In an article titled "Defeating the Son of Andrew" in the February
1994 _Analog_, Leon O. Billig describes a means of extracting enormous
amounts of energy from the air over warm ocean waters.  The invention
is a convection tower which confines a rising air current from the
humid surface layers and prevents the flow from being choked off by
dry air from layers above, which is the mechanism which restricts the
size of most tropical rainstorms.  He touts this primarily as a means
of reducing the energy supply for hurricanes (which avoid the choking
effect due to their size), and secondarily as a way of making fresh
water.  He calculated the power available from falling water inside
the tower, and got a figure of a few gigawatts.

Using the airflow through such towers as a source of energy apparently
did not occur to him.  (It immediately occurred to me...)

He postulates towers which are 5000 feet across at the base, 1000 feet
across at the top, and 6000 meters high (his mixture of SI and English
units, not mine).  His calculations, which are not presented in
sufficient detail for me to reproduce, yield these numbers for what
appear to be fairly common sea-level conditions (yes, he did go to 4
significant figures):

85 degree F / 80% humidity:
Daily inlet airflow: 41.35 trillion ft^3
Fresh water production:  4.53 billion gallons
Exit air temperature: 33.5 F
Exit air velocity: 298 ft/sec

90 degree F / 90% humidity:
Daily inlet airflow: 47.06 trillion ft^3
Fresh water production:  5.775 billion gallons
Exit air temperature: 45 F
Exit air velocity: 350 ft/sec

I don't have standard atmosphere figures for latitudes other than
45 degrees north, so I can't do calculations for the outlet state
at 20-30 degrees north.  On the other hand, using psychrometric
tables I can calculate the composition, density and total mass of
the air flowing through the inlet.

                H2O     Sp. vol,    Sp. vol,
Temp    RH      frac.   ft^3/lbm    ft^3/lbm
                w/w     dry air     mixture

85 F    80%     .02114  14.192      13.898
90 F    90%     .02806  14.476      14.081

From this the 85 F/80% RH mass-flow is calculated to be 2.975 billion
pounds per day (15.62 million kg/sec), of which 2.914 billion pounds/day
(15.29 million kg/sec) is dry air.  For the 90 F/90% RH state, the
mass-flow is 3.342 billion pounds/day (17.54 million kg/sec) of which
3.251 billion pounds per day (17.06 million kg/sec) is dry air.

At the outlet, the air may contain as much as 1.2% water on the hot/humid
day.  The actual state of the air depends on the total humidity of saturated
air at the outlet temperature and pressure.  If we ignore humidity as a
complication and instead assume that only the dry air gets to the outlet, 
the outlet mass-flow rate for the "mild" day is 15.29 million kg/sec and
for the hot day it is 17.06 million kg/sec.

If we assume that the air stream at the top of the tower is diffused
(expanded and slowed) by a 4:1 ratio to convert speed into pressure
and then run through air turbines and generators with a net efficiency
of 80%, I get the following figures for available power:

Day     Mass-flow,      Speed,  Total power,    Available
        kg/sec          m/sec   megawatts       power, MW

Mild    15,290,000      90.8    63,072          50,458
Hot     17,060,000      106.7   97,077          77,661

In contrast, a large coal-fired plant might yield 800 megawatts and
a big nuclear plant 1000 megawatts.  On the "mild" day, 13 convection
towers could yield as much electricity as every plant registered with
the Department of Energy in the year 1998 (650 GW); on a hot/humid
day, it would only take 9.  

The potential power available from convection towers is staggering.
Furthermore, these plants would operate without generating any CO2,
oxides of sulfur or nitrogen, ash or radioisotopes.  If we wished to
race the world for CO2 reductions, that would be a good place to start.
It looks like we could shut down most fossil-fired powerplants for the
summer months, and use any excess power to make electric-intensive
products such as aluminum and magnesium.  If it requires 900 kJ/mole
to extract metallic magnesium from MgO, a plant consuming 5 GW would
produce 11,500 tons of magnesium a day.  Billig estimates 2.7 million
tons of steel for a tower, but if it was built from the same mass of
magnesium the 5 GWe electrolysis plant could make the metal for a new
tower in 234 days.  Magnesium is extracted from seawater; such towers
could literally build themselves out of the oceans.

