The Exotic Power Sources
Today I'll wrap up my discussion of power plants
Except for hyper-controversial nuclear, which I'll return to a bit later
I'll first cover the more "exotic" power generation technologies already in use:
- Tidal Barrage
- Tidal Stream
- Wave
- Geothermal
Then move to even more exotic proposed technologies:
- Wind Generators IN the atmosphere
- Solar Cells ABOVE the atmosphere
- Nuclear Fusion
Tidal Power
Tidal power is really just a different form of hydro power
And as discussed in the earlier lecture on hydro and wind powers
Hydro is ultimately about gravitational potential energy:
D Egravity = M g Dh
Which for a continuous steady flow F (volume / second) gave us:
Phydro = 9.8 (kW-seconds / m4) x F x Dh
(kW = kilowatt)
(Nitpicking: salt water can be a few percent more dense than pure water)
However, big difference: For tides and waves, flows are NOT steady at all!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Alternative forms of tidal power generation
The simplest / oldest might have been some variation of this:
Floating boat / buoy tied via rope and pulleys to onshore counter weight
With movement of onshore weight or pulley used to do some sort of work
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But we can get a lot more power via a tidal dam
Ocean:
Dammed inlet or manmade basin:
Power generated when tide coming in
Power generated when tide going out
(a.k.a. "Tidal Barrage")
Big side benefit: Power generation mechanism is moved onshore
Or at least into the dam, which is connected to the shore
This also concentrates / simplifes that mechanism (e.g. into single turbine)
Circumventing severe difficulty of keeping mechanisms working in saltwater
(Just ask Stephen Spielberg!)
How much power out?
With density of water ρ, reservoir area A, surface gravity of g:
Say tide raises sea level h, then lowers it h: net change in height = 2h
So full tidal rise => Gravitational energy of M g 2h. With mass of raised water:
M = density of water x its volume = ρ (2 h Area) (2h enters again!)
Putting in values for water density and surface gravity:
Egravitational = ρ g (2 h Area) 2h = (1000 kg/m3)(9.8 m/s2) 4 Area x h2
= (9800 kg m2/s2 x 1/m4) 4 Area x h2
= 39.2 kiloJoules /m4 x Area x h2
Tidal cycle is ~ 12 hours ~ 43,200 seconds, so cycle averaged power is:
Powertides = 0.91 Watts / m4 x (Area x h2)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But it's actually 6 hours of rising tide + 6 hours falling:
But we can extract power whichever direction tide is pushing water:
Get power when rising tide PUSHES water into reservoir
AND
Get power when falling reservoir PUSHES water back out to sea
So, it turns out that answer above is still about right
But because salt water is a little denser than fresh water, let's round up to:
Powertides ~ 1 Watt / m4 x (Area x h2)
where h = half tide
Of which we could recover a fraction: εgenerator (efficiency of our hydro generator)
Note: Book gets 2X my number = Power out DURING falling tide (with 0 out during rising tide)
But there is also the "pumping trick"
As described in "Sustainable Energy without the Hot Air" by David J.C. MacKay:
Make your dam a bit TALLER than the high tide level, and add some pumps
At HIGH tide, pump extra water UP into reservoir (expending energy!)
At LOW tide that SAME water will fall a LARGER DISTANCE => More energy back!
