UCSD Physics 12

Renewable Energy IRenewable Energy I

HydroelectricityHydroelectricity

Wind EnergyWind Energy

Spring 2010 2

UCSD Physics 12

Renewable ResourcesRenewable Resources

bull Renewable means anything that wonrsquot be depleted Renewable means anything that wonrsquot be depleted by using itby using itndash sunlight (the sun will rise again tomorrow)

ndash biomass (grows again)

ndash hydrological cycle (will rain again)

ndash wind (sunlight on earth makes more)

ndash ocean currents (driven by sun)

ndash tidal motion (moon keeps on producing it)

ndash geothermal (heat sources inside earth not used up fast)

Spring 2010 3

UCSD Physics 12

Renewable Energy ConsumptionRenewable Energy Consumption

Energy Energy SourceSource

QBtu QBtu (1994)(1994)

Percent Percent (1994)(1994)

QBtu QBtu (2003)(2003)

Percent Percent (2003)(2003)

HydroelectricHydroelectric 30373037 343343 27792779 283283

GeothermalGeothermal 03570357 040040 03140314 032032

BiomassBiomass 28522852 322322 28842884 294294

Solar EnergySolar Energy 00690069 00770077 00630063 006006

WindWind 00360036 00400040 01080108 011011

TotalTotal 63516351 718718 615615 6363

much room for improvementgrowth but going backwards

Slide copied from Lecture 9

Spring 2010 4

UCSD Physics 12

Another look at available energy flowAnother look at available energy flow

bull The flow of radiation (solar and thermal) was The flow of radiation (solar and thermal) was covered in Lecture 9covered in Lecture 9ndash earth is in an energy balance energy in = energy out

ndash 30 reflected 70 thermally re-radiated

bull Some of the incident energy is absorbed but what Some of the incident energy is absorbed but what exactly does this doexactly does this dondash much goes into heating the airland

ndash much goes into driving weather (rain wind)

ndash some goes into ocean currents

ndash some goes into photosynthesis

Spring 2010 5

UCSD Physics 12

The Renewable BudgetThe Renewable Budget

Spring 2010 6

UCSD Physics 12

Outstanding Points from Fig 51Outstanding Points from Fig 51

bull Incident radiation is 174Incident radiation is 17410101515 W Wndash this is 1370 Wm2 times area facing sun (R2)

bull 30 directly reflected back to space30 directly reflected back to spacendash off clouds air land

bull 47 goes into heating air land water47 goes into heating air land waterbull 23 goes into evaporating water precipitation 23 goes into evaporating water precipitation

etc (part of weather)etc (part of weather)bull Adds to 100 so wersquore doneAdds to 100 so wersquore done

ndash but wait therersquos morehellip

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 2

UCSD Physics 12

Renewable ResourcesRenewable Resources

bull Renewable means anything that wonrsquot be depleted Renewable means anything that wonrsquot be depleted by using itby using itndash sunlight (the sun will rise again tomorrow)

ndash biomass (grows again)

ndash hydrological cycle (will rain again)

ndash wind (sunlight on earth makes more)

ndash ocean currents (driven by sun)

ndash tidal motion (moon keeps on producing it)

ndash geothermal (heat sources inside earth not used up fast)

Spring 2010 3

UCSD Physics 12

Renewable Energy ConsumptionRenewable Energy Consumption

Energy Energy SourceSource

QBtu QBtu (1994)(1994)

Percent Percent (1994)(1994)

QBtu QBtu (2003)(2003)

Percent Percent (2003)(2003)

HydroelectricHydroelectric 30373037 343343 27792779 283283

GeothermalGeothermal 03570357 040040 03140314 032032

BiomassBiomass 28522852 322322 28842884 294294

Solar EnergySolar Energy 00690069 00770077 00630063 006006

WindWind 00360036 00400040 01080108 011011

TotalTotal 63516351 718718 615615 6363

much room for improvementgrowth but going backwards

Slide copied from Lecture 9

Spring 2010 4

UCSD Physics 12

Another look at available energy flowAnother look at available energy flow

bull The flow of radiation (solar and thermal) was The flow of radiation (solar and thermal) was covered in Lecture 9covered in Lecture 9ndash earth is in an energy balance energy in = energy out

ndash 30 reflected 70 thermally re-radiated

bull Some of the incident energy is absorbed but what Some of the incident energy is absorbed but what exactly does this doexactly does this dondash much goes into heating the airland

ndash much goes into driving weather (rain wind)

