The capacity of a windmill

After the war, in 1946, the prospects for windmills were extremely gloomy. A great many of them had been damaged or destroyed by acts of war, no repairs had taken place for many years past, everything was disorganized, and confusion reigned, while there were no prospects of recovery.

It was then that the Dutch Windmill Society sounded the alarm and the idea was launched of keeping the windmills turning by making them work in combination with an electric drive to the machinery, which would at the same time make it possible to generate electricity during periods of a 'surplus' of wind.

Before reporting on this matter, however, it is of importance first to devote some attention to the technical properties of windmills in general.

What is the CAPACITY of a large polder mill?

This question has always formed a point of discussion and widely varying answers have been given to it from time to time. Nor is this very surprising. A windmill transmits the power which it derives from the wind. And this actually varies from one moment to another; hence the capacity of the windmill varies too. Moreover it also depends upon the load required.

The wind blows with a certain velocity, but this does not mean that this velocity is constant throughout. On the contrary, it will vary at any moment, and even in an air flow apparently having a constant velocity there will always be gusts and blasts which have a greater velocity. Nor is the amount of energy, accumulated in a given air flow of a given velocity, constant. It depends upon the condition of the air: barometrical height, humidity, and temperature. Any skipper will know that in the winter season the air is 'denser' than in summer and that, even if the wind has the same velocity, it will bear down on the sails more heavily.

The wind blows through the turning sails of a mill, passes on, and thus gives off only a limited part of the accumulated energy to the wind shaft. In the transmission gearing of the windmill some of the energy is lost of course, and the scoop wheel too gives less power (in the form of scooping up water) than the input that is delivered to it by the mechanism of the mill.

A small variation in the velocity of the wind already has a considerable influence on the power output of the mill, for the output is proportional to the cube of the wind speed, and consequently also to the number of revolutions of the sails as far as this number is proportional to the wind speed.

But this proportionality does not always hold good, for in a strong wind the sails have to be reefed, in order that the mill may not perform more revolutions than it can stand up to on account of its construction.

If with increasing wind speed the mill is loaded more heavily, e.g. in a corn mill by adjusting the gap of the stones and the feed of grain, the number of revolutions of the sails may remain practically the same and yet the power output will be higher.

Thus there are a great many variables, and it will be obvious that 'the capacity of a windmill' is not a constant magnitude. It stands to reason that it also varies with the size of the mills: the capacity of a windmill is proportional to the square of the length of a sail.

It is thus not surprising that many different figures have been given for the performance of a windmill and that the figures recorded will often not bear examination.

Besides, the most important point is not the power which a windmill can derive from the wind at a given moment; it is of much greater interest to know what amount of energy a particular mill is able to deliver in a given period of time.

Indeed, this is the crucial point when a windmill is to be judged in its function of draining off the polder water in a given period or of delivering the meal in a given time.

The most recent measurements are those made during the tests on the windmill at Benthuizen.

Without going into details, it became clear in the course of the years that we may establish a few main points in answer to the question with which we are here concerned. The question should therefore really be put as follows: what is the maximum power which a large octagonal windmill can derive from the wind and what is its output during a given period of time?

To answer this question, we shall first have to become familiar with a few elementary concepts.

In order to indicate the strength of the wind by the same international standard, the force of the wind has been arranged according to the Beaufort scale, in twelve different degrees of strength.

Forces 0 to 2 form the 'light breeze' of the weather forecast, the breath of air in which the leaves will rustle. The 'gentle to moderate breeze' is referred to by the numbers 3 to 4 of the scale: leaves, twigs, and small branches will move. The next in order is the 'fresh to strong breeze', forces 5 to 6; at 5, small leafy branches will make swaying movements, crested waves will form on lakes and in canals. At force 6, the 'strong breeze', big branches will move and the wind will whistle in the telegraph wires; larger waves will form, which cause foam patches, and umbrellas can be held only with difficulty.

This 'strong breeze', which is wrongly looked upon as storm and so termed by the man in the street, is followed by the real 'gale', forces 7 and 8 of the scale. At force 7, the 'moderate gale', whole trees will move, we are hampered in movement, and at force 8 twigs will break off and we have to strain against the storm. From now on it is a gale, force 8 and upwards: chimneys and roof tiles are torn off and buildings are damaged.

What wind speeds, in metres per second, correspond to these various forces?

The light breeze, of 0 to 3 metres per second, corresponds to the forces up to 3 on the Beaufort scale. The moderate breeze, forces 3 and 4, has a speed increasing from 3.5 or 4 to 7 metres per second. At forces 5 and 6, the strong breeze, speeds are 8 to 11 or 12 metres per second. The moderate gale, force 7, will have a speed of 12 to 13 and 15 metres per second, and the fresh gale, force 8, a speed of 13 to 15 metres per second and upwards. At 12 and 13 metres per second it is necessary to stop the mill.

Thus far we have spoken about the driving force of the windmill, but what about the power output?

Let us take a drainage mill with a scoop wheel. At a small number of revolutions per minute a scoop wheel requires relatively little power; this increases with the number of revolutions. Owing to its construction it can transmit only a given proportion of the power by which it is driven in the form of output. The latter is realized in raising a certain quantity of water through a certain height in a given time and is expressed in so-called water horsepower (W.H.P.).

