# The Answer is Blowing in the Wind… The Power of Wind.

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The Answer is Blowing in the Wind… The Power of Wind

Disclaimer I am not a wind expert!! Wind turbine blade on I-29 north of Sioux Falls, 10 Oct 2008 aerospace wind

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  AV 3 Subject to: – Effect of air density,  – Effect of sweep area, A – Effect of wind speed, V – Swept Area, A = πR 2 Area of the circle swept by the rotor. R R Kinetic Energy = Work = ½mV 2

The Importance of Windspeed 3 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 Power = Work / t = Kinetic Energy / t = ½mV 2 / t = ½(ρAd)V 2 /t Redistribute: = ½ρAV 2 (d/t) = ½ρAV 3 Power = ½ρAV 3 Kinetic Energy = Work = ½mV 2 d A V

Power of the wind turbine Power = ½ρAV 3, but power of the turbine: Power turbine = C p ½ρAV 3 – C p = Power coefficient – C p is the percentage of potential power converted to actual power Limited by several factors A 1MW turbine with a 30% C p produces ~2,600 MWh that can power 320 homes

An Working Example Wind blows at 7 MPH = 3 m/s  = 1.6 kg/m 3 Blade length = 50 cm → area = 0.785 m 2 Power = ½ρAV 3 Newton

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 Wind turbine parameters: Sweep area = 4 m 2 Wind speed = 5 m/sec Power output = 90 watts Power of the wind (watts) = ½ ρ ⋅ A ⋅ V 3 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 V 3 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 Horizontal Axis High power output Large foot Darrieus-style

Wind….it’s a Drag Goal: Maximize lift-to-drag ratio http://science.howstuffworks.com/wind-power3.htm Relies on wind force only Uses aerodynamics of lift

Blade Aerodynamics Angle of attack (pitch) needs to be 10-15° to get a high enough lift-to-drag ratio (> 10) Drag Lift 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 High solidity (>0.80) = high speed, low torque Solidity = 3a/A R a = total area of blades A = sweep area of blades

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 = 2 π r/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: 4 π /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.omafra.gov.on.ca http://www.awea.org 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 Total US capacity: >20,000 mW (as of 9/2008)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