Tide provided PART of the energy to get
extra water up into reservoir
But YOU then get ALL the energy back
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
With the numbers working out as follows:
Say at (about) high tide, you pump water UP a further height b:
With pump efficiency = εpump and generator efficiency= εgenerator
That requires you to expend an energy:
Eexpended = (1/εpump) M g height =(1/εpump) (ρ A b) g b = ρ g A b2/εpump
But then, at low tide, that
:
Erecovered = εgenerator M g height = εgenerator (ρ A b) g (b + 2h)
Giving ratio of added power out to added power invested
Ratio out / in = (εgeneratorεpump) (b + 2h)/b call εgeneratorεpump = εtotal
If efficiencies were 1, ratio would always be better than 1 => net gain
If efficiencies less than 1, ratio => 1 when b = 2h (εtotal)/(1- εtotal)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Can also pump water OUT near low tide
Putting this ALL together, "Sustainable Energy without the Hot Air" shows:
Net gain for pumping is a "boost factor" of (εtotal)/(1- εtotal)
For εtotal ~ 0.76 (corresponding to pump and generator efficiencies of ~ 87%)
Book generates table (averaged over tidal cycle):
Tidal Half
Amplitude (h)
Optimum
Boost Height (b)
Power
with pumping
Power
without pumping
1 meter
6.5 meter
3.5 W/m2
0.8 W/m2
2 meter
13 meter
14 W/m2
3.3 W/m2
3 meter
20 meter
31 W/m2
7.4 W/m2
4 meter
26 meter
56 W/m2
13 W/m2
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Impressive, however (paralleling conventional hydropower):
We must BUILD those coastal reservoirs
By damming up bays or estuaries. Thereby modifying coasts with ecological value
E.G. water purification and animal rearing value of coastal marshes
And/or: visual / leisure time / vacation residence value
And/or: harbor / industrial value
"Worlds First" tidal power station (1966)
in Rance River estuary,
in Brittany France
62 MW average (240 MW peak)
~ 1/10th of an average U.S. power plant
http://en.wikipedia.org/wiki/Rance_Tidal_Power_Station
Thoughts regarding tidal barrages:
It's worrying to note that while the above Rance tidal barrage claims to be oldest
Rance power output (as cited by most sources) is STILL the largest
Also, misleadingly, many sources cite its peak rather than average power!
Suggesting, in 50 years since, that many have decided against this option
Despite it appearing relatively high power, relatively easy / benign
In addition, regarding the preceding pump enhancement trick:
That calculation assumes ALL the water is pumped up AT high tide
Or out AT low tide (i.e. all the extra water moved in ~ ½ hour)
But optimum "boost heights" were 5-7 times tidal height, making this unlikely
And pumping before or after peak tides => diminished energy gain
Leading to alternative of "tidal stream" power generation
Of which a few exist:
Strangford Loch, N. Ireland: 1.2 MW
~ 1/500th of an average U.S. Power Plant
~ 1 modern wind turbine
HOLD IT! Water is MUCH denser than air
So WHY are water and wind turbines producing COMPARABLE power?
Answer comes from Hydro and Wind Power lecture: Flow Power / Areaintercepted = ½ ρ v3
Water is ~ 1000X more dense than air (~ 1 kg/l vs. 1 g/l)
But tidal currents have ~ 1/10 the speed of winds (few mph vs. few tens of mph)
Water's v3 is thus ~ (1/10)3 = 1/1000 that of wind
Completely wiping out water's density advantage!
http://subseaworldnews.com/2012/01/17/uk-seagen-tidal-turbine-gets-all-clear-from-environmental-studies/
Further, proposals seem hung up on mimicking wind turbine designs:
http://www.bbc.co.uk/news/ukwales-north-west-wales11037069
http://www.darvill.clara.net/alten
erg/tidal.htm
http://www.global-greenhousewarming.com/tidal.html
http://climatekids.nasa.gov/tidalenergy/
http://www.fujitaresearch.com/re
ports/tidalpower.html
Often with minimal serious thought going into such proposals:
http://www.esru.strath.ac.uk/EandE/Web
_sites/10-11/Tidal/tidal.html
Here someone apparently:
Photoshop'ed the image of a vertical axis wind turbine onto an undersea background
The advantage of vertical axis wind turbines is that they can use winds from any direction
But tides flow in one direction (and its opposite), so why use this (flimsier) design?
