The Answer is Blowing in the
Wind…
The Power of Wind
Disclaimer
aerospace
• I am not a wind expert!!
Wind turbine blade on I-29 north of Sioux Falls, 10 Oct 2008
What is a Wind Turbine
• Remember your bicycle dynamo?
A turbine uses wind to
turn shaft connected to
a gearbox, followed by
a generator to produce
electricity
How does a turbine work?
Limits to 100 % Efficiency
• Power in the wind
• Betz limit (air can not be slowed to zero)
• 59.7 % is maximum efficiency
• Low speed losses - wake rotation
• Drag losses – aerodynamics and blade
geometry
• Generator and drive train inefficiencies
The Betz limit
• Albert Betz, a German physicist, concluded that a wind
turbine can convert no more than 59.3% of the kinetic energy
of the wind into mechanical energy turning a rotor (1919)
• For a wind turbine to be 100% efficient it would need to stop
100% of the wind
– This would be a solid, flat disk and have no kinetic energy
vs.
Wind Power…Power of the Wind
• Power in the wind =½AV3
• Subject to:
– Effect of air density, 
– Effect of sweep area, A
– Effect of wind speed, V
– Swept Area, A = πR2
• Area of the circle swept by the rotor.
Kinetic Energy = Work = ½mV2
R
R
The Importance of
• Wind speed is the most
•
•
•
important factor in
determining power
Power is a cubic function of
wind speed: V X V X V
20% increase in wind speed
means 73% more power
Doubling wind speed means
8 times more power
d
V
3
Windspeed
Kinetic Energy = Work = ½mV2
Power = Work / t
= Kinetic Energy / t
= ½mV2 / t
= ½(ρAd)V2/t
Redistribute:
= ½ρAV2(d/t)
= ½ρAV3
Power = ½ρAV3
Power of the wind turbine
• Power = ½ρAV3, but power of the turbine:
• Powerturbine= Cp½ρAV3
– Cp = Power coefficient
– Cp is the percentage of potential power converted
to actual power
• Limited by several factors
• A 1MW turbine with a 30% Cp produces
~2,600 MWh that can power 320 homes
An Working Example
• Wind blows at 7 MPH = 3 m/s
Power
=
•  = 1.6 kg/m3
• Blade length = 50 cm → area = 0.785 m2
( )
½ρAV3
3
3
2
1
Power = 2 (1.6 kg /m )(0.785 m )(3m /s)
Newton
3
2
3
3
1
= 2 (1.6 kg /m )(0.785 m )( 27 m /s )
( )
= 16.95kg m /s = 16.95( kg m /s
2
3
= 16.95(N - m )/s = 16.95 Watts
2
)( m /s)
How good does it get?
• After engineering requirements, the real world limit is
well below the Betz Limit with values of 0.35-0.45
• After inefficiencies in the generator, bearings, power
transmission, etc. only 10-30% of the power of the wind
is ever actually converted into usable electricity.
An efficiency calculation
Power of the wind (watts) = ½ ρ⋅A⋅V3
æ power out ö
% efficiency, h = ç
÷ ´100
è power in ø
Wind turbine parameters:
Sweep area = 4 m2
Wind speed = 5 m/sec
Power output = 90 watts
æ
ö
90
watts
÷
% efficiency, h = ç
3 ´100
3
2
ç 0.597 ´ 1 ´ 1.6 kg/m ´ 4m ´ (5 m/s) ÷
è
ø
2
æ 90 wattsout ö
= ç
÷ ´ 100
è 238.8 watts in ø
% efficiency = (0.376) ´100 = 37.6 %
Factor in Betz limit
Actual efficiency = 22.5 %
The Beaufort Scale
• Gauging wind speed
Wind Speed Distribution
• Average speed does not denote maximum
• Short bursts power carry V3 more power
Weibull distribution
http://www.ceere.org/rerl/about_wind/RERL_Fact_Sheet_1_Wind_Technology.pdf
Modern Windmill Styles
Vertical Axis
• Smaller footprint
• Urban use
• Subject to low windspeeds
Darrieus-style
Horizontal Axis
• High power output
• Large foot
Wind….it’s a Drag
• Goal: Maximize lift-to-drag ratio
Relies on wind force only
Uses aerodynamics of lift
http://science.howstuffworks.com/wind-power3.htm
Blade Aerodynamics
Lift
• Angle of attack (pitch) needs to be 10-15° to
get a high enough lift-to-drag ratio (> 10)
Drag
nasa.gov
Blade Design 101
• A balancing act to keep drag, wind resistance, tip
vortices, etc. to a minimum while simultaneously
putting enough blade in the wind to capture it’s
kinetic energy.
