When we were house-hunting, one of our options had an honest-to-goodness stream flowing in the front yard. The driveway and front path had little bridges. It was awesome.
(But too far from the shops.)
That house popped into my mind when I read about the new Beck Mickle water generator that will, according to its makers, give useful power from the babbling brook in your back yard. Let's assume that you have both a yard and a brook, for the purposes of this argument.
The Beck Mickle Hydro site doesn't have much information yet, but that's OK, because the outer bounds of the system's efficiency are already defined. Quite simple physics tells us the theoretical maximum amount of energy that can be derived from X much water per second dropping distance Y. You can read all about the equation involved in various places; here, for instance, or this PDF for a fancier version.
The big deal about the Beck Mickle generator is supposed to be that it works from very small "heads" - a very small amount of "fall" for the water. There's no problem factoring that into the equation, though; you can just ignore the usual few-feet head that's the minimum (and a major limiting factor) for most "micro-hydro" systems. They have that head limit because we don't live in Physics Experiment Land; inadequate head means the efficiency of the system will fall vastly, possibly even to zero, as the water just doesn't have enough energy to get the generator turning. The Beck Mickle thing is apparently easier to turn. Groovy.
Let's assume the Beck Mickle system really does work just fine from a miserable eight inch head, and let's further be insanely generous and assume it is 100% efficient at turning water energy into electricity (versus the 55% efficiency that's common in current systems).
How much flow would you, then, actually need to achieve the one kilowatt output talked about in the Daily Mail piece?
Well, the equation [New! Improved! Actually correct now!] is Gross Head (in metres) times Flow (in cubic metres per second) times System Efficiency (decimal equivalent, where 100% equals 1) times a constant (9.81 in this case, the acceleration due to gravity in metres per second squared; it's a less neat number if you do the calculation in units other than metric) times the density of water (1000 in this case, because that's the number of kilograms in a cubic metre of water) equals Power (in watts).
(The oregon.gov page I mention above simplifies the equation by giving results in kilowatts and leaving out the water-density figure. I screwed up the first time I worked it out here, using their version of the equation but imagining power was still in watts.)
Assuming you've got a 60 centimetre head - three times the alleged minimum for the system - solving for Flow gives
0.6 * Flow * 1 * 9.81 * 1000 = 1000
So: Flow * 5886 = 1000
And thus: Flow = 0.17 cubic metres per second.
That's quite a lot [though not nearly as much as I thought it was when I had it wrong].
An Olympic swimming pool holds about 2500 cubic metres. You'd have one of those coursing through your back garden every 15 seconds every four hours or so, which isn't quite as spectacular as I first thought, but is still a bit speedy.
(I don't know how many Libraries of Congress per second that is.)
To pay for itself in the quoted two years, at standard UK electricity prices of around ten pence per kilowatt-hour, this £2,000 generator would indeed have to deliver the quoted 28 or so kilowatt-hours per day - even more than a thousand watts of constant power - in order to break even in two years. And that's assuming that it doesn't need any expensive repairs, which would both increase the price and reduce its generating hours.
(Curse my cynical mind for thinking that a v1.0 product might not last for two years just because it is (a) constantly rotating and (b) constantly wet.)
When I had the calculation wrong, I thought the claimed results were utterly ludicrous. Now that I've got it right (thanks, nichyoung!) it's less ridiculous; this thing actually could make worthwhile power, if (a) it works as advertised and (b) you have a decent little stream to put it in.
Of course, it's still unquestionably not actually going to be very close to 100% efficient. Advanced water turbines can manage 80%; backyard hackers are lucky to crack 50%. But, still, could be worth it.
Another reason why this story caught my eye is because, apart from being based on a different element, the claims made for the domestic waterwheels generator sound very much like the claims made for small wind generators.
Small wind turbines look pretty impressive, until you discover that the unremarkable-sounding wind speeds needed for them to start generating properly are actually, often, Beaufort Force Six. The hardy maritime types who came up with that scale may only call Force Six a "Strong Breeze", but it's actually Strong enough that, if it's raining, you may do better to not bother trying to open your umbrella. Few residential areas have Strong Breezes much of the time, because people try not to build towns in places like that.
Awesome dude Tim Hunkin has something to say about all this.
If you actually want to get reasonable power from a wind generator in "normal" winds, you need something like a twenty foot turbine eighty feet up in the air. From that, you will genuinely be able to get a kilowatt of power on pretty much any day when there's what a city dweller would call a breeze, and you'll get a reasonably reliable 2kW or more if you live somewhere more windy, but not startlingly so.
But if you've got a Neighborhood Association, they will not like it.
2 January 2007 at 11:18 pm
You don't seem to have included a density in your calculations there. I'm guessing you took that as 1, but the density of water is only 1 in the right units, such as kg per litre - it's 1000 kg per cubic meter. That reduces the required flow to 0.17 cubic meters per second. That's still 170 litres per second at 100% efficiency though, and that's still a lot of water.
3 January 2007 at 1:30 am
Nichyoung's got a point. The original equation you quoted is actually correct for water only if your units for power are KILOWatts; the factor of 1/1000 cancels out the factor of 1000 due to density to give the right answer. But then you go substituting numbers in and put 1000 for one kilowatt of power, instead of 1.
If you want to use SI units, the correct equation is:
Power output in Watts = Head in m * Flow rate in m^3/s * efficiency as a fraction of 1 * g in m/s^2 * density in kg/m^3.
3 January 2007 at 1:51 am
Yeah, I bollocksed that up pretty good. Fixed now. Device not as sucky as I thought. Mea culpa.
3 January 2007 at 1:59 am
As a "hardy maritime type" myself, I have to put this bit in.
