Melting an Iceberg

[Tuckerfan]

Okay, let's say I wanted to melt an iceberg at one of the poles, roughly the size of Delaware for some fiendish evil overlord plot of mine. Could I do it with a giant fresnel magnifying lens (no doubt at least the size of a football field) in a period of a few days? Assume that I'm attempting to do this during the summer region at that particular pole. Or would I need some kind of exotic superweapon to do it?

[David Simmons]

Okay, let's say I wanted to melt an iceberg at one of the poles, roughly the size of Delaware for some fiendish evil overlord plot of mine. Could I do it with a giant fresnel magnifying lens (no doubt at least the size of a football field) in a period of a few days? Assume that I'm attempting to do this during the summer region at that particular pole. Or would I need some kind of exotic superweapon to do it?

To find out you have to start with the size of the iceberg in grams. It takes 80 calories to convert one gram of ice at 0 C to one gram of water at 0 C. One calorie is 4.186 Joules of energy so it takes 334.9 Joules to melt a gram of ice. If you want to do that in 3 days that's 2.6*105 seconds. Since it is summer I'm assuming the sun is up all of the time. So to melt that gram you need to supply heat at the rate of 334.9/2.6*105 Watts = 1.29 milliwatts.

Look up what the sun's rate of energy delivery to the surface is in Watts per square meter. The sun's input at the surface will vary during the day as the sun angle above the horizon changes but I'll ignore that because I'm lazy and it's too much trouble to take account of. Multiply the heat input/gm of iceberg times the weight of the iceberg in grams to get the total heat required to melt it in 3 days. Divide that number by the sun's surface energy delivery and that gives you the number of square meters required for the lens.

Sure it's possible if you can figure out how to build the lens and keep it stable in the correct position above the berg. Lotta luck.

[David Simmons]

One little, but crucial detail that I didn't add. You have to find out how much of the light from the lens is reflected by the surface of the berg. Since the light hits the berg at various angles because of the rough surface this is going to be a bit of a task. In any case, for example say 80% is reflected. In that case you have to divide the lens size you get from the above method by 0.2. And you also have to figure in the heat transfer between the berg and its environment.

If you want to put it in a sci-fi story of some kind you've got some sticky problems if you want to be accurate. If it's a story for kids I wouldn't use a lens. I'd use a transmogrifier.

[Shagnasty]

I think you have some serious problems with the size of your mirror. There state of Delaware is about 55 billion square feet. A football field sized mirror is only 48,000 square feet. That means that your mirror is over 1.1 million times smaller than the iceberg. Somehow I just can't see the 3 day mark working or even if it ever would.

[oh&s]

Okay, let's say I wanted to melt an iceberg at one of the poles, roughly the size of Delaware for some fiendish evil overlord plot of mine. Could I do it with a giant fresnel magnifying lens (no doubt at least the size of a football field) in a period of a few days? Assume that I'm attempting to do this during the summer region at that particular pole. Or would I need some kind of exotic superweapon to do it?

How's a geo-stationary satellite with a ionised microwave cannon sound. should be cheaper than that magnifying glass. Or you could build a giant trebuchet on the moon and throw boulders at the earth. Then there's the build a nuclear power plant on the pole and send it into melt-down.

[Squink]

Okay, let's say I wanted to melt an iceberg at one of the poles, roughly the size of Delaware...
B-15 (http://www.polar.org/antsun/oldissues2000-2001/2000_1022/bigbergs.html) B-15 was a tabular berg that broke off the ice shelf in March. It measured 180 miles long and 25 miles wide - more than twice the size of Delaware and was probably the largest iceberg ever seen. The only other contender was spied in 1956, but its size could not be confirmed.
...
B-15 stayed close to home and eventually broke into several pieces, now called B-15A, B-15B, etc.
...
•Before it broke apart, B-15 was about the size of Jamaica and weighed an estimated 4 trillion tons.
...
•Most icebergs that calve off the Ross Ice Shelf are thought to be a thousand feet thick or more, only 10 percent of which floats above the surface.
B-15A or B-15B look to comprise about half the original berg, so they're about the size of Delaware, and weigh about 2 trillion tons each. Two trillion tons is 1.8 x 10^15 grams.

[Berkut]

How's a geo-stationary satellite with a ionised microwave cannon soundLike this: "wooooooOOOOOOOOO-BEEEEEEEEEEEEEEEEEEEEEEEE"

[David Simmons]

using Squink's figure for the mass of the berg, assuming a reflectivity of .8, a solar constant of 600 W/m2 and ignoring heat transfere to and from the environment, I get a lens with a diameter of 136 kilometers. In the words of Ralph Kramden, a mere bag a shells.

[Mangetout]

Spray the surface of the iceberg with soot or something (and be prepared to repeat the process periodically as it sloughs off); this will increase the rate of energy absorption.

[InvidiousCourgette]

using Squink's figure for the mass of the berg, assuming a reflectivity of .8, a solar constant of 600 W/m2 and ignoring heat transfere to and from the environment, I get a lens with a diameter of 136 kilometers. In the words of Ralph Kramden, a mere bag a shells.

A 136 km lens is concentrating the light from 156 billion square feet onto an area of 55 billion square feet. So the energy impacting the iceberg will be three times the value that would be there without the lens' presence. I can't see this melting the iceberg in three days. It might be within an order of magnitude or two of the lens size required though.

[David Simmons]

A 136 km lens is concentrating the light from 156 billion square feet onto an area of 55 billion square feet. So the energy impacting the iceberg will be three times the value that would be there without the lens' presence. I can't see this melting the iceberg in three days. It might be within an order of magnitude or two of the lens size required though.

