# Extreme Science: Pacific Rim – Imperial Edition

As soon as I saw a jaeger, I said to the guy sitting next to me in the movies, “I wonder how much that thing weighs?” However, it wasn’t until the book landed in my clammy nerd hands that I finally had a means of finding out.

**BEWARE: MATHS AHEAD**

__Preliminary stuff:__

According to the book, Gipsy Danger is 265 feet tall. Taking this measurement, we can gauge GD’s width at about 98ft and breadth at 49ft.

265 x 98 x 49 = 1 287 220ft^{3}, or Gipsy Danger’s volume. However, because there are places GD is less broad and less tall, I cut the volume in half.

1 287 220 / 2 = 265 225m^{3}

We also need to know the surface area of GD’s feet. Assuming her feet are flat, we get:

98 x 49 = 4844ft^{2}

or 2422ft^{2} per foot.

Easy, right?

Gipsy Danger’s volume: 265 225ft^{3}

Gipsy Danger’s bottom-of-foot surface area: 4844ft^{2}

Let’s get down to business.

**SHE FLOATS LIKE A FEATHER**

If you’re anything like me, this scene is one of the most iconic in the entire movie. Gipsy Danger flies over a stormy ocean carried by eight powerful helicopters. Majestic – but feasible?

We’re obviously not dealing with lightweight machinery here. My estimates for GD’s weight were between 1200 and 6000 tons, and perhaps up to 12 000. Pacific Rim is set in the current day and therefore doesn’t have technology that is not yet at our fingertips. Meaning – can eight modern day helicopters carry a load of 12 000 tons?

__Short answer: no.__

The Mi-26 is the world’s strongest helicopter, able to carry a load of up to 22 tons.

So 8 x 22 = 176

If the helicopters are to be believed, Gipsy Danger weighs 176 tons.

But wait a minute. A cubic foot of seawater weights 64lbs. Cast iron weighs 425lbs/ft^{3}. Gipsy Danger’s hull is made of iron, so she should be at least 125lbs/ft^{3}, even with extra leg room.

If we take Gipsy Danger’s weight – 176 tons – and convert it to pounds– 352 000lbs, then divide it by her volume, we can find her weight per cubic foot.

352 000 / 265 225 =0.5lbs/ft^{3}

0.5lbs/ft^{3}

This means Gipsy Danger has a density about that of a heavy gas.

Oxygen weighs 0.09lbs/ft^{3}: Gipsy Danger is only six times as heavy as air. Is she made of tinfoil? No. Aluminium is 162lbs/ft^{3}, 300x as dense as GD.

GD is in fact so light that if we take the surface area of her feet – 4844ft^{2} – and dump her into the ocean, she would only displace the top 2’4″ of water. If she fell onto her back or front, which she would the moment a kaiju breathed on her delicate, feather-light body, her enlarged surface area would mean she displaced merely the top 3 inches of water. In fact, there isn’t much difference at all between GD and a layer of oil on the surface, except that oil is 100x heavier.

I know what you’re thinking: Gipsy Danger clearly weighs more than compressed carbon dioxide. You remember that scene at the start of the movie where GD is wading up to her head in freezing ocean water. She couldn’t do that if she had the mass of an 265 foot tall rubber duckie. Something must be wrong. *The helicopters* must be wrong.

**AND STING LIKE A BEE WITH THE FORCE OF A DECENT SIZED ASTEROID**

According to both book and movie, Gipsy Danger is able to fully submerge in the water. She can also swim.

But if GD can submerge, then she must be able to displace a volume of water equal to her total volume. Because she’s 265ft tall, that means we also have to take increasing pressure at depth into account.

Seawater at the sea level weighs 64lbs/ft^{3}. Seawater at a depth of 265 feet weighs over 562lbs/ft^{3}. This is because of the downwards force exerted by the water above. For every 33′ of depth, the weight of water effectively doubles. This means that Gipsy Danger isn’t just displacing 265 x 562lbs of water for every square foot of her downwards force (which we calculate as the area of the bottom of her feet.) It means that’s she’s displacing surface pressure seawater equivalent to something 369 x times her height. Wow! That’s like you stepping into the bath and displacing 25 tons of water!

So just how much does Gipsy Danger have to weigh in order to punch her way through the sea?

Let’s take our volume, 265 225ft^{3}.

