Thursday, April 03, 2008

Living inside a giant invisible dome, part 2

One oddity of living in the giant invisible dome thingy is your relationship with water. Water can't penetrate the dome -- rain and snow don't pass through. This is a problem, since water in pipes presumably won't pass through the dome either. But, you do have a handy water source (even though collection might be problematic): atmospheric condensation on the dome.

A bit on how the atmosphere works. You notice how it gets warmer as the day goes on -- this is largely because the sun heats the earth's surface, and this heat radiates. We cool at night by this radiant heat dissipating into the atmosphere (heat can radiate in a vacuum, but with all that air right there, what it effectively does on Earth is heat the air). The convection of this warm air moving is one of the things that makes wind. But in the dome, you don't have a huge air mass to cool you. The radiant heat keeps heating the same air, and the hot air can't escape. This turns your subdivision into a gigantic, 100% efficient greenhouse.

More numbers: according to NASA (I generally trust their data), the sun delivers 1370 watts per square meter at noon at the equator. Energy delivered (in joules) is watts per second; this equates to 4,932,000 joules per hour per square meter. Of course, the sun is rarely directly overhead; over the year, the noon sun's angle of incidence varies by 23 degrees or so. It's directly above the equator at the spring and fall equinoxes; the rest of the year, you can estimate its angle of incidence with something like 23(2*sin(number of days from the equinox/365)). And, in Fort Wayne, Indiana, we're pretty far removed from the equator (41 degrees north); factoring this in, the actual amount of energy we get is 1370*cos(41-23(2*sin{number of days from equinox/365})). I'm skipping showing my work on the calculus here, because it doesn't transcribe to webtext well. But if you integrate this over a 12-hour day, you get an average of 12 million joules of energy per square meter of dome-covered land per day (this peaks at around 18 million on the summer solstice, and bottoms out around 7 million on the winter solstice).

How much of this energy stays in the dome? It depends partially on the albedo (reflectiveness) of what it hits. Asphalt roads only reflect 4% of the light that hits them; concrete roads reflect between 40% and 65% of the light that hits them. Grass reflects 23%. Roofing shingles vary from 10% to 45%, depending on composition and color. Figure our subdivision is 50% lawn, 20% paved with cement, 5% paved with asphalt, and 25% built with some sort of structure (deck, house, patio, pool, etc). I estimate an average 29%; this means you lose around 3.5 million joules per square meter as it reflects back out of the dome. You've still got 8.5 million joules per square meter hanging around in the dome.

More math: air weighs roughly 1.2kg per cubic meter. It takes roughly 1000 joules of energy to heat a kilogram of air by 1 degree (celsius). It takes roughly 800 joules of energy to heat a kilogram of dirt, and a cubic meter of dirt weighs roughly 2500 kg. When the sunlight hits, I'll assume it has to heat everything roughly evenly (this is not true, but makes for convenient math; I'm done with the calculus for now), and has to heat the dirt to a depth of three meters. A dome of radius R contains 2/3*Pi*R^3 cubic meters of air, and 3Pi*R^2 cubic meters of dirt we need to worry about. It absorbs 8.5*Pi*R^2*10^6 joules of energy in a day. It takes 2 million joules to heat each cubic meter of dirt by 1 degree, and 1000 joules to heat each cubic meter of air; the energy required to heat the entire dome by 1 degree is 2000R^3+ 1.8R^2*10^7. Divide this by the energy available, and we see that the temperature goes up by one degree every R/13000 + 2/3 days. This works out to a temperature increase of one degree per day for a dome 8600 meters wide; for much smaller domes, you're stuck with the lower boundary of 2/3 days per degree.

You'll lose some radiant heat at the dome edge, but much less heat than you'd lose if air could actually flow. Even if you lose heat half as fast as normal (a generous estimate), you're still gaining a minimum of 1/3 of a degree celsius per day. So it'll get hot in a hurry.

Back to water: the fact that it'll quickly become significantly hotter inside the dome than outside does have an upside. Water will condense on the cooler inside surface on the dome, so all you have to do is collect it as it runs down the sides. Possibly a system of ditches and troughs could be constructed to channel the condensate to a central pond (or several smaller collection pools). The dome residents also have the option of bathing and washing in water from swimming pools.

There's another option, which is that water might still continue to flow through the water pipes. I theorize thusly: the water in and out travels in metal pipes. This means that the inductive actualization of the force field as it bifurcates the cross-section of the water pipes creates a harmonic reionization field which locally destabilizes the modal kinetic inhibition effect. The transmodulation (I refer, of course, to therionic transmodulation) caused by the flowing water as the dome forms results in this reionization field's reactive nullification of the localized antikinetic effect. This operates (we assume that water was flowing through the pipe as the dome formed) because the metal pipe creates a monaxial phased reactive differential via the conductive/inductive subatomic metallic fluxes present in the latticed metallic matrix of the atomic structure as the ionically-charged water (it helps that it's fluoridated) moves past, inducing microcurrents into the matrix. It makes perfect sense, if you think about it. :-)

Next: beer and cannibalism.


Tina said...

The water flowing in and out would act in the same fashion as a car's radiator, counteracting a small part of your thermal increase.

Additionally, with such ample sunlight, the inhabitants of our fair subdivision are going to tan nicely, and therefore (I would assume) demonstrate slightly altered reflective/absorbtive properties.

Furthermore, semi-tropical temperatures cause hippie-ism to flourish. (Potentially Flawed Evidence A: Global Warming gave us Al Gore. PFE B: Notice how many Democratic candidates are holding campaign rallies in Alaska.) How many days into the experiment do we get before homeowners decide it would be a good idea to plant grass on their roofs? How many days further into hippie-ism before they remove the turfgrass and replace it with, ah... *grass*?

Concern: Are there birds in the dome? Without birds, important life stages for plant life will not occur. Yet, with birds, the glassy outer edge of the dome will slowly accumulate a collection of feathers and all of other the bits of dead birds that tend to come with them. Glass is a foreign concept to birds, and the xenophobic little things tend to die from collisions with it.

Alternate Concern: Is there a feral cat colony inside the dome? This could resolve the bird issue...

Anonymous said...

Stern Rules!!!!!!!!!!