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**Wind Energy: The Myths and the Math**

SWC 2014, Stevens Point- June 18, 2014 Dr. David J. Laino Principal Engineer Endurance Wind Power ©2014 David Laino (used by permission)

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**Myths “Low wind speed design” “No cut-out wind speed”**

“Revolutionary Advancement” “Beats Betz” “Funnels the wind” “More blades is better” “No blades is best” ©2014 David Laino

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**Outline EQUATIONS AHEAD Wind energy Wind Turbine Design Turbine Types**

What is it? How do we extract it? Low and high wind myths Short tower myth Wind Turbine Design Betz Limit Efficiency myths Turbine Types Revolutionary technology myths Rotor solidity myths Areas for Innovation EQUATIONS AHEAD ©2014 David Laino

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**“Science Schmience. It spins!”**

Wind is an ethereal entity, that can neither be smelled nor seen. In this way it is not unlike the ch’i, prana, or the Jedi Force. It is a mystery that we know is there but cannot fully define. Hence, we do not truly understand wind, so harnessing its mysterious power is fertile ground for discovery and experiment. No experience required. “All you need in this life is ignorance and confidence; then success is sure. ” ― Mark Twain ©2014 David Laino

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**Math: Energy in the wind**

Wind is movement of an air mass Moving mass has kinetic energy Newtonian Physics: Ek = ½ mv2 Mass of air = density (r) x Volume Volume = Area (A) x Velocity (v) x Time (t) Kinetic Energy of the Wind: Ewind = ½ r v3 A t A t v ©2014 David Laino

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**The Power in the Wind Power = Energy / time ∴ Ewind = ½ r v3 At**

Pwind v3 Pwind = ½ r v3 A 26% increase in wind speed = 2x Power 2x wind speed = 8x Power ©2014 David Laino

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**Myth: The Power in Low Wind**

MATH: (tiny wind speed)3 = tiny number Real world: Typical cut-in: 4 m/s = 39 W/m2 Claim: Low wind cut-in: 2 m/s = 4.9 W/m2 Reality: Not enough power to overcome real-world inefficiencies ©2014 David Laino

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**Myth: The High Wind Speed Turbine**

Claim: No need to shut down, it operates in hurricane winds! Check: Time at any given wind speed is defined by a distribution Typical cut-out = 25 m/s ©2014 David Laino

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**Math: The High Wind Speed Turbine**

Energy = Power x time Lots of Power! X Hmmm… Reality: No Time = No Energy Wind energy exposure gain = % ©2014 David Laino

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**Lesson: What a wind turbine does**

Convert the kinetic energy of the moving air into electrical energy Input: Wind Less Wind Wind turbine slows the wind as it passes through, reducing the kinetic energy, converting it to mechanical energy. Output: Electricity ©2014 David Laino

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**MYTH: No need for tall towers**

FACT: Obstructions block the wind FACT: Friction with the ground slows the wind FACT: More height = more wind. REALITY: All wind turbines require tall towers to be effective. No, you are not special Wind Shear ©2014 David Laino

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**MYTH: Betz Limit Applies ONLY to Propeller Turbines**

NO Um… ©2014 David Laino

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**mass flow rate through A**

MATH: Betz Limit Proof A vin vout Pwind = ½ r v3 A Pout = ½ {½ r A (vin + vout)/2} (vin 2 - vout 2) mass flow rate through A drop in speed squared Pout Cp = Pout/Pavail = ½ [1-(vout/vin)2] [1 + vout/vin] Cp-max = @ vout/vin = 0.33 Note: Purely mathematical No assumption on turbine type Applies to ANY wind energy machine ©2014 David Laino

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**MYTH: “Breakthrough: 3x – 50x Energy Output!!!”**

CP = Pcaptured / Pwind Power Coefficient Turbine efficiency NO turbine can exceed the Betz Limit Modern designs perform admirably IEC Tested SWT Peak CP 7.42 m2 VAWT 0.22 31.9 m2 HAWT 0.30 290 m2 HAWT 0.42 23.8 m2 HAWT 0.38 23.7 m2 HAWT 0.36 No room for “breakthroughs” ©2014 David Laino

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**MYTH: Ducted Turbines are Special**

FACT: “Swept Area” includes the duct Venturi effect is real Velocity increases in a nozzle Works well for constrained flow A ©2014 David Laino

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**Reality: Wind is Lazy The math looks promising But …**

Pwind v3 But … Wind turbine’s job is to slow the wind, and Wind is NOT constrained inside a hose Wind takes the path of least resistance ©2014 David Laino

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**Myth: More Blades = More Energy**

Myth: Propeller turbines let most of the wind pass between the blades Reality: Space between spinning blades is small. Fewer blades is better High-speed propeller strikes the proper balance between slowing the wind (its job) and letting it pass (so it doesn’t stop) Blade track Blade 1 track wind speed Blade 2 track Blade rotational speed Blade 3 track ©2014 David Laino

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**If High Solidity is Better, May I suggest…**

©2014 David Laino

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©2014 David Laino

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**MYTH: Revolutionary Technology**

New Boat Propeller Slow, quiet operation Fish-friendly Pushes more water Revolutionary design New Wind Turbine Slow, quiet operation Bird-friendly Catches more wind Revolutionary design 9th century Persian Panemone ©2014 David Laino

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**Factors in Wind Turbine Effectiveness**

Four factors affect wind energy capture potential: E = t ½ r V3 CP A dt Air density Wind speed Overall turbine efficiency Swept area ©2014 David Laino

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**Where else will advances come from?**

Economics: cost of energy Ease of installation t = $ Materials >m = >$ Reliability = $ Architecture Mo’ parts = mo’ $ ©2014 David Laino

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