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

**Disclaimer** aerospace wind • 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 =½AV3 • 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. R R Kinetic Energy = Work = ½mV2

**The Importance of Windspeed3** • 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 Kinetic Energy = Work = ½mV2 Power = Work / t = Kinetic Energy / t = ½mV2 / t = ½(ρAd)V2/t Redistribute: = ½ρAV2(d/t) = ½ρAV3 d V Power = ½ρAV3 A

**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 • = 1.6 kg/m3 • Blade length = 50 cm → area = 0.785 m2 Power = ½ρAV3 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** Power of the wind (watts) = ½ ρ⋅A⋅V3 Wind turbine parameters: Sweep area = 4 m2 Wind speed = 5 m/sec Power output = 90 watts 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 Horizontal Axis High power output Large foot • Smaller footprint • Urban use • Subject to low windspeeds Darrieus-style

**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** • Angle of attack (pitch) needs to be 10-15° to get a high enough lift-to-drag ratio (> 10) Lift 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

**noiseNoiseNOISE!!!** • 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