Note:  Plants such as this could only be built along the Gulf and southern
Atlantic coasts of the USA.  There is a cold current which runs south along
the coast of California, which creates so much of the pleasant weather
there but also prevents the conditions which allow the operation of a
convection tower.  Regardless of the local desire to be environmentally
correct, California will have to solve its power difficulties in some
other fashion.

15 responses total.

Of course, it would be misleading to think of this as 'free' power in an
environmental sense.  If these towers also fulfilled their primary purpose
of reducing hurricanes, there'd be all sorts of interesting side effects.

Now, in a "terraforming a story planet" sci-fi story, these would be the
perfect gadget.  The image of self-building towers is especially nice.

Yeah, I think these would inevitably affect the climate downwind of 
them, though how much I can't say.  (In fact, in a later copy of Analog, 
someone wrote in to suggest that such towers could *deliberately* be 
used to make the climate in some parts of the US more suitable for 
farming!) I'd also love to see the FAA's comments on a tower that stuck 
up well into the flight levels.  I have to wonder how much it'd cost to 
build such a monstrosity, and who would get sued and for how much when 
it fell over.

Re #1:  Wind generators also affect the weather downwind of them, to
a similarly small degree.

One of the effects of global warming is supposed to be an increase in
the intensity of storms, including hurricanes.  This has environmental
effects too, as does our diversion of surface water and unsustainable
mining of groundwater.  Reducing the strength of hurricanes would bring
their effects on terrestrial ecosystems (like forests) back into line
with historical levels, and substituting tower condensate water for
groundwater would similarly improve matters in places like Florida and
Texas.  How'd you feel about piping condensate from towers on the Gulf
coast to the interior of Texas and Oklahoma to refill the Ogalala
aquifer?  If you were willing to build heavy enough pipes you could
even let it flow by gravity.  Mind the welds, if you get a leak that
stream is going to cut like a knife...

Re #2:  The FAA has long required registration of towers and other
objects which present hazards to navigation, and they can be a couple
of thousand feet tall.  This is only different in quantity, not
quality.  You mark it on the charts like any other mountain.

I have a solution to the falling-down problem:  Make it out of something
that corrodes in seawater (except the skin coatings), and put it offshore
by more than its height.  If it falls over, it's no big deal.  You
salvage what you can, let the rest rust, and build another one.  The
biggest cost is going to be losses from the industries you shut down
for lack of power.  (See "California".)

Cost is a big issue.  On the other hand, if carbon taxes start adding
5 cents to the price of a KWH of electricity that 50 gigawatts adds
up to 60 million dollars a day, or 7.2 billion dollars over a 120-day
generating season.  If engineering and legal costs raise the total
structure cost to $3000 per ton, that's only 8.1 billion dollars.  Pay
that off in a bit over a year, the rest is gravy; 88% annual return
on investment, it's a venture-capitalist's wet dream.

The current price of steel is a couple hundred bucks a ton.  Peanuts.

Billig makes prominent mention of fresh water, but I hadn't looked
at the issue before. 

I did a little bit of research today, and found that the city of
Austin TX (micklpkl's home) has a freshwater purification capability
of 250 million gallons per day.  4.53 billion gallons of fresh water
per day is enough to supply 18 Austins.  Place a few of these towers
on the Texas gulf coast and drought quickly becomes irrelevant to
the cities taking their water from the condensate.  (They'd also
have no problems keeping the lights on.)  Barton spring would never
again be at risk of going dry.

Power transmission might be an issue.  At a power output of 50
gigawatts and a diameter of 1000 feet, you'd have to transmit
about 16 megawatts per linear foot of circumference!  It looks
like a tower built for power production is going to have a large
fraction of the bulk of its upper sections devoted to power lines.

Would a smaller version - say about 500 megawatts - be feasible?

Transmission losses are a big issue too.  Especially when you only have a few
plans servicing a large area.  I wonder about smaller, scaled down versions
too.  A 19,500 foot tall structure is also difficult for me to fathom.

I would ask whether there is any means of construction that would
prevent a tower of those dimensions not to collapse under its
own weight.

Tapering.

Re #5:  Read the article, it answers that question implicitly.