I live aboard a sailboat(in the USA), and happen to own a Southwest Windpower Air-X Marine wind turbine (http://www.etaengineering.com/windpower/air-x_marine.shtml Ask for it by name - they are the best! ), and I am very happy with it.
In Watts / $, it fails miserably compared to my Coleman 1500W Generator( which cost me $300 on sale, and sips gasoline at about $3/Gal if you don't shop around, $2.25 at the moment if you do).
However, the advantage of wind power(and, for that manner, solar panels as well) in maritime applicatios is that they do not require gasoline, diesel, or even for the boat to be moving. This is VERY handy when you happen to be sailing across an ocean, or anchored out in the arse end of nowhere(say, the less populated islands in the South Pacific), where there simply isn't a supply of fuel.
The reason that wind generators work extremely well for sane boaters(sailboats) is that we have a very low energy budget. I use perhaps 50A @ 12V DC (600W) in the course of a day. This is 0.6kWh. The biggest consumer I have at the moment is this damned laptop, with a 60W power supply, and my 13" TV. This is a rather sizable downgrade from the consumption when I lived ashore, where the EIGHT computers I had in my bedroom(I was 17 at the time. I won't go into the amount in the "server room" in the basement) blew my 10A breaker if I turned on too many lights(In the US. the lights are normally on the same circuit as the wall outlets. Less wiring, I suppose)
Sooo.... If you happen to have a nice, low, power budget, wind, water, or solar power will work very nicely with a small installation. You'll need batteries, and an inverter if you HAVE to have 120/240V AC service, but 12/24V DC works well enough.
If I need more power, I have that 1500W generator, after all.
3 January 2007 at 2:30 am
Yeah - one of the things Tim Hunkin mentions is that one of the prerequisites for "alternative power" to start being really useful is everybody using a lot less electricity, thanks (for domestic applications) to more efficient appliances.
Of course, that ain't happening yet. What with plasma TVs and more and more air conditioners around the world, per-home electricity budgets are still rising. It's not all going one way, of course - efficient lighting's becoming quite normal, and there's a promising movement towards eliminating "vampire" devices that suck juice while "off".
Home alternative power solutions also don't have to have a battery bank. If you've got a grid connection as well, your solar/wind/whatever can supplement that and, in more enlightened countries, allow you to run the meter backwards if you're making more than you need.
3 January 2007 at 5:01 am
The problem with not having a battery bank is that it eliminates one of the best possibilities about solar setups - power when the grid has failed! My workplace just moved into a new custom built office building complete with a 170kW solar array. "Nice" I thought to myself "environemtally conscious and a ready source of power when the grid drops!". That power when the grid drops is kind of important for us as we are considered 'critical infrastructure' in community emergencies (you know, plagues, floods, fires, earthquakes - times when power is likely to be flakey). Now I know solar won't let us run all night at full power but we could easily keep our core systems up with a moderate battery bank... but we don't have one. We spend 1.2 million on our solar system and cheap out on the additional $150K it would have cost for a battery bank. Brilliant. So our solar system actually connects directly to the grid and not to our building at all. Since we have no battery bank we have to do this so that the power load from the solar can be properly balanced. Sure it saves us some money over time... but we're now going to wipe that savings out by purchasing and installing a 75kW diesel generator system and a large, ugly, and no doubt leaky, above ground diesel tank. This will give us 24 to 36 hours of backup power before we are out of fuel. Which, if power is down that long, will likely be a real problem as I doubt a refill of the tank would be coming anytime soon. To top it off, we will be spending about $15,000/year on a maintenance contract. The maintenance contract (including replacement of cells) for the battery system we'd need would run $10,000 to $12,000.... and provide us a system that can give us power indefintely in an emergency. Bunch of pointy haired masterminds around here I tell ya!
BTW - it's winter here and even on the rainiest day we've seen yet (very rainy) the system was producing 60kW. So the system itself is wonderful... the implementation of it stinks though.
3 January 2007 at 9:19 am
Oh the things I could do with a 170kW solar array. Like, auction most of it off for spending money and use about 5kW use for myself.
The biggest problem with installing a shore-based solar array given current solar technology, is that, short of a 100% reliability rating on the panels, they'll never make it worth the money or trouble....
Just be glad its a private business, not the US Government isn't installing solar panels on the Pentagon... Somehow it would be a 1.2 BILLION dollar installation, and still only have 170kW peak rating, and.... you get the idea.
3 January 2007 at 6:51 pm
It is actually much worse though. They say that efficiency is around 70%. Let us of course assume they don't exagerate at all and we can regularly expect to run at 70%.
Using their minumum of 20cm head, then we actually need a water flow of .73 cubic meteres per second. 730 literes per second. IF I am reading the flow on the Don river in Melbourne it is actually higher then it's low flow!
Even if we assume as you did a 60 centimeter head you still need a pretty good flow. Around 240 literes per second using a 70% efficiency.
Definately a great investment... Provided you happen to own the niagra falls.
3 January 2007 at 10:13 pm
You know, Dan, I enjoy reading your posts, and you always link to some great stuff.
But I think it might be a mistake to link to Tim Hunkin's site... it's like calling a subroutine that never returns! I just spent (another) few hours over there, before realising that I hadn't finished reading what you'd written. Did you also see this piece about playing with technology?
http://www.timhunkin.com/a118_technology_is_human.htm
Perhaps you should only link to Tim's site at the ends of your posts? Like I didn't.
4 January 2007 at 2:54 am
"Inadequate head"? "Miserable eight-inch head"? I have seriously underestimated the humour potential of hydroelectricity.