One W.H.P. corresponds to raising 75 litres of water per second through a height of 1 metre.

With a reasonable number of r.p.m. about 50 per cent of the H.P. which the mill generates from the wind will be given off by the scoop wheel in W.H.P. Under certain circumstances the scoop wheel of an unimproved mill will be able to give off a maximum of 20 W.H.P., provided the mill and its components are in good condition. when the number of r.p.m. decreases, i.e. when the wind becomes lighter, the power output will soon become considerably lower. For the unimproved mills this begins already as soon as the wind speed decreases below 8 metres per second.

The earlier - unimproved - windmill only started to turn at a wind speed of 5 to 6 metres per second. It would then turn only very slowly, and the scoop wheel would displace hardly any water, only just enough to force open the sluice gate. As the wind increased, the mill, in 'full sail', would begin to displace water, and above 8 to 8.5 metres per second it would feel really in its element, while with the wind gathering strength it would attain full speed, say about 75 to 85 'enden' (i.e. ends), as it is called in miller's terms.

The number of 'enden' is the number of times the tip of a sail passes by per minute, i.e. four times the number of r.p.m. of the wind shaft. With this number the mill will generate about 50 H.P. from the wind. When the wind increases even further, the sails will have to be reefed, from wind speed about 10 metres per second on, and from 12 metres per second on the miller will work the mill with the sail-cloths furled. Then the wind has already gathered to a gale and it will not be long before the mill has to be stopped and anchored. The maximum number of r.p.m. which a windmill can stand up to is generally about 90 'enden', sometimes slightly more. This involves the risk of the mill running away, for the scoop wheel will then rotate at too high a speed: the water will splash to the sides and whirl round rather than being raised, for the flow of the polder water cannot keep up with it; it has hardly time to flow to the scoop wheel and the 'buckets' of the latter are not filled sufficiently. It does not give a sufficient load to the mill, and there is a risk of everything going to pieces.

In industrial mills it is usually possible with increasing speeds to increase the load somewhat and in that case the power output of the mill will be slightly greater, perhaps 60 H.P., with occasional peaks of 75 and sometimes even 90 H.P.

And now for the difference between the unimproved and the improved,version of the windmill.

An improved windmill will already turn at a wind speed of 3.5 to 4 metres per second; at 5.5 meters per second its power output will be equal to that of a normal mill at 8 metres per second. At the same wind speed an improved mill will attain to a considerably larger number of r.p.m. than a normal mill.

That is a great gain. With stronger winds the difference in effect is not so great, for the sails of an improved mill will have to be reefed sooner, a normal mill on the other hand will then still turn in full sail and the number of 'enden' of the two mills will be approximately equal.

In the course of the tests with the windmill at Benthuizen, a mill with a span of 86 feet and improved sails, it was found that (with 66 'enden') the average power output in one hour was 55 H.P., but that momentarily it was two and three times greater!

An improved windmill has two advantages: the greater power output at a given wind speed and the longer working hours; the latter is due to the fact that an improved mill can utilize the many hours of lighter wind, which are of no value for a normal windmill.

From the wind statistics of the Netherlands Meteorological Institute it appears that for a number of years there will be an average of 3,754 hours a year when the wind has a speed of less than 4 metres per second. Between 4 and 6 metres per second this figure is 1,771 hours, and wind speeds of 6 to 8 metres per second occur during 1,332 hours a year, wind speeds of 8 to 12 metres per second during 1,339 hours a year.

A normal windmill therefore can utilize no more than a total of 2,671 hours a year, but an improved mill will utilize 4,442 hours. An enormous difference indeed! And if the hours of the lightest wind in which the mill will still turn were to be included in the reckoning, the total would be greater still. However, it has to be conceded that very little water will be displaced during these hours; but the same also applies mutatis mutandis to a normal windmill.

The annual output of an improved windmill may therefore be assumed to be approximately twice as great as that of a normal windmill.

Of course even an improved windmill presents the drawback of every mill, that it cannot turn when there is little or no wind; also that the periods when there is much work to be done by the mill do not always coincide with periods of good wind.

With drainage mills this drawback was always met as best it could by the provision of extensive water storage in the polders as well as in the basins. Nowadays this drawback can be overcome in a simple way by the installation of an electric auxiliary pumping plant. This can easily be accommodated somewhere; if necessary, in the mill itself or close by. It does not spoil the appearance of the mill.

From the above the conclusion might be drawn that the improvement of the windmill might be utilized even better if it were loaded with machinery capable of absorbing a considerably greater power than normal. Up to a certain point this is true, but the question then arises whether the construction of the mill as a whole is really adapted to this. The windmill may be said to have been greatly perfected through the ages, but its construction was always based on an understanding of the forces to which it was subject. If higher demands are made in some respects, the harmonious whole will be disturbed. When a component part is broken, it can be replaced by a new one, so strong that it will break no more; but then another component will soon give way, and so on. In our opinion therefore the question can only be answered in the negative.

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