Especially because the force on a turbine = Flow momentum transferred from fluid / time
= (momentum/volume) (volume/time) = (ρv) (Area v) = A ρ v2
=> (1000X) (1/10X)2 = 10X times force on comparable wind turbine
So corresponding tidal turbine would have to be ten times thicker / stronger!
And here an even dumber idea (from a certain U.S. agency):
http://www.ecofriend.com/ecotech-nasa-s-jpl-develops-a-costeffective-way-to-harness-oceanenergy.html
Instead of producing electricity AT the undersea turbines,
and then delivering it to shore via simple efficient ELECTRICAL CABLES
They propose using water turbines to mechanically pump water,
through BIG LONG PIPES,
all the way to an onshore hydro power station!!
Can you imagine the energy lost to friction & turbulence in those long pipes?
(to say nothing of the difficulty in laying down those long pairs of pipes!)
Instead, a particularly good idea might be to "lay low:"
That is, DON'T build a tall structure resembling ANY sort of wind turbine
Instead, just sink to / cling to the ocean bottom
Removing any surface obstruction to navigation (= target for ship collisions!) AND
Removing the need for VERY hard to construct undersea foundations (=$$$)
I.E. instead of this (foundations added):
http://www.marineturbines.com/3/news/article/37/an
glesey_tidal_energy_plan_moves_forward_
Something that could just be sunk on site:
http://news.bbc.co.uk/2/shared/spl/hi/pop_ups/07/uk_e
nl_1193829329/html/1.stm
Which IS being pursued up in Maine:
Intended for Maine's Passamaquoddy and Cobscook bays:
http://www.pressherald.com/2012/07/21/maine-company-leading-way-as-tidal-energy-comes-of-age_2012-07-22/
Press Herald headline: "Maine company leading way as tidal energy comes of age:"
HOWEVER: 50 kW prototype ( ~ 1/10,000th of an average U.S. Power Plant)
"Much of the industry’s near-term expansion is expected to be in Nova Scotia . . .
(for units) that are community-owned"
These might indeed be very important for more remote / isolated locales
But for a larger impact, I'd suggest:
Use float-into-place / sink / cling-near-to-the-bottom (foundationless) designs
In "farms" which might then be compatible with ship navigation
Allowing placement in very high tidal flow mouths of large bays
For instance these (where I've experienced the force of tidal flow):
Google Earth
(Just a suggestion . . .)
An alternative: Wave power:
Name sort of says it all (and we have all experienced it)
Trick is HOW to capture it. Existing protoypes:
http://www.biggreensmile.com/greenglossary/wave-power.aspx
http://www.bluebirdelectric.net/wave_power_energy_generation.
htm
Or extrapolations:
http://www.biggreensmile.com/green-glossary/wave-power.aspx
Common Theme:
Flexing at joints / pivot points => Pumps fluids => Drives generators
In other words, hydropower => hydraulic power => electric power
Flaws (possibly fatal) that I perceive:
1) Water's power is ONLY collected from immediate vicinity of mechanism
That is why whole fleets of such units are envisaged
Vs. Tidal Barrage where turbine collected power from whole reservoir
2) (Red mechanism): All of mechanism is exposed to highly corrosive seawater
At multiple joints vs. single propeller shaft seal of Tidal Flow turbine
3) (Red mechanism): Floating on surface, it completely obstructs navigation
4) (Yellow mechanism): Massive toilet bowl floats, from shore? (gimme a break!)
What power outputs have actually been achieved?
Wikipedia identified a couple of dozen projects (http://en.wikipedia.org/wiki/Wave_power)
But cited power outputs for only a handful:
2.25 MW of Povao de Varzim, Portugal
3 MW off Scotland (exact location / ID not provided)
20 MW (expandable to 40 MW) off Cornwall UK
19 MW of Portland, Victoria, Australia
1.5 MW off Reedsport Oregon
Meaning LARGEST was ~ 4% the size of single average US Power Plant
With all falling in power range of ~ 1-10 modern wind turbines
So it's time to move on to: Geothermal Power
Which resurrects earlier lecture's theme of getting heat (from somewhere)
Using it to boil something
With fluid to vapor expansion then driving turbine generator
Ultimate source of heat: Earth's molten core (heated by radioactive decay!)
