WINDMILL PUMPING PERFORMANCE.

Various basic physical relationships are necessary to understand
windmill performance.

The power available from the wind varies according to air
density. Windmills must be derated for altitude.

The torque generated by a windmill varies as the square of the
wind speed.

The power available from the wind varies as the cube of the wind
speed.

The potential power of a windmill varies according to the square
of the windmill diameter.

Further the vane tip speed of an American type windmill is
slightly greater than, but linearly proportional to, the wind
speed.

It can be deduced from the above that once a windmill overcomes
the starting torque required to lift the body of water in the
pipes then if the wind speed further increases the power of the
wind available will exceed the windmills ability to absorb this
power as the power utilization goes up linearly, as the windmill
rotation speed is linearly proportional to the wind speed, but
the power available from the wind goes up with the cube of the
wind speed.

The American style windmill is designed to generate maximum
torque and therefor has a solid wind wheel.

LOADING/PUMPING CAPACITY OF WINDMILLS.

Southern Cross windmills are designed to commence pumping at a
wind speed of 11 km/hr and reef at a wind speed of 40 Km/hr. A
pumping table has been drawn up indicating the size (diameter) of
pumping cylinder which may be fitted so that the windmill will
commence turning at a wind speed of 11 Km/hr (elsewhere on this
web site http://www.southx.co.za/table.htm  ). The upper speed is fixed by the reefing system.

It is however possible to overload or under load a windmill to
enhance it's performance or increase the depth from which it will
pump water.

The load on a windmill is a function of the depth from which it
is to pump as well as the square of the diameter of the pump
piston.

Bearing in mind the relationships given above:

The starting speed of a windmill varies as the square root of the
depth to be pumped.

The starting speed of a windmill varies linearly with piston
diameter.

The amount of water pumped each stroke varies as per the square
of the piston diameter.

Taking a 4,3 m diameter windmill lifting water from a depth of
140 metres it will deliver 3.590 litres per day (this is based on
an assumed wind speed distribution which approximates to a wind
speed exceeding 11 km/hr for a period exceeding 8 hours per day.)
The size pumping cylinder to fit is given at the top of the table
as 44 mm in diameter. If a 51 mm diameter cylinder were to be
fitted instead the windmill starting speed would increase to
12,75 km/hr but the amount of water pumped per stroke would
increase by 34 %. One would accordingly need to asses whether the
time lost in pumping (the period where the windmill would
previously have functioned in the wind interval 11 km/hr to 12,75
km/hr) is more than compensated for by the extra water pumped per
stroke.

Many windmill manufacturers give pumping capacities for their
windmills at wind speeds of 25 km/hr or more and state this as
being so many litres/second etc. When comparing windmill
performances it is necessary to ascertain the windmill starting
speed so that it is possible to draw up an accurate estimate of
actual water pumped per day. It is of no assistance giving a
large water pumping rate at an inflated wind speed if the area in
which the windmill is to be located rarely experiences such a
high windspeed. An example of windmill performance "cooking" is
given below.

Using as an example a Southern Cross 7,5 metre diameter windmill
fitted with a 64 mm diameter cylinder pumping from a depth of 
216 m, 11.800 litres per day will be pumped assuming a standard
wind speed distribution. The windmill will start pumping at 11
km/hr and have a stroke rate of 0,5 strokes per second or 30
strokes per minute at a wind speed of 30 km/hr. The flow rate at
this wind velocity is 0,388 litres per second. The output power
is 821 watts. The input power assuming an air density of 1
kg/cubic metre is 12,8 kw giving an efficiency of 6,4%. Fitting a
102 mm diameter cylinder will still result in a stroke rate of
0,5 strokes per second but the flow rate is now 0,984 litres per
second giving an output power of 2,086 kw and an efficiency of
16,3%. The new windmill starting speed is 17,53 km/hr. In the
African tropical low windspeed environment one would select
Southern Cross standard windmill loading however if this windmill
was in the North Sea, gale force winds most of the time, one
would chose the latter loading.

Potential windmill purchasers should accordingly be wary of
windmill manufacturers who cite windmill pumping performances at
high wind speeds which are close to the stall speed of the
windmill. American style water pumping windmills are at their
most efficient close to their stall speed. Loading a windmill so
that it has a high stall speed and then giving the pumping
capacity close to this stall (Starting) wind speed is the oldest
trick in the windmill manufacturers book.

A further variation in altering a windmills performance is in
pumping from a depth greater or less than the recommended depth
specified for a particular windmill - pump cylinder combination.
Using the same example above let us assume that the depth of the
water in the borehole is reduced to 140 metres and not 216
metres. The windmill will then start pumping at a wind speed of
8,85 km/hr (starting speed varies as per square root of depth).

The object of the above is an attempt to illustrate that windmill
performances can be tailored to climatic conditions and
manufacturers wishes. In light wind areas windmills should be
under loaded whereas in high wind areas overloading is possible.

In all of the above it must be remembered that the theoretical
maximum efficiency of a windmill cannot exceed 59%. In the case
of American style water pumping windmills this maximum is 35%.
The graph below sets out the best efficiencies of various types
of windmills. (This graph is copied from "Windpumps, a guide for
development workers", published by IT publications, 103-105
Southampton Row, London WC1B 4HH, United Kingdom. This
publication is a must for all serious development workers
contemplating windpump system installation).


To check windmill manufacturers claims regarding their products
pumping capacity is relatively easy as the power available from
the wind at a specific elevation and air temperature is a known
and the power required to move a certain flow rate of water
against a certain head is also known. The calculation of
efficiency is accordingly easy.

In fact the only way to compare windmill performance is to
calculate the energy imparted to the water during a typical
pumping day assuming a typical windspeed distribution. (In short
Joules per day). Alternatively (and a poor second best) one
should specify a starting speed and ascertain the claimed floe
rate at a windspeed halfway between the given staring speed and
say a windspeed of about 40 km/hr (above which the windmill
should have reefed to protect itself). Any supplier whose claims
indicate an efficiency above 25% at this intermediate point can
safely be further questioned with not a little scepticism.