Pancake Universe

[Elegast]

if there is no tornado occuring, no numbers of butterflies flapping could ever create one.

Yes and no. 

If tornadoes never happens, then yes butterflies do nothing.

If there is a tornado one year out of two, then a butterfly may change which year it happens.

In the real world, weather is changing, with colds spells and hot ones. If Mab is somewhere, all the cold ones will come near her.

[Elegast]

ok, ill duck out on this one. youre missing the whole point and then half.. conservation of energy in the DF does still apply. any secnario you ahve metioned would cause worldwide changes, whcih is not what happened. You dont like my conclusions, fine. you dont have too.

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.

[knnn]

ok, ill duck out on this one. youre missing the whole point and then half.. conservation of energy in the DF does still apply. any secnario you ahve metioned would cause worldwide changes, whcih is not what happened. You dont like my conclusions, fine. you dont have too.

Fair enough.

I think you are wrong on the hurricane angle, but I will admit that I'm less convinced of my stance regarding the snow in Chicago during Summer.  I personally don't think Harry would have noticed worldwide changes if they had occurred (he was busy), but this is certainly a point I have to work around.

Regarding conservation of energy, what if Mab simply opens a portal to Arctis Tor for a few months?  The temperature there is so low that it is bound to cool off the surrounding areas.  Add in a bit of thermodynamics and you get snow at minimal cost.

[wizard nelson]

Fair enough.

I think you are wrong on the hurricane angle, but I will admit that I'm less convinced of my stance regarding the snow in Chicago during Summer.  I personally don't think Harry would have noticed worldwide changes if they had occurred (he was busy), but this is certainly a point I have to work around.

Regarding conservation of energy, what if Mab simply opens a portal to Arctis Tor for a few months?  The temperature there is so low that it is bound to cool off the surrounding areas.  Add in a bit of thermodynamics and you get snow at minimal cost.

since arctis tor is the wellspring for winter, she kinda did in a roundabout way. she drew power from her strong places to fuel the may winter. this brings up the question, is mab stronger when she draws from arctis tor like harry is with DR. its totally possible she could create that connection while elsewhere btw. like i think harry will do with his new staff.

[Ms Duck]

Fair enough.

I think you are wrong on the hurricane angle, but I will admit that I'm less convinced of my stance regarding the snow in Chicago during Summer.  I personally don't think Harry would have noticed worldwide changes if they had occurred (he was busy), but this is certainly a point I have to work around.

Regarding conservation of energy, what if Mab simply opens a portal to Arctis Tor for a few months?  The temperature there is so low that it is bound to cool off the surrounding areas.  Add in a bit of thermodynamics and you get snow at minimal cost.

that was the second calculation.. shed have to bring in 6,535,600 Kg of cold air, and maintain it to equalize the required pressure drop.( ammount would have to constantly refreshed at a rate determined by the pressure differnce (in degrees k)(to the fourth power) and area of surface action) (it would have to be very fast) (yall can do that math, assume a hemisphere with a volume of the city of chicago...)(ive done enough math) (lol)

I still think from a purely physics point of view, just 'making things colder' by use of some magic cold force is much cheaper energy wise then either bringing in tons of cold air, or diverting large scale climate forces, or any of the other suggestions... consideirng bleed off, youre talking about bringing in the equivalent of an empire state building a day there (365,000,000 kg)

and when it comes down on it, do you realy want to mess with a being that could toss an empire state building at you? shes still many bhundreds of times stronger then all the white council put together.. much like Jim said.

[Ms Duck]

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.

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.

 

[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]

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.

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."

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.

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

[Ms Duck]

No, i was an engineering/ applied math major for three years before ending up in accounting.

and i am way out of date on this stuff.. if a meteorologist wants to chip in and tell me im wrong, please feel free.

[wizard nelson]

ahh a numeromancer 

[Ms Duck]

ahh a numeromancer 

yep. i drove one of my DM's nuts years ago when i played a mage that cast spells in calculus.

 

[wizard nelson]

yep. i drove one of my DM's nuts years ago when i played a mage that cast spells in calculus.

 

lmao... i really gotta find some people to bring me into the old school rpg loop. i like it but i don't know anyone nerdy enough they actually play

[Ms Duck]

I cant sleep

so dont take this too seriously, im juts thinking aloud.. too much coffee does this too me.

whats the worst case Mab could be?

if 10^18-10^20 joules is a conservative estimate, whats an outer limit?

well.. lets assume that mabs was not doing it on purpose. ergo, it was a side effect from her pressence on earth... which was on demon reach

thats about 250 km from chicago, more or less, according to descriptions from Jim. throw in another 100 km to hit Joliet ( Murphy's place) and we can assume a cylinder with a height of 8.5 km and a rough radius of 350 km.

or 3,271,183,350,550,372 cubic meters

at 1.205kg per cubic meter, at average temp we get..

about 3,941,775,937,413,198,260 grams

now it take 1 joule to cool 1 gram of air (with considerable fudging for humidty, etc..)

so 21 c to 0 ..

82,777,294,685,677,163,460 joules. to accomplish this for one second. in may.

hmm thats not too bad..close to original figure.

ok, how much power does she lose in one second based on surface contact?

(asuming no convection, because there was no reports of tornados tossing the sears tower into the lake.)

(also assuming instant transfer, as im not getting into special relativity and times cones here.)

gives us via fourier's heat equation a transfer of  0.006804  calorie/centimeter^2-second

hmm now the surface area of that cylinder was (in cm):

  934,623,814,442,963 cm^2 (asuming contact surfaces only)

so along with the inital cost, she was burning 6,359,180,433,469 joules per second just to keep it cold.

thats another 4,944,898,705,066,212,572 just in the few days we saw in GS.


total cost of the cooling alone:


132,226,281,736,339,289,182 joules

or 2,098,829 small atomic bombs.

dont worry, im sure we can take her. all it will take is one iron bullet, right? um, peeps? who wants to shoot first?