Guide to the Wind
Turbine Shadow Calculator
The calculator on the following page allows you to simulate shadows from
a wind turbine on a plane, horizontal landscape any minute, hour, day, month,
or year anywhere on the globe.
Plots Will Take Their Time - and lots of RAM
If you wish to compute shadows for a whole year, it may take your computer
from 20 minutes to a couple of hours or more, depending on the speed of
your browser and your machine, and how fine a map resolution and time resolution
you choose. A fine map resolution (down to 3 pixels square) or a large plot
area increases processing time and the required amount of RAM on your computer
The shadow calculator is an extremely powerful, but computationally demanding
If you use Internet Explorer
4 for this calculator, be sure to enable Microsoft's Just-in-time
also give you the option of being able to read the number of minutes of
shadow anywhere by moving the mouse cursor around the screen, if you select
that option in your setup.
Netscape 4 will work,
as well, and on some platforms it is occasionally (but rarely) faster than
Unfortunately Netscape up to version 4.05 for
Macintosh appear to have a bug which means that they do not do "garbage
collection" (cleanup after disused variables) properly. This
means that the programme will run more and more slowly, until you quit your
browser. Netscape has one advantage, however: You may let the programme
run in the background while you do something else. (Version 4.06 seems to
be safe, and faster than its predecessors).
Netscape 3 is quite fast, but it may very easily get a stack
overflow and crash, if you use squares of much less than 25 pixels. Netscape
3 also stops and asks you if you want to continue every time you have completed
1 million iterations (i.e. repeated calculation steps). Since each month
takes about 5 million iterations, you'll have to sit around and click "Yes"
quite a few times. The solution is to upgrade, of course.
The grey colours in your plot are selected automatically by the programme,
so that the most shadow affected areas are shown in pure black, while the
least affected areas are shown in white, regardless of whether you run the
programme for 1 minute or a year. The unaffected areas remain green.
If you have a screen with millions of colours, you will find that the grey
shadows vary very smoothly across the screen. If you like to be able to
see the different "bands" of shadow minute values, like we have
done in our images on this web site, set your monitor to thousands of colours,
or even 256 colours.
Can Save Your Shadow Maps
If you have generated a shadow map which you want to look at later, or compare
with another map, you may save the page (e.g. onto your desktop), just like
any other web page in HTML format, if you use Internet Explorer 4. Just
choose Save from your file menu, (and take care where you save it,
and what you name it).
the Number of Minutes of Shadows in Each Cell
if you have an Internet Explorer 4 browser, and you leave this option on
when you generate the map, you can do an exact readout (in the status line
of your browser) of the number of minutes there may be shadows in each cell
by moving the cursor around on the shadow map.
May Recolour Your Result
The plot uses a number of standard colours which look logical on a colour
screen. The colours, however, may not be optimal if you wish to print the
result on a black and white printer. We have therefore included a facility
which allows you to change the colour scheme without redoing the long calculations:
You may use a particular colour in a "shadow zone" around the
turbine. If you use a large high resolution map, it may take a few minutes
for your programme to do the recolouring (IE 4 is slower than Netscape 4
Your Shadow Zone
You may modify your plot to show you any zone with a certain minimum number
of minutes of shadows in a certain colour. Be warned, however, that with
a large high resolution map, it will take several minutes to complete that
Incidentally, this calculator is very practical for photographers who wish
to know where the sun is before they go out to take a picture of their favourite
motive in ideal lighting conditions. (We tested it when photographing wind
turbines, of course). You may also use it if you wish to know how to place
a terrace in your garden (regardless of whether you want shadow or sun).
You may either specify your turbine location using the pop up menu which
gives the longitude and latitude of a number of cities around the globe,
or you may enter the longitude and latitude in degrees and minutes directly,
together with your time zone.
The time zone is automatically included, if you use the pop up menu with
city names. You may enter your time zone relative to GMT from the pop up
menus, or you may enter the standard time zone meridian, i.e. the longitude
relative to Greenwich which your local time system uses as a reference,
which is generally a multiple of 15 degrees, corresponding to a one hour
time difference. (India and a few other places have a time zone which is
a multiple of 7.5 degrees, i.e. half an hour).
You may enter date and time to see the sunrise and sunset times, plus the
current direction of the light coming from the sun.
Enter the hub height and the rotor diameter. A typical hub height for a
600-750 kW wind turbine is 45 to 60 m, a typical rotor diameter is 43 to
48 m. (You may find typical hub heights and rotor diameters using the Wind Turbine Power Calculator turbine
pop up menu).
If you wish to study shadows in areas which are lower than the base
of the wind turbine, you can cheat, and increase the hub height of the turbine.
Conversely, you can lower the hub height, if you wish to study areas which
are higher than the base of the turbine.
If you enter, say 0.5 for the rotor diameter, you may use the programme
to study the behaviour of a shadow from the top of a mast, or the corner
of a building. (Or you can use it to build your own sundial).
You can specify the time range for which you like your shadow images computed.
You can select a minute, an hour, a day, a month, or a year.
You may set the plot area to fit your screen size (and/or paper
output). If you have enough RAM (and time) you may even specify a map larger
than your screen. The default size prints well on A4 paper in landscape
The resolution parameter determines the area covered by each
3-25 pixel square. We recommend that you let each square represent less
than half the rotor diameter to get a decent plot. Or, even more cleverly,
you may set it to match your map resolution, and print your output on an
acetate (overhead) foil as an overlay to a map of a prospective wind turbine
location. (One printed pixel is 1/72 of an inch (1 inch = 2.54 cm)).
