1. 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)

2. 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

3. 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

4. “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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. MYTH: Betz Limit Applies ONLY to Propeller TurbinesNO
Um…
©2014 David Laino

13. 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

14. 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

15. 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

16. 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

17. 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

18. If High Solidity is Better, May I suggest…
©2014 David Laino

19. ©2014 David Laino

20. 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

21. 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

22. Where else will advances come from?
Economics: cost of energy
Ease of installation
t = $
Materials
>m = >$
Reliability
 = $
Architecture
Mo’ parts = mo’ $
©2014 David Laino