ndash some goes into ocean currents

ndash some goes into photosynthesis

Spring 2010 5

UCSD Physics 12

The Renewable BudgetThe Renewable Budget

Spring 2010 6

UCSD Physics 12

Outstanding Points from Fig 51Outstanding Points from Fig 51

bull Incident radiation is 174Incident radiation is 17410101515 W Wndash this is 1370 Wm2 times area facing sun (R2)

bull 30 directly reflected back to space30 directly reflected back to spacendash off clouds air land

bull 47 goes into heating air land water47 goes into heating air land waterbull 23 goes into evaporating water precipitation 23 goes into evaporating water precipitation

etc (part of weather)etc (part of weather)bull Adds to 100 so wersquore doneAdds to 100 so wersquore done

ndash but wait therersquos morehellip

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 3

UCSD Physics 12

Renewable Energy ConsumptionRenewable Energy Consumption

Energy Energy SourceSource

QBtu QBtu (1994)(1994)

Percent Percent (1994)(1994)

QBtu QBtu (2003)(2003)

Percent Percent (2003)(2003)

HydroelectricHydroelectric 30373037 343343 27792779 283283

GeothermalGeothermal 03570357 040040 03140314 032032

BiomassBiomass 28522852 322322 28842884 294294

Solar EnergySolar Energy 00690069 00770077 00630063 006006

WindWind 00360036 00400040 01080108 011011

TotalTotal 63516351 718718 615615 6363

much room for improvementgrowth but going backwards

Slide copied from Lecture 9

Spring 2010 4

UCSD Physics 12

Another look at available energy flowAnother look at available energy flow

bull The flow of radiation (solar and thermal) was The flow of radiation (solar and thermal) was covered in Lecture 9covered in Lecture 9ndash earth is in an energy balance energy in = energy out

ndash 30 reflected 70 thermally re-radiated

bull Some of the incident energy is absorbed but what Some of the incident energy is absorbed but what exactly does this doexactly does this dondash much goes into heating the airland

ndash much goes into driving weather (rain wind)

ndash some goes into ocean currents

ndash some goes into photosynthesis

Spring 2010 5

UCSD Physics 12

The Renewable BudgetThe Renewable Budget

Spring 2010 6

UCSD Physics 12

Outstanding Points from Fig 51Outstanding Points from Fig 51

bull Incident radiation is 174Incident radiation is 17410101515 W Wndash this is 1370 Wm2 times area facing sun (R2)

bull 30 directly reflected back to space30 directly reflected back to spacendash off clouds air land

bull 47 goes into heating air land water47 goes into heating air land waterbull 23 goes into evaporating water precipitation 23 goes into evaporating water precipitation

etc (part of weather)etc (part of weather)bull Adds to 100 so wersquore doneAdds to 100 so wersquore done

ndash but wait therersquos morehellip

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 4

UCSD Physics 12

Another look at available energy flowAnother look at available energy flow

bull The flow of radiation (solar and thermal) was The flow of radiation (solar and thermal) was covered in Lecture 9covered in Lecture 9ndash earth is in an energy balance energy in = energy out

ndash 30 reflected 70 thermally re-radiated

bull Some of the incident energy is absorbed but what Some of the incident energy is absorbed but what exactly does this doexactly does this dondash much goes into heating the airland

ndash much goes into driving weather (rain wind)

ndash some goes into ocean currents

ndash some goes into photosynthesis

Spring 2010 5

UCSD Physics 12

The Renewable BudgetThe Renewable Budget

Spring 2010 6

UCSD Physics 12

Outstanding Points from Fig 51Outstanding Points from Fig 51

bull Incident radiation is 174Incident radiation is 17410101515 W Wndash this is 1370 Wm2 times area facing sun (R2)

bull 30 directly reflected back to space30 directly reflected back to spacendash off clouds air land

bull 47 goes into heating air land water47 goes into heating air land waterbull 23 goes into evaporating water precipitation 23 goes into evaporating water precipitation

etc (part of weather)etc (part of weather)bull Adds to 100 so wersquore doneAdds to 100 so wersquore done

ndash but wait therersquos morehellip

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 5

UCSD Physics 12

The Renewable BudgetThe Renewable Budget

Spring 2010 6

UCSD Physics 12

Outstanding Points from Fig 51Outstanding Points from Fig 51

bull Incident radiation is 174Incident radiation is 17410101515 W Wndash this is 1370 Wm2 times area facing sun (R2)

bull 30 directly reflected back to space30 directly reflected back to spacendash off clouds air land

bull 47 goes into heating air land water47 goes into heating air land waterbull 23 goes into evaporating water precipitation 23 goes into evaporating water precipitation