So it gets hotter with depth = Geothermal Gradient ~ 25-30°C / km of depth
That's an averaged number, applicable away from tectonic boundaries
NEAR tectonic boundaries (e.g. in Iceland) gradient can be much higher
Allowing Iceland to generate 25% of its power from geothermal1 OR
California's 15 geothermal plant "Geysers" system2 to reach 725 MW (!)
1) Orkustofnun – National Nower Authority: www.nea.is/geothermal/
2) www.geysers.com/geothermal.aspx
Geothermal energy is thus all about maps:
From the European commission: Extrapolated temperatures at 5 km depth
Conclusion? Not much - Turkey, a bit of Spain, plus the Balkans . . .
Source: http://ec.europa.eu/research/energy/eu/index_en.cfm?pg=research-geothermal-background
Or for the U.S.
U.S. National Renewable Energy Lab (NREL) map:
Conclusion? Build geothermal plants in the West/Northwest
Source: http://www.nrel.gov/gis/images/geothermal_resource2009-final.jpg
But how MUCH power?
Let's first try to read fine print on NREL map:
Black dots – "Identified hydrothermal site"
"Map does not include shallow EGS sources
located near hydrothermal sites"
Huh? Aren't those the best locations?
Is intent here to find only NEW power sites?
Of new "deep" class called out in title?
"Includes temperature at depth of 3 to 10 km"
"N/A regions have temperatures less than 150°C
at 10 km depth
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
We clearly need better understanding to guess at likely power out
Coverage of geothermal in my textbook collection is very thin
But the best of my textbooks identifies three classes of geothermal:
Class 1: Shallow plants for sole purpose of heating surface buildings
Which would SAVE power but not produce it => Geothermal Heat Pump
Class 2: Systems using naturally produced steam (e.g. from geysers)
Requiring minimal drilling. Instead letting the steam come to you
Occuring in very limited locales: Iceland, Geysers CA, Yellowstone . . .
Class 3: Systems reaching depths deep enough / hot enough to boil piped in water
Called "Enhanced Geothermal Systems" or EGS
So we are mostly interested in EGS = What NREL map was also focusing on!
Diagram of EGS (enhanced geothermal system):
With detailed components given as:
1) (Surface) Reservoir
2) Pump house
3) Heat exchanger
4) Turbine Hall
5) Production Well
6) Injection Well
7) Hot Water to District Heating
8) Porous Sediments
9) Observation Well
10) Crystalline Bedrock
Source: http://en.wikipedia.org/wiki/Geothermal_electricity
We've been over this ground enough to figure out the rest:
Pump house (2) => To push supply water down into the
Injection Well (6) to then diffuse water through the deep extremely hot
Porous Sediments (8) causing the water to boil, exiting as steam via the
Production Well (5) from where it is then routed to the
Heat exchanger (3) boiling clean mineral-free water, with THAT steam going to
Turbine Hall (4) with small diversion to nearby shivering people via
Hot Water to District Heating (7) and rest of steam continuing on to
Surface Reservoir (1) where steam condenses (via cooling tower/river/lake) with
Crystalline Bedrock (10) to keep most injected water from wandering away and
Observation Well (9) being the only thing still in need of explanation:
Which Wikipedia forgot to explain but I'd guess could monitor how much
plant is cooling earth (and thus be used to fine tune plant operation)
But what is Geothermal's potential?
