdot m^{-3}\), we get that the power as a function of incident area is given by:
\[P_{\text{wind averaged}}\approx 264\cdot A\,\,\, W\]
So supposedly its enough for every person to have about 9 square meters to his name in the constellation of a private windmill to account for all our earthly needs.
Enter windmill efficiency at a staggering 36% (the theoretical boundary is actually about 60% but wind drag, mechanical stress etc. account for further efficiency loss), so every person must now have about 27 square meters, which is not that much right?
Really? 2% of the energy a commercial aircraft needs to take off ?
The Energy needed for an empty Boeing 747 at 170 tons to take off and achieve cruise altitude of about 10km is about \(2\cdot 10^{10}\,\,\,W\) which means we need a windmill with a blade length of about 5km or about 1000 150m blade turbines, or 10,000 50m blade turbines.
What about just take-off speed? average takeoff speed for a 747 is about 80 m/s, and you'd have to maintain that speed for the duration of the takeoff, but let's calculate just for one second shall we?
\[E_{\text{one second}}=10^9\]
So we would need about 1km long blade to account for that plane taking off, and a 50-store blade spells about 150 meters blade which means about \(1.9\cdot 10^{7}\, W\) and that really is about 2% of the energy needed for an empty 747 to take-off...
So you see? the guy in the video was right!!! or was he?
Cheap rhetoric or outright sham?
well no, that argument is just throwing sand in the public's eyes because supposedly if we had enough turbines to cover the world's energy needs, a spike in demand as reflected by a taking-off event would not even show on the overall scale, with about 4 to 5 orders of magnitude difference...
The real consideration has to be this one:
in order to provide for humanity's power needs, we need about \(2\cdot 10^{11}\) square meters dedicated to power production. factor in spacing issues (a factor of 6 times the rotor blade length means about 36 times the area). thus we get about \(8\cdot 10^{12}\,m^2\) which means about 5% of the land area available on earth.
Again, this is about the size of Europe, and I didn't even go into wind regiment as a function of height consideration, or considering blackout times and backup requirements as the wind DOES tend to stop at rather inconvenient times (for instance when it's hot as hell outside and there's no wind, and you want to turn on the AC, but guess what - no wind means no electricity means no AC!!! damn you green energy advocates!!)
I read somewhere (an incomplete) analysis that concluded it calls for covering the surface of the earth with some kind of a wind capturing apparatus a 150 meters high in order to manufacture enough energy for us to live the way we do. I'm not that pessimistic, but let's just say wind power is no more a true messiah than solar power is...
So you see, this field is indeed highly politicized, the green energy advocates would have you believe that so called green energy is a magic pill solution, with no downsides, when really, at best it's a small part of the solution.
While the people who basically side up with the petroleum industry will try to sell you imaginary numbers, or otherwise hammer you down with irrelevant comparisons, conclusions and data.
If I might add my 2 cents - Wind power as well as Solar power, are part of the solution and it's very important for us to develop these further. a 100% efficiency is impossible, but imagine what could happen if we had 80% efficiency on Solar&Wind energy production? we could maybe minimize (not eliminate mind you!) our trace on the environment, while also lessening our demand for energy production dedicated land. together with another 2-3 sources of clean energy, we may very well create a society that is both abundant in food,water and energy and as non-obtrusive as can be.
I know, this post might have bored you to death, I was sick when I wrote it so it might be lacking in humor, wits or logic, but I do hope later posts will be better that way...