etc (part of weather)etc (part of weather)bull Adds to 100 so wersquore doneAdds to 100 so wersquore done

ndash but wait therersquos morehellip

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 6

UCSD Physics 12

Outstanding Points from Fig 51Outstanding Points from Fig 51

bull Incident radiation is 174Incident radiation is 17410101515 W Wndash this is 1370 Wm2 times area facing sun (R2)

bull 30 directly reflected back to space30 directly reflected back to spacendash off clouds air land

bull 47 goes into heating air land water47 goes into heating air land waterbull 23 goes into evaporating water precipitation 23 goes into evaporating water precipitation

etc (part of weather)etc (part of weather)bull Adds to 100 so wersquore doneAdds to 100 so wersquore done

ndash but wait therersquos morehellip

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 7

UCSD Physics 12

Energy Flow continuedEnergy Flow continued

bull 021 goes into wind waves convection currents021 goes into wind waves convection currentsndash note this is 100 times less than driving the water cyclendash but this is the ldquootherrdquo aspect of weather

bull 0023 is stored as chemical energy in plants via 0023 is stored as chemical energy in plants via photosynthesisphotosynthesisndash total is 401012 W half in ocean (plankton)ndash humans are 6 billion times 100 W = 061012 Wndash this is 15 of bio-energy 000034 of incident power

bull All of thisAll of this (bio-activity wind weather etc) ends (bio-activity wind weather etc) ends up creating up creating heatheat and re-radiating to space and re-radiating to spacendash except some small amount of storage in fossil fuels

Q2

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 8

UCSD Physics 12

The Hydrologic CycleThe Hydrologic Cycle

Lots of energy associated with evaporationboth mgh (4 for 10 km lift) and latent heat (96) of water

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 9

UCSD Physics 12

Energetics of the hydrologic cycleEnergetics of the hydrologic cycle

bull It takes energy to evaporate water 2250 J per It takes energy to evaporate water 2250 J per gramgramndash this is why ldquoswamp coolersrdquo work evaporation pulls

heat out of environment making it feel coolerndash 23 of sunrsquos incident energy goes into evaporation

bull By contrast raising one gram of water to the top By contrast raising one gram of water to the top of the troposphere (10000 m or 33000 ft) takesof the troposphere (10000 m or 33000 ft) takes

mgh = (0001 kg)(10 ms2)(10000 m) = 100 J

bull So gt 96 of the energy associated with forming So gt 96 of the energy associated with forming clouds is the evaporation lt 4 in lifting against clouds is the evaporation lt 4 in lifting against gravitygravity

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 10

UCSD Physics 12

Let it RainLet it Rain

bull When water condenses in clouds it re-releases this ldquolatent When water condenses in clouds it re-releases this ldquolatent heatrdquoheatrdquondash but this is re-radiated and is of no consequence to hydro-power

bull When it rains the gravitational potential energy is When it rains the gravitational potential energy is released mostly as kinetic energy and ultimately heatreleased mostly as kinetic energy and ultimately heat

bull Some Some tinytiny bit of gravitational potential energy remains bit of gravitational potential energy remains IFIF the rain falls on terrain (eg higher than sea level where it the rain falls on terrain (eg higher than sea level where it originated)originated)ndash hydroelectric plants use this tiny left-over energy itrsquos the energy

that drives the flow of streams and rivers

ndash damming up a river concentrates the potential energy in one location for easy exploitation

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 11

UCSD Physics 12

How much of the process do we get to keepHow much of the process do we get to keep

bull According to Figure 51 40According to Figure 51 4010101515 W of solar power goes W of solar power goes into evaporationinto evaporationndash this corresponds to 161010 kg per second of evaporated water

ndash this is 35 mm per day off the ocean surface (replenished by rain)

bull The gravitational potential energy given to water vapor The gravitational potential energy given to water vapor (mostly in clouds) in the atmosphere (per second) is then(mostly in clouds) in the atmosphere (per second) is thenmgh = (161010 kg)(10 ms2)(2000 m) = 321014 J

bull One can calculate that we gain access to only 25 of the One can calculate that we gain access to only 25 of the total amount (and use only 125)total amount (and use only 125)ndash based on the 18 land area of the US and the maximum

potential of 1477 GW as presented in Table 52

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 12

UCSD Physics 12

Power of a hydroelectric damPower of a hydroelectric dam

bull Most impressive is Grand Coulee in Washington Most impressive is Grand Coulee in Washington on Columbia Riveron Columbia Riverndash 350 feet = 107 m of ldquoheadrdquo

ndash gt 6000 m3s flow rate (Pacific Northwest gets rain)

ndash each cubic meter of water (1000 kg) has potential energy mgh = (1000 kg)(10 ms2)(110 m) = 11 MJ

ndash At 6000 m3s get over 6 GW of power

bull Large nuclear plants are usually 1Large nuclear plants are usually 1ndash2 GWndash2 GWbull 11 other dams in US in 1ndash2 GW range11 other dams in US in 1ndash2 GW rangebull 74 GW total hydroelectric capacity presently74 GW total hydroelectric capacity presently