Thermodynamics' Carnot cycle gives maximum "heat engine" efficiency of
Max efficiency (%) = (1 – Tlow / T
high)
x 100
For geothermal heat engines, Tlow ~ earth surface temperature ~ 300°K
And Thigh might be 200°C higher, e.g. 500°K giving theoretical limit of
Max geothermal efficiency ~ (1- 300 / 500) x 100 ~ 40%
Compared to wind's 40%, IGCC fossil fuel's 50% or hydroelectricity's almost 90%
But heck, with geothermal the "fuel" IS free!
But, 40% of WHAT? Of the thermal power flowing up through the earth's crust:
Wikipedia specs this as 65 mW / m2 on land (vs. 110 at ocean bottom)
USGS and book "Hot Air" give about the same at ~ 50 mW / m2
From which:
Carnot limited extraction = (~ 40%) x (50 mW / m2) = 20 mW / m2
Total dry land area of world ~ 150 x 106 km2
Multiplying this land area by the capturable geothermal flow:
Powermax ~ (20 mW / m2) x (150 x 106 km2) ~ 3 x 1012 Watts
Divide this by world population of ~ 7 billion
Max personal geothermal power ~ 428 Watts
Which, while not trivial, is certainly not that impressive, especially when it requires
Geothermal power from TOTAL land area, at max efficiency possible
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Reality check?
US Energy Information Agency gives geothermal total of 16,517 GW-hr in 2013
1
=> Total US Geo power of 1.88 GW (~ 4 average US power plants)
Out of total US renewable sourcing of 522,464 MW-hr (=> Geo ~ 3.16%)
But, from Hydro / Wind Power lecture, US renewables ~ 11% of total
So Geothermal contributed about 0.35% of US power in 2013
What about new deep water injected EGS (Enhanced Geothermal Systems)?
Despite apparent promise, the technology appears to be still in its infancy
With biggest experimental plant (Cooper Basin, Australia)
Only targeting 25 MW output
1) Source: http://www.eia.gov/electricity/monthly/epm_table_grapher.cfm?t=epmt_1_01_a
Takeaway message on Geothermal?
Don't try it anywhere, do it where there is a lot more natural heat
USGS 1: Yellowstone averaged 50X higher, and peaked 2000X higher
than typical earth surface location
Ideal sites might be along "ring of fire" tectonic plate boundary locations:
But even then:
It's still very hard to estimate cost / potential
Because more site accommodating EGS tech
Has had only small-scale testing
And even less costing out
1) Source: http://volcanoes.usgs.gov/volcanoes/yellowstone/yellowstone_sub_page_53.html
2) http://pubs.usgs.gov/gip/dynamic/fire.html
2
What about more ambitious and/or futuristic ideas?
To start with, here are two that are variations on existing technologies:
Flying Wind Turbines:
Motivated by earlier discussion of wind speed vs. altitude:
Plus the fact that wind power increases as velocity to the third power!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
So to get up into even faster moving winds . . .
Early turbines
Current turbines:
Future Turbines (?):
Which might actually end up looking more like this:
Being assembled in Massachusetts: The Altaeros Buoyant Air Turbine
- Helium filled cylindrical lifting body
- Altitude to 2000 feet / Winds to 75 MPH
Prototype:
- Fourteen feet long
- Designed for 30 kW power out
- Larger model to produce 200 kW (with megawatt unit envisioned)
Markets?
- Remote sites with weak sunlight (=> grant from Alaska Energy Authority)
- Temporary industrial sites (e.g. construction or well drilling)
- Sites with low ground wind speeds
"The Quest to Harness Wind Energy at 2000 Feet" - Popular Science Magazine – October 2014
Or it might be simpler to just: Go Fly a Kite
Get rid of balloon (and its expensive lifting helium)
And keep the heavy electrical generator on the ground
Side benefit: Far less flying mass to fall on something / someone!