Re #6:  Superconducting power lines are now a commercialized
technology.  I would also expect a lot of power-intensive industry
to be located at the towers themselves.  Besides, with such an
embarrassment of riches the transmission losses wouldn't be much
of a factor.

Re #7:  Billig proposes to use corrugated construction, with a web
between inner and outer skins.  All parts of the sandwich would be
aligned to bear compression loads.  I haven't tried to analyze buckling
failure since second-year ME classes, but this sounds to me like a
promising approach.  Geodesic strut structures are another possibility.

On the other hand, the three biggest elements are quite simple:
1.)     Build it out of steel (stronger than rock, and mountains
        reach almost 30,000 feet on Earth),
2.)     Use a low ratio of L/D, for stiffness, and
3.)     Taper it (as noted by Drew).

The requirement for a low L/D ratio sets a minimum diameter for the
tower to be self-supporting (I have no idea how guy wires might
complicate the issue).  In turn this would set a minimum mass-flow
rate for given conditions, and minimum power available.  You could
always opt not to capture all the power at hand -- but why?

It's just as hard for me to imagine a structure stretching 6000 meters
into the air, but when the base is a mile across it is proportionate.
If you assume an exponential taper by 5:1, the effective height is only
about 3000 meters (integate e^(-.000268 x) dx from 0 to 6000, you'll
get about 2985).  The base is about 1600 meters wide; that's fairly
squat and sturdy.

Stiffness (resistance to buckling under compression) is a big issue.
A wide member is much stiffer than a narrow one, so low density is
a plus.  Magnesium looks better and better in this regard.  My table
of Mg alloys shows that they're about 1/4 the strength of steel, but
magnesium is only about 22% of the density of iron.  It may not be
worth the fire-fighting gear necessary to use it, but the idea of
growing a structure out of the materials of the ocean is seductive.

Could the magnesium be alloyed with something to make it more difficult
to burn?

(You might consider why mountains on earth are *only* less than 30,000
feet high. 

Going along with the game, however: it might make more sense to put the
turbines for power generation around the base. You would not have to
expand to obtain pressure: the interior would be under reduced pressure
(yes, which could collapse the structure...one problem at a time....). 

Concentric cylindrical walls with an interstitial honeycomb 
structure would be an efficient and strong construction...

Easy enough to say - but let's see the calculation. The stress at the
top of a 6000 meter long wire at best exceeds only marginally the
tensile strength of aluminum and magnesium alloys. Titanium is somewhat
better, but with little margin of safety. The tapered structure and
the fact it would be in compression brings in other issues, such
as the longitudinal stability of compressed shells. 

Re #11:  I don't know, ask a metallurgist.  However, I am inclined
to doubt it; magnesium is usually alloyed with other combustible
metals like aluminum, and even iron will burn if it gets hot enough.

Coating magnesium members with something less combustible might be
a feasible approach; iron can probably be plasma-sprayed, giving a
refractory coating which would take insults like lightning strikes
without catching fire.  (Lightning control would be a big issue
for a tower like this!  It would need thousands of lightning rods.)

Using steel for the skins and magnesium for internal structure might
work too, but you'd have to be very careful about managnig failures
such as blown or shorted power lines.  Gigawatt arcs could ignite
just about anything.  Filling with dry nitrogen might be required
(you can't use CO2, magnesium will burn in pure CO2).  You can't
use water for fire suppression, either.  You might have to have a
way to remove the burning section and get it clear instead of trying
to fight a fire.  Testing something like this sounds like a real mess.

Re #12:  I thought about putting turbines near the base, but I didn't
think that internal suction would help with the structural issues.
Capping the top improves things; it adds internal pressure near the
top (which creates "balloon" stiffness) and it also creates lift
against the cap.  The lift is only about 160,000 tons under the
scenario I checked, but that's still not bad; it would support about
the top 1300 meters of the tower under Billig's design, or the full
set of generators at 500 W/lb plus about the top kilometer.

Turbines could also be located in the middle.  The 10,000 foot level
might not be a bad spot, allowing for maintenance by workers without
supplemental oxygen (though just barely).

Re #13:  Or thinwall tubes and sandwich sheets filled with metallic
foam.  If you've got twenty thousand feet of tower to play with, you've
got a perfect place to build a drop-tube for making metallic foams in
microgravity.  This only works for the second one, of course.

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