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Extreme Science: Pacific Rim – Imperial Edition

PRimperial

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

pr0

*You might get some funny numbers by replicating these figures. End totals reflect the original metric rather than my rounded up feet and pounds.

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 220ft3, 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 225m3

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

98 x 49 = 4844ft2

or 2422ft2 per foot.

Easy, right?

Gipsy Danger’s volume: 265 225ft3

Gipsy Danger’s bottom-of-foot surface area: 4844ft2

Let’s get down to business.

SHE FLOATS LIKE A FEATHER

screenshot_6_17_13_9_32_pm1

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/ft3. Gipsy Danger’s hull is made of iron, so she should be at least 125lbs/ft3, 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/ft3

0.5lbs/ft3

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

Oxygen weighs 0.09lbs/ft3: Gipsy Danger is only six times as heavy as air. Is she made of tinfoil? No. Aluminium is 162lbs/ft3, 300x as dense as GD.

GD is in fact so light that if we take the surface area of her feet – 4844ft2 – 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

Quack

Quack

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/ft3. Seawater at a depth of 265 feet weighs over 562lbs/ft3. 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 225ft3.

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 = 4844ft2

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 134ft3

2 899 134 x 0.032 (weight of seawater ft3) = 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

Oh dear God. More math.

Oh dear God. She’s speaking in equations.

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.

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Extreme Science: Pacific Rim

Final_Four_Jaegers

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

pr0

Metric WHAT? Find the Imperial Edition here!

Preliminary stuff:

According to the book, Gipsy Danger is 81 metres tall. Taking this measurement, we can gauge GD’s width at about 30m and breadth at 15m.

81 x 30 x 15 = 36 450m3, or Gipsy Danger’s volume. However, because there are places GD is less broad and less tall, I cut the volume in half.

36450 / 2 = 18 225m3

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

30 x 15 = 450m2

or 225m2 per foot.

Easy, right?

Gipsy Danger’s volume: 18 225m3

Gipsy Danger’s bottom-of-foot surface area: 450m2

Let’s get down to business.

SHE FLOATS LIKE A FEATHER

screenshot_6_17_13_9_32_pm1

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 1000 and 5000 tons, and perhaps up to 10 000. 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 10 000 tons?

Short answer: no.

The Mi-26 is the world’s strongest helicopter, able to carry a load of up to 20 metric tons.

So 8 x 20 = 160

If the helicopters are to be believed, Gipsy Danger weighs 160 tons.

But wait a minute. A cubic metre of seawater weights 1025kg. Cast iron weighs 6800kg/m3. Gipsy Danger’s hull is made of iron, so she should be at least 2000kg/m3, even with extra leg room.

If we take Gipsy Danger’s weight – 160 tons – and convert it to kilograms – 160 000kg, then divide it by her volume, we can find her weight per cubic metre.

160 000 / 18 225 = 8.78kg/m3

8.78kg/m3

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

Oxygen weighs 1.43kg/m3: Gipsy Danger is only six times as heavy as air. Is she made of tinfoil? No. Aluminium is 2600kg/m3, 300x as dense as GD.

GD is in fact so light that if we take the surface area of her feet – 450m2 – and dump her into the ocean, she would only displace the top 71cm 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 8cm 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 81 metre 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

Quack

Quack

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 81m tall, that means we also have to take increasing pressure at depth into account.

Seawater at the sea level weighs 1025kg/m3. Seawater at a depth of 81 metres weighs over 9000kg/m3. This is because of the downwards force exerted by the water above. For every 10m of depth, the weight of water effectively doubles. This means that Gipsy Danger isn’t just displacing 81 x 1025kg of water for every square metre 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 23 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, 18 225m3.

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

36 x 10 (for each 10 metres of depth) = 360

360 + 9 (for that last 1m) = 369m depth equivalent

Surface area of GD’s feet = 450m2

450 x 369 = 166050 equivalent cubic metres of seawater displaced

166050 / 2 (so volume reflects GD’s irregular shape) = 83 025m3

83 025 x 1.025 (weight of seawater m3) = 85 101 metric tons

There you have it. For Gipsy Danger to walk up to her antenna in ocean, she must have a mass of at least 85 101 tons.

Which means those hearty choppers were carrying 10 637 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

Oh dear God. More math.

Oh dear God. She’s speaking in equations.

The really fun thing about a giant robot that weighs 85 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 160kph (100mph), then her strike would hit at about 12000psi. That’s four times the pressure of a high-powered bullet from a hand the size of a banquet table.

In fact, a 350kg banquet table would have to be travelling at 250 000 metres 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.