Kite tugs out rope turning ground based generator (motor)
Motor (generator) then reels back in partially collapsed kite - then repeat
Prototype kite:
Ground generator unit
"Go Fly a Kite" – IEEE Spectrum Magazine, December 2012
online at: http://spectrum.ieee.org/energy/renewables/the-benefits-of-airborne-wind-energy
Lots of such projects – but still very little data:
With announced targets of only 1 MW = 1/500th of an average U.S. Power Plant
"Go Fly a Kite" – IEEE Spectrum Magazine, December 2012
To finally have a BIG impact, what about: Orbiting Solar Farms?
As proposed by the Japanese Aerospace Exploration Agency (JAXA):
Said to be possible within twenty five years with 1 GW power output
Beamed down to earth via microwave radio or laser beams
Would weigh more than 10,000 tonnes and be several kilometers across
How Japan Plans to Build an Orbital Solar Farm, IEEE Spectrum Magazine, April 2014
online at: http://spectrum.ieee.org/green-tech/solar/how-japan-plans-to-build-an-orbital-solar-farm
Motivation (at least) is crystal clear:
As described in Solar Power lecture:
Atmosphere absorbs ~ 1/4 of sunlight: 1.35 kW / m2 => 1 kW / m2
Remaining is diluted when incident at shallow angles (i.e., not at noon)
And totally blocked by earth itself (for a particular location) half the time
Net result (from U.S. National Renewable Energy Lab calculator website):
But 1 kW-h/m2/day = 41.6 W / m2
So BEST U.S. sites have annual average incident solar power of ~ 200 W / m2
http://rredc.nrel.gov/solar/old_data/nsrdb/1961-1990/redbook/atlas/serve.cgi
Versus orbital solar farm:
Once aimed at the sun, it should stay aimed at the sun (ignoring tidal effects)
And, when not blocked by the earth, satellite receives the constant 1350 W / m2
Almost 7X better than our BEST U.S. sites
And ~15X better than our poorer (contiguous 48 state) sites!
But (first) big caveat is "when not blocked by the earth"
Time for a little orbital mechanics:
Want object (solar farm) to orbit at a distance r above earth's center
Acceleration of object due to earth's gravity = G M / r2
Inducing a centripetal acceleration on object = v2 / r
Where v = orbital circumference / orbital period = 2 p r / T
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Equating gravitational and centripetal forces to get orbits:
G M / r2 = (4 p2 r2 / T2) / r which yields (4p2 / GM) r3 = T2
G (universal gravitational constant) = 6.67 x 10-11 m3 / (kg – s2)
Earth parameters:
M = 5.97 x 1024 kg
Radius = 6371 km
So earth's circumference = 40,029 km
(Which I remember as 24,000 miles => Equator spins at 1000 MPH!)
Constant (4p2 / GM) in equation then becomes: 9.913 x 10-14 s2 / m3
Some space agency is going to have to launch pieces of solar farm into orbit
Most launches are into LEO (low earth orbit) 160-2000 km above surface
ISS orbits ~ 400 km above earth => orbital radius of 6800 km, calculating period:
T = √[9.913 x 10-14 s2 / m3 x (6.8 x 106 m)3] = 5,583 sec = 93 minutes
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Problems with low earth orbit (LEO):
Earth will block the sun half the time
We just lost half of our potential power enhancement!
Satellite won't stay above our location
Assuming that world is not willing to share cost and benefit of satellite,
How do WE (the builders / financers of farm) get all of its power?
We'd have to store power until farm's orbit passed overhead ≠ once / orbit
It passes overhead far less frequently
Because earth is rotating under its orbit:
Figure suggests flyovers ~ once in 8 orbits
=> twice a day (only!)
So we'd also need HUGE orbiting energy storage capacity (!$#$!@$!!)
Figure: http://www.universetoday.com/89063/must-see-video-falling-nasa-uars-satellite-observed-while-still-in-orbit/
So, go to a geosynchronous orbit!
