The Dresden Files > DF Reference Collection
Pancake Universe
Ms Duck:
--- Quote from: Elegast on December 13, 2012, 10:03:47 PM ---It would create worldwide changes, but very minor: the rest of the world would be very slightly hotter. The law of conservation of energy is conserved.
--- End quote ---
not in the case of diverting major currents..then static forces would be realized. its what causes ice ages.. for example, diverting heat from the chicago area to the artic would cause artic ice to melt at an accelerated rate, which would change the salinity of the water level. this casues a change in the thermocline level ( the vast majority of the water in the oceans is actauly below freezing, but held liquid due to pressure and salinity).. drasticaly rasing the water level, which then increases the amount of heat we absorb from the sun..
then this:
is Harry's fault.
;D
knnn:
So let's take a look at the math.
1) First of all, I think you are overstating the need to "maintain pressure". It's true, given enough time the cold Mab brings in will dissipate over the entire planet, but as you yourself noted, the only way heat can transfer is through the surface of the sphere around Chicago. Given that air at different temperatures will create their own natural insulation, and I don't think you need to worry as much about "bleeding energy".
As an example, take the inverse scenario, the Urban Heat Island. Temperatures difference of 10F inside the city are regularly, simply because the amount of vegetation is less. Note that this temperature is generally sustained even at night, despite winds/etc., because heat transfer in the atmosphere is so inefficient.
Historically, there have been years when the average temperature in Chicago during the month of May has been as low as 50. Lets take 55 degrees as a start. best snow temperature is when it just gets to 32F in the air, call it 35F on the ground (remember, if it is too cold -- you don't get snow). You really need 32F on the ground for snow to stick, but remember that the snow could have accumulated earlier in the winter. Once enough snow is on the ground it can last a long while, because as the top layer melts, it cools the air around it. So really, you only need keep things cooler than the surrounding area by around 20F, and since the area around is cooler than the city itself to start with, 55 in the city can easily mean 50 in the surrounding area.
So what do we know? A differential of 10F will stay relatively easy without any special power (just make sure it doesn't get too windy), but you need a differential of 15-20F. How long do you need to maintain it? Not as long as you'd think -- it could easily have been naturally cold during the Winter, and Mab only needed to keep it until Harry came back in mid-end of May. Heck, if it was a really snow-heavy winter, you still have snow on the ground till May slowly melting and keeping things cool. So, what's the real energy requirement?
2) The rules for heat transfer are quite complicated, so instead of computing estimate for the various methods of transfer, lets take a shortcut:
- When the sun goes out at night, the temperature drops very quickly. For Chicago this number comes out on average to about 30 degrees Fahrenheit, over the course of the eight hours of the night much more than the 20F I'm looking at. And remember that isn't just about sustaining a lower temperature -- the temperature actually drops. Huge difference.
- So let's assume we need need 1 Watt per square foot to keep things cool. Bear in mind that this is still probably over-estimating things by a factor of 10-100. With snow on the ground, your energy absorption is going to be much lower anyhow, so you don't need to worry as much about cooling. Note that 1 watt per square foot also matches with the energy requirements for melting snow, so this isn't a bad estimate.
3) Using your numbers, I've got a surface area of ~30,000 square kilometers (P.S. I like how you took the largest possible estimate for "Chicago" - including all of the suburbs. The size of the city itself is 50-60 times smaller), that's roughly 300,000,000,000 square feet, coming out to a total of 3 Trillion watts as an upper bound.
-- Actually this number is much bigger than I thought it would be. For comparison, an average nuclear power plant produces about 1 billion watts, so this is on the order of 1000 nuclear power plants. Another comparison would be to say that this is about 7-8 times the amount of power to run everything in the US.
Granted, I've made some grandiose assumptions (i.e. we can use a number at least 10 times smaller size for Chicago, more efficient cooling, energy from snow melt, average temperature for May, etc.), but the power to cool down Chicago is not insignificant.
madness:
--- Quote from: knnn on December 14, 2012, 04:15:12 AM ---Granted, I've made some grandiose assumptions (i.e. we can use a number at least 10 times smaller size for Chicago, more efficient cooling, energy from snow melt, average temperature for May, etc.), but the power to cool down Chicago is not insignificant.
--- End quote ---
I think that is why she was getting a little bit testy. No matter how you work it out the power involved is on a different scale completely from most of the beings that we are familiar with.
Ms Duck:
two thoughts:
the law of heat transference says that energy transfers between the two points to the exponetial power of the differnce between the two, limited by the area of the surface and the resistance of the material.
ie , the greater the differnce, the faster the energy ballances.
various liquids cooling
in the case of heat bloom from a city, the differnce- 10 f- is not that much. furthermore, much of the difference is not in the air but trapped in the ground, which has a very high resitance. put your hand on black asphalt at miday, its dang hot. and it holds that heat, and raidates it all night long. the old joke about streets so hot you can cook on them.. is actually true in some places
snow in may is more like 90 degrees F difference. and shes fighting the heat bloom effect.. all that lovely heat coming down on all those streets..
now in the case of that extreme a temp differnce, the rate of heat transfer is so fast it should be more then the air can hold, and thus become kinetic energy (this is a very simplified view of where storm fronts come from).. the largest such differnetial ever recorded in the US was the Great Blue Northeaster on 11,11, 1911. the hot front was 76 f, the cold 11 f. it caused multiple tornados throughout the missippi valley ( nine in illinois alone), blizzards in ohio, and dust storms in oklahoma. its effects were felt accross the continental US.. this is what you would expect from a natural or triggered event, widespread damage and change accross all of north america.
now, we dont know what happened outside chicago in GS. But i think if there were massive tornados using the midwest for a game of whack a mole for months someone would have mentioned it. ;)
as harry himself snarks, when told that mortals belive the snow is being caused by global warming " youd think magic would be more believable."
--- Quote from: madness on December 14, 2012, 04:35:53 AM ---I think that is why she was getting a little bit testy. No matter how you work it out the power involved is on a different scale completely from most of the beings that we are familiar with.
--- End quote ---
yea sorry if i was getting grouchy there. (hugs)
wizard nelson:
ms duck are you some kinda ferromancer? ???
your making einstein look like an apprentice :o
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