I also questioned this size and I suspect my WAG of 0.8 for the reflectivity is too low. Those with better numbers can have at it.

[BadBadger]

There's a nice article about B15 today in the times. You could always test the mirror first and help these little guys.... right before you cause mass extinction of course..

The Times (http://www.timesonline.co.uk) (just search on B15)

[Tuckerfan]

B-15 (http://www.polar.org/antsun/oldissues2000-2001/2000_1022/bigbergs.html)
B-15A or B-15B look to comprise about half the original berg, so they're about the size of Delaware, and weigh about 2 trillion tons each. Two trillion tons is 1.8 x 10^15 grams.
Yeah, that's a good one, since it's a penguin killer!

[Tranquilis]

Sorry, Tuckerfan!
:D

Looks like you'll have to do it the hard way - can't do it on the cheap.

OTOH, if you wanted, you could build a satellite program, and send a series of big honkin' mirror arrays into orbit. Then you can put a beam of sunlight on it nearly 24x7. Of course, it'll still cost. Savin' penguins ain't cheap. :p

[Tranquilis]

B-15a, by rough calculation, contains ~ 180 cubic miles of ice. Give or take a few tens of cubic miles... :eek:

~90 miles X ~20 miles X ~.1 mile thick

(thickness ranging from 100 meters to 270 meters, depending on which edge you're on)

[Tuckerfan]

Sorry, Tuckerfan!
:D

Looks like you'll have to do it the hard way - can't do it on the cheap.

OTOH, if you wanted, you could build a satellite program, and send a series of big honkin' mirror arrays into orbit. Then you can put a beam of sunlight on it nearly 24x7. Of course, it'll still cost. Savin' penguins ain't cheap. :p
Yeah, but look at the benefits (http://www.fourmilab.ch/documents/rocketaday.html) of doing something. And we'd be saving baby penguins in the process! Won't someone please think of the baby penguins? :D

[moriah]

Well, if it were in the antarctic, it would get sunlight 24/7 during the winter months, albeit at an oblique angle. You'd want to set up hundreds of thousands of mirrors all over the ice shelf to catch the sunlight on a more direct angle and reflect it downward on the ice.

You'd be able to regain the expense of the project by selling tanning bed spaces on your Antenordic Tanning Shelf Spa!

[kanicbird]

Could we use nukes, I think the N. Korians are willing to sell a few?

[Squink]

Could we use nukes, I think the N. Koreans are willing to sell a few?Nukes would work. Using Simmon's 334.9 Joules to melt a gram of ice, and a mass of 1.8 x 10^15 grams, it'd take 6.03 x 10^17 Joules to melt the berg.
A megaton of TNT puts out about 4.18 x 10^15 Joules, so we'd need the total heat from a 144 megaton burst.
Because the berg is so thin relative to its length and width, you'd probably have disperse the nukes in 144 one megaton packages, each buried under 300 feet of ice.

[EmeraldGrue]

You'd need a 1920's-style death ray.

:ducks & runs:

[kanicbird]

Because the berg is so thin relative to its length and width, you'd probably have disperse the nukes in 144 one megaton packages, each buried under 300 feet of ice.

Wow, I would think more would be needed, but then again many ice blocks will be blown away and not melted, others will be vaporized and remove much of the heat, so I still think we would need more then 144 MT's.

[oh&s]

You'd need a 1920's-style death ray.

:ducks & runs:

Oi Cobber.
What do you think a ionised microwave cannon is?

[Squink]

I still think we would need more then 144 MT's. Yeah, that was a calculation of the absolute minimum needed. It showed that a nuclear solution is feasible, but in real life, heat loss through the rising fireball and vaporized water would push the megatonage required up by a good big coefficient.

[Tuckerfan]

Yeah, that was a calculation of the absolute minimum needed. It showed that a nuclear solution is feasible, but in real life, heat loss through the rising fireball and vaporized water would push the megatonage required up by a good big coefficient.
Nah, I mean after all, if NASA can send a bunch of guys up there to drill that far into an asteroid the size of Texas, drop a nuke down the hole, and then have it split the thing cleanly in two when it goes off, 144 warheads should be more than enough on something like an iceberg. ;)

[David Simmons]

Nah, I mean after all, if NASA can send a bunch of guys up there to drill that far into an asteroid the size of Texas, drop a nuke down the hole, and then have it split the thing cleanly in two when it goes off, 144 warheads should be more than enough on something like an iceberg. ;)

The problem is explosions, as was pointed out earlier, is that they blow things apart and don't couple the available energy into the berg in such a way as to melt it. That's a problem with the reactive material of the explosive itself. The explosive charge, or the reactive mass in the case of nuclear, has to be contained long enough for the chemical or nuclear reaction to reach all or the greatest possible fraction, of the active elements.

My computation of 136 km diameter ignored the interchange of energy between the berg and the environment. I don't think that was a very good thing to ignore. It really doesn't matter because no one is actually going to do the experiment asked about in the OP. If someone were to try it, the melting of an iceberg floating in the ocean is a lot more complicated than just putting the proper amount of energy into it and then standing back.

[Sam Stone]

What would happen if something the size of B-15 rolled over? Would it create a Tsunami or something?

[danceswithcats]

Thanks Mangetout. Now I've got the blasted Rolling Stones stuck in my head. ;)

[The Cat]

Just for the record building a nuclear powerplant and "melting it down" would definetly not melt an iceberg the size of delaware althought it might melt a hole in it. Hitting the ice berg with a nuclear warhead would probably not melt an ice berg the size of the deleware. If you could somehow put the iceberg in direct contact with the great nuclear reactor in the sky we call the sun it would melt.