Making a Comparison of the
VAWT and the HAWT
Document 1 of 2
There is a significant difference in the wind energy collection abilities between a conventional propeller bladed (horizontally axis mounted) compared to vertical mounted Savonius shaped rotor.
The vertical height the Savonius rotor for out performs the propeller type because of the geometry difference.
A propeller type with 50ft blades has a rotation covering 100ft, and has a swept area of 31,400.
A 100ft Savonius with a diameter of only 33.3ft has a swept area of 87,220!
That is correct the Savonius rotor has 2.78 times more power and only 1/3 the width of the propeller type for the same height.
A 71.5ft high by 24ft wide Savonius rotor will produce the same amount of power that a propeller type will.
As you double the vertical height of a wind rotor the swept area increases:
The bladed propeller type swept area increases by 4 times
The Savonius swept area increases by 8 times and remains 1/3 the width by comparison.
The Savonius can increase efficiency by an additional 40% by adding wind foil technology.
According to standard formula such as found at the following web site: web :http://www.energy.iastate.edu/Renewable/wind/wem/windpower.htm
Here is the formula w = 1/2 r A v3w is power
r is air density
A is the rotor area
v is the wind speed
I took the example from the Danish Wind Industry site of a 48-meter blade producing 1,000 kw.
In applying this formula to a 48 meter blade, at 35% co-efficiency, with a swept area of 150.79 m/sq. (48 X 3.1416) to produce 1,000 watts, the wind speed would need to be 34 KPH
This formula looks like this
| Blade length m | 48 |
| r | A | v |
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| density | swept | KPH | Max possible | Co-efficient 35% |
| Swept Area | 150.7968 | 0.5 | 1.112 | 150.7968 | 34 | 2,851 | 998 |
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Using the same formula applied to the VAWT of 48 meters,
it looks like this:
Height m | 48 | 0.50 | r | A | v |
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Width m | 16.0 |
| density | swept | KPH | Max. Possible | Co-efficient 35% |
Area | 768.00 | 0.5 | 1.112 | 768.00 | 34 | 14,518 | 5,081 |
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| Enhancers 40% | 47.6 | 20,326 | 7,114 |
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In applying this formula to a 48 meter VAWT blade, at 35% co-efficiency, with a swept area of 768 m sq.
(48 X 16), wind speed of 34 KPH, the watts produced climbs to 5,081 kilowatts, adding enhancers to speed up the wind a conservative 40%, increases the output to 7,114 kilowatts.
This works out to 5 times the output of the HAWT.
With enhancers, it is 7 times more.
WAWT Vertical Access Wind Tower
HAWT Horizontal Access Wind Tower
Making a Comparison of the
VAWT and the HAWT
Document 2 of 2
The principals that apply to calculating the power taken from the wind are quite simple and easy to understand, and have been accepted by researches and developers for centuries. For example, it has been accepted that doubling the size of a rotor blade (propeller type) will increase the power output four times, and when you double the speed of the wind, the power increases eight times.
Why does doubling the rotor blade increase the power four times?
Simply because the swept area has increased four times.
As an example this is a quote from http://otherpower.com/otherpower_wind_tips.html
There is really only one important measure of windmill size...the swept area.That's how many square feet (or meters, if you are into that sort of thing) of area the windmill's blades cover during a rotation. The formula for swept area is Pi r^2, where Pi is 3.1415 and r is the radius of your propeller. The available power from the wind increases dramatically with the swept area...but so do the stresses on your blades, tower, bearings, tail. More stress means stronger engineering and materials are required, and a much larger, more complicated and expensive project.
The formula for swept area is Pi r^2, where Pi is 3.1415 and r is the radius of your propeller.
To show how the principal of increasing four times the swept area when you double the size of the blade may be seen in the chart below.
The first column shows the length of the blade, it is the same as the radius or the second column, because it is the distance between the center of the circle and the outside of the circle. The third column is the calculation shown above (Pi R2). That means the radius multiplied by it’s self then multiplied by Pi.
Using a three-foot blade as indicated on the top row, the calculation would look like this.
((3 X 3) X 3.141 = 28.274) (Rounded off in the chart to 28.3)
Doubling the length of the blade length as indicated on the second row, the calculation would look like this
((6 x 6) X 3.1416 = 113.097) (Rounded off in the chart to 113.9)
Notice how the Swept area of the 6-foot blade is four times the swept area of the three-foot blade. So four times as much energy from the wind is expected from the six-foot blade as the three-foot blade.
Notice also from the above quote that “how many square feet (or meters, if you are into that sort of thing) of area the windmill's blades cover during a rotation”
The same principals that apply to the horizontal blades also apply to the vertical blade. With just a slight variation the horizontal blades spin on a horizontal axis with a blade that pivots into the wind.
The vertical blade spins on a vertical axis always facing the wind, so the area of the blade or the swept area is calculated slightly different.
The horizontal blade is thought of a spinning within a circle where the vertical blade must be thought of as spinning within a cylinder.
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Here is the formula as stated from Wikipedia, the online encyclopedia http://en.wikipedia.org/wiki/Cylinder_(geometry) also see: http://www.mathguide.com/lessons/Volume.html
A right circular cylinder A cylinder is one of the most basic curvilinear geometric shapes: the surface formed by the points at a fixed distance from a given straight line, The axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity. In common usage, a cylinder is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by 
• the area of the top +
• the area of the bottom +
• the area of the side .
And its surface area is:
Notice because of the geometric differences in the blades there is a difference in the swept area as the length of the horizontal blade (propeller type), and the height of the vertical blade doubles. Remember that the vertical blade revolves on an axis within a circular area. Notice too when the height of the vertical blade doubles the swept area increases by a factor of eight. That is twice as much as the swept area increase of the vertical blade (propeller type).
To Make More Comparisons.
To go up to the same height as the vertical blade, the horizontal blade would only need to be half the size. So we compare the three-foot long blade of the horizontal (propeller type), to the six foot height of the vertical. Notice the swept area of the vertical blade is 28.3 feet2, where the swept area of the horizontal is 18.8 feet2. They are both covering an area six feet high, however the horizontal swept area is considerable more than the vertical. Now compare the same two blades as they double in size. The swept area of the vertical blade is now 113.9 ft 2. Where the swept area of the horizontal blade is now 150.7 ft.2. They are both now 12 ft. high, however the swept area of the vertical blade now is greater. In order to put that in perspective let us compare the swept area of a 50-foot long horizontal blade with a 100-foot high vertical blade. They would both be 100 feet high. For the horizontal 50 ft blade (propeller type), (50 X 50) X 3.1416 = 7,8542 ft For the vertical 100 ft by 33.3 ft, (½ of 33.3 ft to get the radius) = 16.65 (16.65 X 16.65) X 3.1416 X 100 = 87,0922 ft.
Going back to the statements made above by http://otherpower.com/otherpower_wind_tips.html
“There is really only one important measure of windmill size...the swept area. That's how many square feet (or meters, if you are into that sort of thing) of area the windmill's blades cover during a rotation.”
We would conclude, as we double the size (height) of both the vertical and horizontal blades, the swept area on the vertical blade increases twice as much as the swept area of the horizontal blades. So if the statement made by otherpower.com as well as endless others, is true, then increasing the swept area means increasing the power output proportionately.
We conclude then that there is a great advantage for the vertical tower over the horizontal tower when height restrictions are important factors.
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Problems With The Blade Design 01