# DIY Wind Turbines — Size And Power

### The rated speed

Most people are unlikely to bother with buying an anemometer: if you want to build a wind turbine you will probably simply go ahead and build one.

What you need to know is how big to make it and how much power it is likely to produce.

The first thing to consider is the ‘rated speed’ of the wind turbine.

This is the wind speed at which the machine produces its maximum output. The BRE suggests rated speeds for values of V_{50} as follows:

V_{50} in m/sec rated speed in m/sec

- 3.0 – 7
- 3.5 – 8
- 4.0 – 9
- 4.5 – 11
- 5.0 – 11
- 5.5 – 13
- 6.0 – 14

The value for V_{50} for your site can be taken from a wind speed map if you do not plan to set up an anemometer and take measurements over a year. The rated speeds in the table are chosen to give the maximum output per year from the wind turbine for the values of V_{50} shown. If you make the rated speed too high or too low you will fail to collect the energy from low or high wind speeds so you will collect less overall than if you use the values in the table. Say you design a wind turbine for use in an area where the map suggests that V_{50 }is 4m/sec. According to the table the rated speed will need to be 9m/sec if the machine is to be efficient.

### Generators and alternators

The starting point for the design must be the use to which the machine will be put. If it is for generating electricity the important factor is your choice of generator or alternator. The alternator will determine the maximum output of electricity from the wind turbine, and this is the output that must be generated at the rated speed. For example, if your alternator has a maximum output of 500W, you must size the wind turbine to produce 500W at its rated speed, which is 9m/sec in this example.

However, whatever alternator you choose it will not be 100 per cent efficient in its conversion of the mechanical energy of the wind turbine shaft into electricity. Most alternator manufacturers give a figure for the power absorbed to drive the alternator at a given number of revolutions per minute, and a curve showing electrical output related to revolutions per minute. The output in Watts at a given speed, divided by the power input in Watts at the same speed, gives the efficiency.

For example, if the power input is given as 1kW at 3500rpm, and the electrical output is 500W at 3500rpm, the efficiency 500 divided 1000 = 0.5 or 50 per cent. Some alternators have the power absorbed given in horsepower, and you will have to multiply this figure by 746 to convert it into Watts. If the output of the wind turbine is to be 500W and the alternator is 50 per cent efficient the wind turbine will have to be able to produce 500/0.5 = 1000W at its rated wind speed. If you can find a 70 per cent efficient alternator the wind turbine will have to produce only 500/0.7=714W to provide the same amount of electricity.

### Gearboxes and V belts

The amount of energy the wind turbine will have to produce will increase if the gearing is inefficient. A properly designed gearbox used to increase the speed of the wind turbine shaft is likely to have an efficiency of about 94 per cent, while a V belt on pulleys might have an efficiency of 90 per cent. If the wind turbine uses more than one set of pulleys or a gearbox and V belts, the efficiency of each set must be allowed for in the calculation of the total energy that the wind turbine will have to produce. Gearboxes that will step up in a ratio of 1:20 are available, but V belts are not practicable for an increase greater than about 1:7.

### The power formula

Let us suppose you calculate that your wind turbine must produce a total power of 1200W to allow for the inefficiencies of gears, V belts and alternator, so it is to have an electrical output of 500W. Your job now is to calculate the diameter of wind turbine required to produce 1200W at the chosen rated wind speed, in this example 9m/sec. The power obtained from a wind turbine at a given speed is calculated from the formula P=0.00064 x A x V^{3}C_{p}.

P is the power output in kW. A is the swept area of the wind turbine in square metres. V is the velocity of the wind in m/sec.