Meaning that we now want an orbital period of one day to match our rotation
Put T = 24 hours = 86,400 seconds into (4p2 / GM) r3 = T2 and solve for r:
r = [(8.64 x 104 s)2 / (9.913 x 10-14 s2 / m3)]1/3 = 42,227 km
Subtracting out earth's radius = 35,856 km above earth surface
How much time will orbiting solar farm then spend in earth's shadow?
Orbital circumference is now 2 p x 42,227 km ~ 265,000 km
Width of earth's shadow ~ earth diameter = 2 x 6371 km = 12,742 km
So fraction of time in shadow ~ 12,742 / 265,000 ~ 4.8%
So we would get almost full 7X–15X enhancement of solar energy to array!
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
But a couple of problems remain:
Cost of launching pieces to orbit:
NASA figure for cost to launch into (unspecified) orbit is $10,000 / kg1
This, almost certainly, refers to low earth orbit only!
Gravitational potential energy goes as 1/r
r for high geosynchronous orbit is ~ 6X r for low earth orbit
If cost scales as potential energy of orbit, geosynchronous cost => ~ 60 k$ / kg
Japanese JAX station was estimated as 10,000,000 kg => $6 x 1011 to launch
If provided 1 GW (106 kW) power for 20 years (limited by cell lifetimes):
Launch cost (only!) = $6 x1011 / [(20x365x24 hours) x (106 kW)]
= 3.42 $ / kW-hour vs. current power cost of 10-20 cents /kW-h
1) http://www.nasa.gov/centers/marshall/news/background/facts/astp.html_prt.htm
AND you are going to beam down 1 GW of radiation:
Which will be aimed at offshore receivers:
But beams inevitably spread out a bit
(And could be diverted as a weapon!)
Proof of RF radiation harm (~ heat) is very slim
But we do worry about cell phones & AC power lines
For which US / Euro power limits are currently
1.6 / 2 W of RF radiation / kg of tissue
1
How Japan Plans to Build an Orbital Solar
Farm, IEEE Spectrum Magazine, April 2014
~ 1 GW / (25 km x 25 km) => I sure wouldn't go near the above power receiver
1) http://en.wikipedia.org/wiki/Mobile_phone_radiation_and_health
What about the holy grail of power: Nuclear Fusion
Fusion typically refers to energy released when H or He atoms combine:
OR
Problem (according to Newton): Positive protons strongly repel one another
Force (direct from 1st Maxwell Equation / "Gauss's Law") = (1/4πεo) (nq)2/r2
Where q = is magnitude of proton charge = 1.6 x 10-19 Coulombs
εo = permitivity of free space = 8.85 x 10-12 Coulombs/Volt-meter
n = number of protons in each nucleus (one or two)
r = separation of the nuclei
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Integral of this force = Repulsive potential energy
Which would then be = (1/4πεo) (nq)2/r which would plot something like this:
r
With this repulsion, nuclei would never fuse if not for another force:
Mysterious "strong nuclear force" which binds protons & neutrons
"Mysterious" because is only strong at separations < 1 femtometer (10-15)
At 1 femtometer and below, nuclear force overpowers charge repulsion force
Drawing nuclei together and, in the process,
releasing vast amounts of ("fusion") energy
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
So combined potential energy would look something like this:
Charge Repulsion Energy
r
1 fm
1 fm
Nucleon Attraction Energy
To get over that barrier, nuclei must get an incredible running start
Huge kinetic energy => Converted to potential energy climbing barrier
Temperature must supply that kinetic energy – But how high a temperature?
Kinetic energy of particle (at temperature T is) ~ k T
k = Boltzmann's constant = 1.38 x 10-23 kg-m2/s2 °K
Barrier Height = Charge repulsion AT 1 fm = (1/4πεo) (nq)2/(1 fm)
Equating and solving for required fusion temperature:
T = (1/4πεok) (nq)2/(1 fm)
Putting in numbers for hydrogen nuclei (n=1):
= (1.6x10-19 C)2/(4π)(8.85 x 10-12 C/V-m)(1.38 x 10-23 kg-m2/s2 °K)(10-15 m)
= 17 billion °K (C-V / kg-(m/s)2) things in parenthesis = Joule/Joule => 1
Temperature to initiate hydrogen fusion ~ 17 billion degrees (K) (!!!)