The step length in minutes determines how many rotor images the
programme projects onto your ground surface. The default step length of
4 minutes corresponds to the sun azimuth changing
on average 1 degree between each simulation. You may save processing time
if you choose a longer step length. For a 1 month or 1 year simulation results
are generally not affected much by using 8 minute steps - and it is 8 times
faster than 1 minute steps. If the shadow image is not smooth, (or if it
is asymmetrical in the East-West direction even if you are not running with
a fixed rotor direction or a wind rose), your step length may be too large.
If you double the step length, the programme assumes that the rotor shadow
stays in the same place for twice as long, i.e. for each rotor image projected
onto the ground, it adds the step length to a shadow counter for that particular
You may choose rotor direction as random (default), which means
the rotor may be facing in any direction (random azimuth), you may choose
worst case, where the rotor always faces the sun.
You may choose a fixed rotor azimuth angle from -90 to 90 degrees.
The angle is measured relative to South, and the solar angle is positive
before noon, regardless of hemisphere. 0 means that the wind is coming form
the South or North. Southeast/Northwest is 45 degrees in the Northern hemisphere,
and -45 degrees in the Southern hemisphere. East/West is 90 or -90 degrees.
To help you select the correct angle, you may use the pop up menu.
Finally, you may choose to enter a wind rose with a frequency
distribution for your wind directions. Since a normal propeller type wind
turbine is symmetrical about its rotor plane, you should add the percentages
for North and South, and so forth in each of your directions. The programme
accepts 8, 12 and 16 compass directions, which means that you specify 4,
6, or 8 percentages. The program checks that the sum is exactly 100, before
it is willing to do the simulation. Please note that wind roses are specified
with the North as 0 degrees, and that the degrees are given in a clockwise
direction (retrograde direction).
You should specify the fraction of daytime hours the turbine will
be running. 0.75 is a typical fraction. The basic result in terms of
minutes of shadows is multiplied by this fraction.
You should specify the fraction of daytime hours with bright sunshine.
The basic result in terms of minutes of shadows is multiplied by this fraction.
If you have accurate statistics on the number of bright sunshine hours
per month, you may instead use that data in your calculations, by filling
out the sunshine table at the bottom of the page. In that case the
programme uses the table data for each month instead of the average. We
have included sunshine data for 3 Danish locations (you select them from
the pop up menu). If you have reliable monthly data available for your location,
please e-mail us (giving the source) so that we may include it in the city
pop up menu. Remember to check the box that says you want to use the table
for your calculations. (A clever trick: If you wish to see the pattern of
shadows during e.g. June, July, and August only, you may set the sunshine
percentages for the three months only, and leave the rest of the months
at zero, and then run a simulation for a year, using the sunshine table).
You may set a maximum distance from the wind turbine for the
shadow plot, since it is usually not relevant to look at distances above
7 to 10 rotor diameters or 1,000 m at the most.
Finally, you may choose to have your output displayed with mouse-sensitive
shadow readout (for I.E. 4 browsers), which means that you may read
the number of minutes of shadow in each cell on the map in your browser's
status line by placing the mouse cursor on a particular cell. Using this
mechanism increases RAM demand.
In this programme the sunrise time is defined as the moment a straight line
to the centre of the sun passes the horizon in the upwards direction on
the date you have entered in your data. In your local newspaper, you may
find that the sunrise is defined as being some minutes earlier, when the
upper edge of the sun reaches the horizon. In addition, the refraction (bending
of the light) in the atmosphere means that you can actually see the sun
before it reaches the horizon. The sunrise is in local time, or daylight
saving time, if the Daylight saving time box is checked.
The solar noon is when the sun reaches it highest point in the sky, i.e.
the solar altitude is at its maximum. Noon is in local time, or daylight
saving time, if the Daylight saving time box is checked.
In this programme sunset time is defined as the moment a straight line to
the centre of the sun passes the horizon in the downwards direction on the
date you have entered in your data. In your local newspaper, you may find
that the sunset is defined as being some minutes later, when the upper edge
of the sun reaches the horizon. In addition, the refraction (bending of
the light) in the atmosphere means that you can actually see the sun after
it goes below the horizon. The sunset is in local time, or daylight saving
time, if the Daylight saving time box is checked.
The declination is the angle between the earth's equatorial plane, and the
earth-sun line. As the earth rotates, it spins around its
axis which points to the North Star. This axis is inclined 23.45° relative
to the plane in which it orbits the sun. The angle between the equatorial
plane and the earth-sun line thus varies between +/-23.45° during the
year, being approximately zero on the 21/3 and 23/9 (Equinox), and reaching
its extreme values on 21/6 and 21/12 (Solstice). (Its precise value varies
a bit from year to year since a year is 365.25 days long).
This is the number of minutes and seconds it takes for the solar disc to
move the 0.531° between the bottom and the top of the sun at sunrise
or sunset. At the equator the sunrise and sunset last little more than two
minutes. As you move towards the polar regions, the duration increases significantly,
particularly in winter, as you may verify by altering the latitude.
The solar azimuth is the angle in the horizontal plane between the South
and the sun at the moment in time you have entered in your data. The angle
is positive before noon, negative after noon (regardless of hemisphere).
The solar altitude is the angle between the horizontal plane and the sun.
form the Sun (Sun Vector)
If you are standing in the centre of the turbine with your back towards
the South, and you move x units of length to the right (East), y ahead (North),
and z up (or rather -z down), then a straight line from your new position
to the centre of the turbine will be pointing directly to the sun. The values
for x, y, and z are given in the three boxes.