C_{p} is the coefficient of performance: this is the amount of power that the wind turbine can extract from the wind. Various people have shown that a 100 per cent efficient wind turbine could extract 59.3 per cent of the energy in the wind or that it would have a performance coefficient of 0.593. No wind turbine can, of course, be 100 per cent efficient and typical values of C_{p} for various types of wind turbines are as follows:

- Savonius rotor 0.15
- traditional grinding mill 0.17
- Cretan wind turbine 0.3
- steel multi-blade pumping mill 0.3
- Darrieus rotor 0.35
- high speed propeller 0.45

### Selecting a wind turbine — design

The only type of wind turbine that we would recommend for do-it-yourself assembly is the Cretan. The Savonius rotor can be built easily from an old oil drum but its C_{p} is very low so it will not provide much power. The high speed machines, such as the Darrieus and the propeller mills, can be dangerous because of their rapidly turning blades. Conventional wisdom says that a wind turbine that generates electricity must rotate very fast because a generator must turn fast to produce electricity. If the wind turbine revolves at high speed there will be little or no need for speed-increasing gearing which would absorb energy and make the whole thing less efficient.

The problems with high speed wind turbines are, firstly, that they must be very accurately balanced or they can shake themselves to pieces, and, secondly, that their speed must be governed. If this is not done the propeller would rotate so fast in high winds that it would fly apart. Even commercially manufactured wind generators, seemingly built to withstand hurricane force winds, have suffered blade failures which resulted in pieces of wreckage all over the place.

Detail of the sails ravelling for hundreds of metres and the failures of home made high speed machines have been numerous.

To prevent you or your neighbours becoming alternative technology’s first martyr we suggest you build only the Cretan type of wind turbine. His has canvas sails instead of aerodynamically designed blades, and it turns very slowly so that accurate balancing is not important. If it rotates too fast the sails begin to flap and then spill the wind, which slows it down. It needs a lot of gearing to generate electricity; but because it is very cheap to build you can simply increase its diameter a bit to provide the extra power needed to drive the gearing. Finally, if anything does break, it will not send pieces lying about the neighbourhood.

### The formula for size

To return to the calculations, we now have all he figures needed to find how big the wind turbine must be if it is to produce 1200W of power at he shaft (in order to drive a 500W alternator) in wind of 9m/sec.

Remembering that P=0.00064 x A x V^{3} x C_{p}:

P=1.2kW (1200W) A is the swept area in m^{2}

V is 9m/sec, the rated windspeed

C_{p} is 0.3 for a Cretan wind turbine

Putting these values into the equation we get

1.2=0.00064 x A x 9^{3 }x 0.3, thus:

A =1.2/0.00064×9^{3}x 0.3 = 8.57 m^{2}

The formula for the area of a circle is A=pi^{2}, where A is the area, pi is 3.142, and r is the radius; so, we can use A to find the radius:

8.57 =3.142 r^{2}

r ^{2}=8.57/3.142=2.73

r=1.65m.

So the required diameter (twice the radius) is 3.3 metres.

### Step-up gearing

All that remains now is to find what ratio of step-up gearing you will need to drive the chosen alternator from the shaft of the wind turbine. All wind turbines have a characteristic called the ‘tip speed ratio’ which is the ratio of the speed at which the tips of the blades travel to that of the wind speed. In a wind turbine with a tip speed ratio of 5 the blade tips will be travelling at 25m/sec in a 5m/sec wind. Some typical tip speed ratios are as follows:

- Savonius rotor 1
- traditional grinding mill 2-3
- Cretan wind turbine 1
- steel multi-blade pumping mill 1
- Darrieus rotor 6
- high-speed propeller 5-6

Using the tip speed ratio you can calculate the speed at which the wind turbine shaft rotates at the rated wind speed. In our example the rated speed is 9m/sec and the tip speed ratio is 1: so, at the rated speed, the tip of a blade travels 9 metres in one second. The circumference of the circle swept by the blades is given by piexd, where d is the diameter of the wind turbine, which we know to be 3.3 metres. This gives a figure of about 10.4 metres for the circumference. In one second the blade tip travels 9 metres, so it will take a little over a second to make one full revolution. In 60 seconds it will travel a total of 9 x 60=540m. Dividing this figure by the circumference gives the number of revolutions turned by the shaft in one minute, i.e.: rpm.