Q2

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 13

UCSD Physics 12

Importance of HydroelectricityImportance of Hydroelectricity

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 14

UCSD Physics 12

Hydroelectric potential by region in GWHydroelectric potential by region in GW

RegionRegion PotentialPotential DevelopedDeveloped UndevelopedUndeveloped Developed Developed

New EnglandNew England 6363 1919 4444 301301

Middle AtlanticMiddle Atlantic 9898 4949 4949 500500

East North CentralEast North Central 2929 1212 1717 413413

West North CentralWest North Central 6262 3131 3131 500500

South AtlanticSouth Atlantic 139139 6767 7272 482482

East South CentralEast South Central 8383 5959 2424 711711

West South CentralWest South Central 7373 2727 4646 369369

MountainMountain 286286 9595 191191 332332

PacificPacific 644644 382382 262262 593593

TotalTotal 14771477 741741 736736 502502

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 15

UCSD Physics 12

Hydroelectricity in the futureHydroelectricity in the future

bull Wersquore almost tapped-outWersquore almost tapped-outndash 50 of potential is developedndash remaining potential in large number of small-scale units

bull Problems with damsProblems with damsndash silt limits lifetime to 50ndash200 years after which dam is

useless and in fact a potential disaster and nagging maintenance site

ndash habitat loss for fish (salmon) etc wrecks otherwise stunning landscapes (Glenn Canyon in UT)

ndash Disasters waiting to happen 1680 deaths in US alone from 1918ndash1958 often upstream from major population centers

Q

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 16

UCSD Physics 12

Sorry try againhellipSorry try againhellip

bull So hydroelectricity is a nice ldquofreebeerdquo handed to So hydroelectricity is a nice ldquofreebeerdquo handed to us by nature but itrsquos not enough to cover our us by nature but itrsquos not enough to cover our appetite for energyappetite for energy

bull Though very efficient and seemingly Though very efficient and seemingly environmentally friendly dams do have their environmentally friendly dams do have their problemsproblems

bull This isnrsquot the answer to all our energy problems This isnrsquot the answer to all our energy problems though it is likely to maintain a role well into our though it is likely to maintain a role well into our futurefuture

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 17

UCSD Physics 12

Wind EnergyWind Energy

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 18

UCSD Physics 12

The Power of WindThe Power of Wind

bull Wersquove talked about the kinetic energy in wind Wersquove talked about the kinetic energy in wind beforebeforendash a wind traveling at speed v covers v meters every

second (if v is expressed in ms)ndash the kinetic energy hitting a square meter is then the

kinetic energy the mass of air defined by a rectangular tube

ndash tube is one square meter by v meters or v m3

ndash density of air is = 13 kgm3 at sea levelndash mass is v kgndash KE = frac12(v)v2 = frac12v3 (per square meter)

bull 065v3 at sea level

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 19

UCSD Physics 12

Wind Energy proportional to Wind Energy proportional to cubecube of velocity of velocity

bull The book (p 134) says power per square meter is The book (p 134) says power per square meter is 061061vv33 which is a more-or-less identical result which is a more-or-less identical resultndash might account for average density in continental US

(above sea level so air slightly less dense)

bull So if the wind speed doubles the power available So if the wind speed doubles the power available in the wind increases by 2in the wind increases by 233 = 2 = 2222 = 8 times2 = 8 times

bull A wind of 10 ms (22 mph) has a power density of A wind of 10 ms (22 mph) has a power density of 610 Wm610 Wm22

bull A wind of 20 ms (44 mph) has a power density of A wind of 20 ms (44 mph) has a power density of 4880 Wm4880 Wm22

Q

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 20

UCSD Physics 12

Canrsquot get it allCanrsquot get it all

bull A windmill canrsquot extract A windmill canrsquot extract allall of the kinetic energy of the kinetic energy available in the wind because this would mean available in the wind because this would mean stoppingstopping the wind entirely the wind entirely

bull Stopped wind would divert oncoming wind Stopped wind would divert oncoming wind around it and the windmill would stop spinningaround it and the windmill would stop spinning

bull On the other hand if you donrsquot slow the wind On the other hand if you donrsquot slow the wind down much at all you wonrsquot get much energydown much at all you wonrsquot get much energy

bull Theoretical maximumTheoretical maximum performance is 59 of performance is 59 of energy extractedenergy extractedndash corresponds to reducing velocity by 36

