### The Case for Tiny Wind

Working squeezed/scrunched up in the belly of the Army Aeroflightdynamics Directorate 7’x10’ wind tunnel gives one lots of time to think about the world and our place within it, and how these “tiny” wind generators (the term “micro” has already been claimed for systems up to 5000 watts) can help contribute to an improved quality of life for some. Remember the target market is people who either have zero access to electricity, or who perhaps depend on charging worn out car batteries in distant grid connected towns – you pay bus drivers to transport your battery back and forth – to get a trickle of power. How people use that *first few watt-hours of high quality energy* they have access to fascinates me, since while we sometimes have an impression that everyone else wastes scarce resources too, in reality people with scarcity tend to know the value of conservation and wise use best – especially when their costs are high.

Extending their day by a few hours with an efficient light is usually the first use – most unconnected places seem to be close to the equator where the days are __always__ short, and recurring costs for candle/kerosene lighting are cumbersome/prohibitive – allowing people to read, do homework, and maybe even earn extra income. Charging batteries – for flashlights, the radios all campesinos carry to the fields, and cell phones – is another priority, hopefully reducing the number of discarded disposable ones that litter the ground. Both of these applications require very little energy – for us it would be worth just pennies worth a day, but for people who all year around are used to calling 6 pm bedtime… priceless! And yes, one of the first appliances to appear is the ubiquitous television, often for soap operas and soccer matches, but also news and education.

Just a hundred watt-hours a day will do all kinds of things when the appliances

s are efficient, and in a breezy location it shouldn’t take an expensive turbine to provide this. As a slightly technical aside, it is best to remember that people use **energy** to do things while we have a tendency to express the output of wind generators (and photovoltaic panels, and microhydro installations, and nuclear power plants) in units of **power** (watts). The wind tunnel tells us how many watts we might generate at a given wind speed, but winds fluctuate so we can’t count on getting that much all of the time. Commercial turbines are almost invariably rated just in watts, and you always have to ask “At what wind speed?” – and you’ll quickly find that they choose to rate at some phenomenal (and usually unrealistic) value, like 25 miles/hour (~11 meters/sec). Southwest Windpower (http://www.windenergy.com/products/whisper_100.htm) has now started doing the right thing by helping you estimate how much energy (in watt-hours… each one of these helping to perform a useful task, such as a one watt LED lamp aiding a kid do homework for one hour) you might expect to generate from their products, after making some assumptions about your local **wind speed distribution**.

This brings us to the question “How do we extract power (and energy) from the wind – which comes originally from the sun?” The __maximum__ power *available* from the wind, per square meter of turbine swept area, can be easily calculated from the equation

Power = ½ rAV^{3}

where r is the density of air, A is the swept area of the turbine, and we see that the power increases as the cube of the windspeed (doubling the windspeed gives 8 times as much power), so that while there is lots of power produced at high wind speeds there is almost none available at very low speeds. Our Lenz blades sweep out an area of .75 m^{2} (the Savonius configuration we tested is .45 m^{2}) and we know that we can only realistically have a fraction of the energy the wind contains – Albert Benz said that 59% is the maximum, but more like 30-40% is typical for small tubines like ours. So the amount of power you can tap into depends on how much the wind blows, and with like so many other things (like per capita income) the *averages* provided to us by the government don’t always do us enough good – some days it doesn’t blow, some days it blows too much, and luckily some days it blows just enough for your turbine to fill up your batteries for the coming week. That’s the concept of the distribution (vs. and average), and luckily the wind speed variability tends to follow a Weibull distribution (http://en.wikipedia.org/wiki/Weibull_distribution), a statistical function, where just two variables describe the distribution. These are the average wind speed and a number related to the general amount of time with no or low winds (the shape parameter), and this site http://www.reuk.co.uk/Calculate-kWh-Generated-by-Wind-Turbine.htm does a much better job of explaining it than I can here – and they allow you to type in your power vs. wind speed data (such as from wind tunnel testing), plug in a shape factor, and get the anticipated energy output (say in watt-hours/day) at your target location. Now you can buy the right number of storage batteries to get you through the wind-less doldrums, and compare the cost of your tiny wind system with your other electricity alternatives – including continuing to charge your car battery for the equivalent of $3/kW-hr, and waiting a long time for the grid to arrive.

Taking the raw wind tunnel data Tyler showed (torque and power vs. RPM) we can determine the __maximum__ amount of power a given blade set or configuration can extract from the wind at each speed and plot it – that upward curved shape is very important because it tells us that not much power is available to us at low wind speeds (say, less than 10 mph) Our experimental method did not include a generator to turn the winds power into the electrical power we need to run appliances, and there will be losses in this conversion process – we expect it to be ~75% efficient - so we have to take this into account, giving us the ability to get about 25% of the energy embodied in the wind – not bad if the resource is free.

As mentioned, a single “power rating” for a turbine is not very useful (and only meaningful if the wind speed it was measured at is associated with it), but people are used to hearing just one number so we may need one. Catapult Design will tend to rate these turbines (a set of blades plus the associated generator) at more realistic wind speed values, like 15 mph (7 m/sec), and then we’ll do our best to try and characterize the wind resource at a specific locale. If we choose to rate at 15 mph, for example, then the real power output of the Lenz blades is ~30 watts, and the wind will need to blow at that particular speed for ~3.5 hours/day to provide 100 watt-hours of energy per day to a family or small business. Blowing at half that speed for twice as many hours does not do us much good, since the blades of VAWTs often don’t start turning until 8 mph, and at 10 mph we might have to rate these tiny turbines at only a watt or 3. For estimation purposes, Weibull wind speed distributions with very low shape parameter values would be an example where it blows very little, much of the time.

Its unfortunate that life is never as simple as it needs to be – it seems like that if a family wanted to consider buying a tiny turbine at X dollars, to decide whether it is worth it they need that power performance curve for it, decent information on their local wind conditions, and some idea how much electricity is worth to them (for example based on how much they are presently using and the cost for charging that car battery, or how much more they want to use – say if their neighbors pay them for charging cell phones). Now if we just knew the probable lifetime and annual maintenance costs we could start to understand the cost of each *future* watt-hour… what an exercise, and don’t forget that investing in all forms of renewable energy is tantamount to buying at one time __all__ the electricity you will use for the rest of your life, which is not an easy decision to make.

An interesting resource for evaluating the performance (energy generated per unit time) and financial characterisitics of a wind investment can be found here: http://estimator.solar-estimate.org/index.php?page=wind-calculator and while you have to play some tricks on it to simulate this size of wind generator (technically it would be rated at ~200 W at a traditional wind speed like 25 mph) in an off grid location where electricity is presently very expensive to acquire. It is a good tool for showing what steps are required for determining fiscal suitability, and along the way it will teach you a little about wind energy - for example, at my home in Berkeley it says that I should expect an average wind speed of 10 mph and a Weibull distribution shape parameter of 2 (I may disagree, unless they mean at the sailing marina). It is not detailed enough to take into account our specific turbine characteristics, like efficiency and cut in speed, but nevertheless is is interesting to consider their estimate of 75 kW-hrs per year of energy generation for this turbine and location. My utility bill says that last month I used 127 kW-hrs of electrical energy (needing 175 watts of power capacity), for the privilege of which I paid a grand total of $16, or ~$.13/kW-hr. Clearly a turbine providing only 75 kW-hr/year would give me $10 of energy annually and just meet a minuscule part of my demand - hog that I am, with all my phantom loads from consumer electronics - but if my cost of electricity was instead several dollars per kW-hr instead of a fraction of one then the situation changes, and tiny wind may make sense for my family or business.