• Good blade design has:
– Smooth surfaces
– Tapered edges
– Sharp tail edge
– Low thickness-to-length ration
Blade Design 101
• A balancing act to keep drag, wind resistance, tip vortices,
etc. to a minimum while simultaneously putting enough
blade in the wind to capture it’s kinetic energy.
Low angle of attack
Medium angle of attack (10-15°)
High angle of attack (> 20°)
Solidity, Speed, and Torque
Low solidity (0.10) = low speed, high torque
Solidity = 3a/A
R
a = total area of blades
A = sweep area of blades
High solidity (>0.80) = high speed, low torque
How high does the Windmill need to be?
• Tower height of 30 feet wind
power increased by 0 %
• Tower height of 60 feet wind
power increased by 41%
• Tower height of 90 feet wind
power increased by 75%
• Tower height of 120 feet wind
power increased by 100 %
• Tower height of 150 feet wind
power increased by 124%
U.S. DOE
Those blades look slow?!?
• Turbines usually operate at 30 – 60 RPMs
• Standard US electricity functions on 60 Hz AC power
– This amounts to a sinusoidal curve flipping from +1 to -1 60
times per second
– With a direct connection from blades to generator, the blades
would have to spin at 1200-1800 RPMs (20-30 rev per second)
– This is roughly 2x the speed of sound
• Gearboxes are the key!
– Gear ratios can increase hub
speed while keeping the blades
turning at a moderate pace
– Ratios are typically 1:50
– Blade rotations ~30 RPM
Tip Speed Ratio, λ
= tip speed/wind speed
• Tip speed = 2πr/t (distance/time)
• Tip speed ratio is key to good blade design
– If blades are too slow, a lot of wind is “missed”
– If blades are too fast, the turbine acts like a solid disk
• The perfect tip speed is determined to be:
4π/n, n is the number of blades
• For 3 blades, the optimal TSR is 4.18
– Knowing the average windspeed for an site, the best TSR
can be calculated
– Adjustments in RPM can be made (speed) by
increasing/decreasing load on the turbine in design
Blade Size and Sound
http://www.awea.org
http://www.omafra.gov.on.ca
Sound decreases by -6 dB
on doubling distance
noise
Noise NOISE!!!
• Large wind turbines have a maximum sound
level of 60-70 dB
• Background noise of an office environment
• Most turbine noise
is imperceptible at
distances > 120m
• Noise is a human
perception
U.S. Wind Energy Map
Current Wind Capacity
http://www.awea.org/pubs/factsheets/Market_Update_Factsheet.pdf
Wind Capacity by State
Texas
Iowa
California
Minnesota
Washington
Oregon
New York
Colorado
Kansas
Illinois
Oklahoma
Wyoming
North Dakota
Indiana
New Mexico
Wisconsin
Pennsylvania
West Virginia
Montana
South Dakota
Missouri
Nebraska
Idaho
Michigan
Maine
Hawaii
Tennessee
New Hampshire
Utah
New Jersey
Ohio
Vermont
Massachusetts
Alaska
Rhode Island
Planned
State
Capacity
0
1000
2000
3000
4000
5000
Capacity (MW)
Total US capacity: >20,000 mW (as of 9/2008)
6000
7000
8000
9000
Data compiled from NWEA
Sites with More Information
• KidWind Project:
www.kidwind.org
• Danish Wind Industry:
http://www.windpower.org/en/tour.htm
• American Wind Energy Association:
http://www.awea.org/
• The U.S. Department of Energy:
http://www1.eere.energy.gov/windandhydro/
• Wind turbine noise and perception:
http://www.windpoweringamerica.gov/pdfs/workshops/
mwwg_turbine_noise.pdf