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 21

UCSD Physics 12

Practical EfficienciesPractical Efficiencies

bull Modern windmills attain maybe 50Modern windmills attain maybe 50ndash70 of the ndash70 of the theoreticaltheoretical maximum maximumndash 05ndash07 times 059 is 030ndash041 or about 30ndash40

ndash this figure is the mechanical energy extracted from the wind

bull Conversion from mechanical to electrical is 90 Conversion from mechanical to electrical is 90 efficientefficientndash 09 times 030ndash041 is 27ndash37

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 22

UCSD Physics 12

Achievable efficienciesAchievable efficiencies

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 23

UCSD Physics 12

Typical WindmillsTypical Windmills

bull A typical windmill might be 15 m in diameterA typical windmill might be 15 m in diameterndash 176 m2

bull At 10 ms wind 40 efficiency this delivers about 100 At 10 ms wind 40 efficiency this delivers about 100 kW of powerkW of powerndash this would be 800 kW at 20 ms

ndash typical windmills are rated at 50 to 600 kW

bull How much energy per yearHow much energy per yearndash 10 ms 610 Wm2 40 240 Wm2 8760 hours per year

2000 kWh per year per square meter

ndash but wind is intermittent real range from 100ndash500 kWhm2

ndash corresponds to 11ndash57 Wm2 average available power density

bull Note the really high tip speeds bird killersNote the really high tip speeds bird killers

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 24

UCSD Physics 12

Average available wind powerAverage available wind powerrecall that average solar insolation is about 150ndash250 Wm2

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 25

UCSD Physics 12

Comparable to solarComparable to solar

bull These numbers are similar to solar if not a little These numbers are similar to solar if not a little biggerbiggerndash Letrsquos go to wind

bull BUTBUT the ldquoper square meterrdquo is not land area the ldquoper square meterrdquo is not land areamdashitrsquos mdashitrsquos rotor arearotor area

bull Doesnrsquot pay to space windmills too closelymdashone Doesnrsquot pay to space windmills too closelymdashone robs the otherrobs the other

bull Typical arrangements have rotors 10 diameters Typical arrangements have rotors 10 diameters apart in direction of prevailing wind 5 diameters apart in direction of prevailing wind 5 diameters apart in the cross-wind directionapart in the cross-wind directionndash works out to 16 ldquofill factorrdquo

Q

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 26

UCSD Physics 12

Current implementationsCurrent implementations

bull Rapidly developing resourceRapidly developing resourcendash 1400 MW in 1989 up to 6400 MW in 2003ndash but still insignificant total (compare to large dams)ndash cost (at 5ndash7cent per kWh) is competitivendash growing at 25 per yearndash expect to triple over next ten years

bull Current capacity 116 GW (April 2007)Current capacity 116 GW (April 2007)ndash Texas 2768 MW (recently took lead over California)ndash California 2361 MWndash Iowa 936 MWndash Minnesota 895 MWndash Washington 818 MWndash httpwwwaweaorgnewsroomreleasesAnnual_US_Wind_Powe

r_Rankings_041107html

Spring 2010 27

UCSD Physics 12

Flies in the OintmentFlies in the Ointment

bull Find that only 20 of rated capacity is achievedFind that only 20 of rated capacity is achievedndash design for high wind but seldom get it

bull Only 12 of electrical capacity in US is now windOnly 12 of electrical capacity in US is now windndash total electrical capacity in US is 948 GWndash tripling in ten years means 36ndash but achieving only 20 of capacity reduces substantially

bull If fully developed we If fully developed we couldcould generate an average power generate an average power almostalmost equal to our current electrical capacity (764 GW) equal to our current electrical capacity (764 GW)ndash but highly variable resource and problematic if more than 20

comes from the intermittent wind

Q

Spring 2010 28

UCSD Physics 12

AnnouncementsAssignmentsAnnouncementsAssignments

bull Read Chapter 5 sections 1 2 3 5 7Read Chapter 5 sections 1 2 3 5 7bull HW 6 to be posted today (510)HW 6 to be posted today (510)

Spring 2010 28

UCSD Physics 12

AnnouncementsAssignmentsAnnouncementsAssignments

bull Read Chapter 5 sections 1 2 3 5 7Read Chapter 5 sections 1 2 3 5 7bull HW 6 to be posted today (510)HW 6 to be posted today (510)