THIS is what makes fusion so difficult:
1) We must give nuclei HUGE starting kinetic (heat) energy
2) The nuclei must retain that huge energy long enough to collide
Step 1 can be accomplished by using electromagnetic fields to push protons
Step 2 can be the harder part
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm
Keeping nuclei hot long enough for them to collide:
First, must get rid of much cooler ambient gases => ultrahigh vacuum
To which nuclei would otherwise prematurely share their heat
Second, must keep nuclei from colliding with walls of vacuum chamber
Now generally done via a "magnetic bottle"
Which comes right out of our "first right hand rule:"
Magnetic field always pushes protons sideways
With result that they spiral down magnetic field lines:
http://www.swapyournotes.com/a
rticledetail/articledetail.html/632/
http://astarmathsandphysics.com/a-level-physics-notes/electricity/a-level-physics-notes-the-magnetic-bottle.html
Magnetic bottle completed by squeezing field together at both ends:
http://astarmathsandphysics.com/alevel-physics-notes/electricity/alevel-physics-notes-the-magneticbottle.html
Done well enough, protons should just spiral back and forth
Until they collide and, given enough energy/temperature, fuse
We got individual protons to do this fifty years ago
Problem is getting ENOUGH protons to do this, so get more energy out then put in
A BREAKTHROUGH (!)
Has been promised "within the next decade" since I was in high school
This 50 years of little progress strongly suggests:
It's time to try something REALLY different!
And you may well have heard a lot of buzz about new approaches to Fusion:
- Lockheed Martin's secret mini reactor (that will fit on a truck!)
- Lawrence Plasma Physics' proton-boron fusion reactor
- Helion energy's magnetic compression reactor
1
2
3
- General Fusion's liquid metal vortex shockwave reactor
- University of Washington's "Dynomak" variation on existing Tokomak
But none of these have been built (or there's zero public proof of this!)
And some are no more than crowd funding solicitations!
So regarding Fusion: "Stay Tuned . . . (indefinitely?)"
1) http://www.lockheedmartin.com/us/products/compact-fusion.html
2) http://spectrum.ieee.org/energywise/energy/nuclear/how-far-can-crowdfunded-nuclear-fusion-go
3) http://spectrum.ieee.org/energywise/energy/nuclear/silicon-valley-goes-long-on-nuclear-fusion
Conclusions on the "exotic" energy production alternatives:
Despite decade(s) of development, their power outputs are small to miniscule
Making most of them attractive (at best!) in:
- Countries Locations lacking an effective energy distribution Grid
- Remote locations difficult to otherwise supply with energy
Wilds of Alaska, Australian Outback, remote islands . . .
Others (e.g. satellite solar farms) COULD generate huge amounts of energy
But look to be at least an order of magnitude more expensive
Nuclear fusion promises an energy Holy Grail
But, unfortunately, it seems to be as elusive as the original Holy Grail
Leaving us in a bit of a corner => My upcoming discussion of nuclear fission
Credits / Acknowledgements
Some materials used in this class were developed under a National Science Foundation "Research
Initiation Grant in Engineering Education" (RIGEE).
Other materials, including the "UVA Virtual Lab" science education website, were developed under even
earlier NSF "Course, Curriculum and Laboratory Improvement" (CCLI) and "Nanoscience Undergraduate
Education" (NUE) awards.
This set of notes was authored by John C. Bean who also created all figures not explicitly credited above.
Copyright John C. Bean (2016)
(However, permission is granted for use by individual instructors in non-profit academic institutions)
An Introduction to Sustainable Energy Systems: www.virlab.virginia.edu/Energy_class/Energy_class.htm