And then a shortcut for our equivalent seawater measurement: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

36 x 33 (for each 33 feet of depth) = 1188

1188 + 9 (for that last 3’4″) = 1197ft depth equivalent

Surface area of GD’s feet = 4844ft^{2}

4844 x 1197 = 5 798 268 equivalent cubic feet of seawater displaced

5 798 268 / 2 (so volume reflects GD’s irregular shape) = 2 899 134ft^{3}

2 899 134 x 0.032 (weight of seawater ft^{3}) = 93 807 tons

There you have it. For Gipsy Danger to walk up to her antenna in ocean, she must have a mass of at least 93 807 tons.

Which means those hearty choppers were carrying 11 725 tons apiece! That is a truly magnificent demonstration of lift. One must wonder that when those helicopters let Gipsy Danger drop into the ocean, they don’t shoot off into the air so fast they escaped the Earth’s atmosphere.

**AND NOW IT GETS CRAZY**

The really fun thing about a giant robot that weighs 93 thousand tons, is that all it needs to do to kill you is to fall on you. But Gipsy Danger is a fighting robot, and she doesn’t lie idly by. If she were to karate chop you at the baseball-pitching speed of 100mph, then her strike would hit at about 12000psi. That’s four times the pressure of a high-powered bullet, exerted across the entire side surface of a hand the size of a banquet table.

In fact, a 770lbs banquet table would have to be travelling at 820 000 feet per second to hit you that hard.

If you consider that a) Gipsy Danger has much longer arms than a human, and b) longer arms means a greater radius and so greater pitching speed, you see that there is virtually no weapon Gipsy Danger could be carrying that would be deadlier than her backhand.

So, can any living creature possibly stand up to a karate chop that would render concrete into a fine mist? Or are tough kaiju more like total kai-woo?

If you’d like to know, shout about it in the comments. I’m also more than happy to have any corrections, considerations, and hilarious bits of information about your everyday. It’s lonely here in the Pacific Rim Nerdpit, and I could use the company.

Until then,

Spend your tokens wisely.

Posted on August 27, 2015, in Blog and tagged funny, mecha, pacific rim, physics, sci fi. Bookmark the permalink. 6 Comments.

I recently did some giant-robot calculations for a story, although I kept them to about 20 feet high. At that height, it would be possible to have a robot with a walking ground-pressure of an elephant standing still… if you could make it out of carbon fullerene. Kind of not feasible right now.

Good thinking. The momentum physics get crazy quickly. Plus the energy requirements are terrific – how did you power your robots?

Ehh, by the time you can make a robot out of carbon fullerene, I figure a superconducting magnetic coil system would probably be viable for power storage. Or a tiny fusion plant. Either of those is what shows up in the walkers in my 2400 stories, but, that’s 400 years future tech. For the near future, I have heard about some strides in lithium ion technology that have brought the power density considerably closer to gasoline. I think that’s with the air-absorbing variety. And then, there’s always gasoline. When something is built like a 20 foot human, there should be some room to stick a gas generator somewhere.

For 200+ foot tall robots I believe the first problem is always that most materials won’t put up with the strain. Not the ground, and not the support structure of the robot itself.

That’s the beauty of future tech: you can do almost anything. I was surprised to read Gipsy Dagger’s hull was made of iron. Then again, the core of her nuclear reactor is described as exposed. There’s no excuse for that: the writer just hasn’t done his research.

Out of curiosity, since you’ve evidently crunched the numbers, what weights/ speeds did you come up with for your robots? You’re welcome to include a link to your books.

Nothing’s finished. For the math, I kinda cheated, because physics is not my forte, nor math. I found out the density of a human of average height, as well as the ground contact (square-inches of contact for the feet), then used the square-cube rule to figure out how those figures would work out at different heights. Then found out the density of carbon fullerene, which is actually not very, and figured out what the ground pressure would be for a human made of carbon fullerene at various heights, keeping all other proportions the same (I love the square cube rule. I use it to keep the sizes of ship classes sensible too). So, my figures are very rough, but I think workable for keeping a story out of insanity-territory. Of course, a robot can also have flatter/bigger feet than a human to further decrease ground pressure, but I mainly intended it as a workability check, to make sure something built out of the proposed material wouldn’t be sinking into the pavement. I would have no idea how to calculate speed, but if I can find which notebook I did the calculations in I could find the weights.

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