You now have to look at the alternator figures to see at what rpm the alternator gives its maximum output. Suppose the answer is at 3500rpm, the gearing-up must be in the ratio 3500/52=67:1 to provide the correct speed for the alternator. The best way to achieve such a high ratio is probably to use an industrial gearbox to do the first stage, with a V belt final drive to the alternator, as most vehicle alternators are designed to be driven by belts and pulleys off car engines. If the gearbox gives a step-up of 20:1, you will need in addition a V belt and pulley system that can step up 3.35:1. The step-up values are multiplied to give the final ratio from the wind turbine shaft to the alternator shaft, thus: 20:1 x3.35: 1=67 :1.

### Choosing a tower and maintenance equipment

Having worked out your wind turbine design you are not finished yet. You will need a tower to mount it on, so that it is able to catch the wind. The ideal tower should be 15-20 metres high, but such a structure would be expensive to build and frightening to climb, so most people settle for something smaller. The cheapest tower is probably a second hand telegraph or electricity pole, bought as scrap from the GPO or the local electricity board. If they are replacing poles anywhere near where you live they will drop one off at your address for a couple of pounds. If used poles seem in short supply, and sometimes there is a twelve month waiting list, try asking the GPO where they buy the new ones. The price will be higher but the pole will not have been standing out in all weathers for fifteen years before it gets to you. If you buy a new one make sure that it is Tanalised rather than creosoted, as the creosote will rub off on you every time you climb up to oil the wind turbine.

As well as a tower you will need a safety belt with which to tie yourself on when you reach the top. Try asking the GPO maintenance workers who climb the poles what they use, or look in the Yellow pages under ‘Safety Devices and Equipment’. A typical belt is made in the same way as car seat belts and it is attached by a very thick rope to a large hook which can be screwed shut.

### Wind turbine maintenance

You climb the tower, taking care hot to trip yourself up with the rope, put the rope round the tower, clip the hook on to a ring on the belt and screw it shut. One sees photos of heroic Swiss wind turbine repairers, supported by the belt alone and using both hands to adjust the machine; but it is more comforting to hold on to something solid with at least one hand while you wield the spanner and the grease gun. wind turbine maintenance is quite an art. The essential thing is to have all the tools and bits you need within easy reach, and to have extras of most things. It is very annoying to drop a vital washer and have to climb down to fish it out of the vegetable garden. Put everything in a bucket before you start, and tie a string to the bucket handle so that you can pull it up once you are at the top and tie it on to the tower.

### Installation

If you use a telegraph pole as a tower it will need guy wires to stop it falling over, and these must be anchored solidly into the ground. A machine with a 3 metre diameter might need guy wire anchorages consisting of a hole 900mm deep and 600mm square filled with concrete. For a 5 metre diameter wind turbine you will need a cubic metre of concrete. It is important to make everything very strong to prevent disasters during winter storms, but as a final safeguard the tower should be further than its height from your house; then at least if it does fall over it will not come through your roof!

It is best to erect the tower first, then .attach the wind turbine to the top of it, as this prevents damage to the wind turbine should the tower fall over while you are putting it up. You will find that wind turbine building and installation are best carried out on a cooperative basis, as it is not possible for one or two people to put up a wind turbine safely by themselves. Ask some people to steady the tower as you pull it into position and to hold it steady until it is finally anchored and guyed. Never try to do any of this on a windy day: even a gentle breeze could blow down the tower before it is secured and someone might be hurt.

As an alternative to a telegraph pole you might consider a self-supporting pylon tower. This type of tower needs no guy wires, and you can more easily fit platforms to it which will allow you to stand comfortably to carry out maintenance on the wind turbine. Ladders to the platform can be fitted inside the pylon to make the whole business of climbing up and down as easy and safe as possible. This type of tower may cost you more than a telegraph pole because it contains more wood, and it will be more difficult to make, but its advantages make it preferable.