SCI/TECH/Physics

There might be a good reason to go see "The Day After Tomorrow," but so far, the only reason we can find is this scathingly funny, spot-on movie review, courtesy of the folks at Intuitor.

Stupid movie physics: Intuitor.com
reviews "The Day After Tomorrow":

This movie looks like a contender for the distinction of Worst Physics Movie Ever. However, it was mostly guilty of gross exaggeration, as opposed to total nonsense like “The Core”.

Jack Hall (Dennis Quaid) is a typical brilliant but tortured scientist who single-handedly figures out that Earth is about to enter an ice age triggered by global warming.

As if this were not burden enough, he's also wracked with guilt over having neglected his teenage son Sam (Jake Gyllenhaal) and alienated his wife. It seems to be the inescapable fate of one who pursues the demanding life of a climatologist.

By contrast, his wife has, apparently, been dedicated to their son. She is a physician and, of course, there are no all-consuming demands there.

As the weather rapidly deteriorates, Sam goes on a trip to New York City and is trapped by a terrifying flood caused by a massive climate-altering storm.

All cell phone service is out and so he calls home on a miraculous water-proof pay phone, which only costs a quarter for a long distance call and connects perfectly. Apparently New Yorkers are so used to the cells that it never occurs to them to jam the land lines with panicky calls for help.

Meanwhile, Jack has run a computer simulation which has forecast the impending weather in New York with almost mystical accuracy. He urgently instructs Sam to stay inside and wait out the storm or he'll be frozen to the sidewalk.

Jack concludes the conversation by promising Sam he'll come for him, never mind that Jack is in Washington DC around 204 miles (328 km) away and the roads are all but impassable due to blizzard conditions.

Okay, maybe we're overly skeptical about Jack's computer simulation. After all, it is based on infallible ice core samples, but there's a reason for doubt.

It's called the butterfly effect and is part of chaos theory. Edward Lorenz discovered this effect in the 1960s while using early computers to model weather.

He found that even tiny differences in starting conditions yielded remarkably different simulated weather. This extreme sensitivity to initial conditions is typical of chaotic systems like weather.

Lorenz postulated that a butterfly flapping its wings in Beijing could eventually trigger a storm in Kansas, hence, the term “butterfly effect”.

Computerized models of chaotic systems such as stock market prices have been built based on historic data. Sometimes they seem to predict short term prices and have attracted investors who should know better.

However, these models typically only work temporarily and invariably fail miserably during times of change. Having an ice age appear in a matter of days would certainly qualify as a time of change.

Surprisingly, “The Day After Tomorrow” never mentions chaos theory. The movie is a montage of scenes inspired by earlier movies.

There are tornadoes from “Twister” (1996), an eerie bird scene from Alfred Hitchcock's “The Birds” (1963), the Statue of Liberty image symbolizing the downfall of human civilization from “Planet of the Apes”, (1968), frozen New York and flooded Statue of Liberty scenes from “AI” (2001), etc.

Yet, "The Day After Tomorrow" takes no inspiration from “Jurassic Park” (1993) scenes in which Malcolm (Jeff Goldblum) babbles endlessly about chaos theory.

The idea that dumping massive amounts of CO2 into the atmosphere can cause global warming is widely accepted but an ice age brought on by global warming seems to defy common sense. How can warming up the climate cause it to become bitter cold?

Yes, the movie does offer some explanation but it might actually make more sense in the context of chaos theory. Chaos theory has its roots in meteorology and causes one to expect weather paradoxes.

After calling home, Sam tries to dissuade others from leaving the relative safety of the library where they have taken refuge from the storm.

Obviously this effort is doomed. No one ever listens to teenagers, let alone nerds or brilliant but tortured scientists. When a nerdy teenager quotes a brilliant but tortured scientist who says to stay put, of course they leave.

True to his word, Jack packs his arctic gear along with his enchanted tent in his trusty pick up and sets out with two plucky friends to rescue his son.

They make it all the way to Philadelphia, a distance of 80 miles (128 km) from New York City, before the road becomes totally impassable. No big deal, they strap on their snow shoes and start walking.

Even though the snow is not packed and the drifts are as high as shopping malls, the snow shoes float effortlessly on top.

When it's time to stop for the night, they have the enchanted tent. The wind may howl and temperature plummet but all is well inside the enchanted tent. No one even sees their breath within its shelter.

Even our limited experience with blizzards indicates it's virtually impossible to see or navigate in such conditions.

It's like wearing a white bucket over one's head. Yet, Jack and his party forge ahead.

True, they do have a GPS system and snow shoes but we doubt that even an Inuit could travel in such conditions. The level of visibility depicted in the movie was crystal clear compared with what would be experienced in a real blizzard.

There are at least two logical ways to dramatize global warming effects:

1) Assume an extremely fast change, say in decades. Show the effects of global warming on several generations of characters - "The Godfather": with polluters rather than criminals.

2) Assume a more reasonable rate of change, say thousands of years. Jump forward a few millennia and depict the aftermath -- a futuristic “Mad Max” with snowmobiles.

“The Day After Tomorrow” does neither, but then it's not about global warming effects. It's about special effects.

The near submersion of the Statue of Liberty is possibly the most notable special effect and illustrates our point.

Using the 305 ft (93 m) tall (including the pedestal) statue as a reference, we estimate the maximum "wind induced storm surge" height to be about 240 ft (72.8 m).

This is about 215 ft (65.2 m) higher than the unusually high storm surge during hurricane Camille (1969) caused by maximum wind speeds near 200 miles per hour (322 km/hr)

A 240 foot (72.8 m) high storm surge would be virtually impossible without help from a catastrophic event like an asteroid strike or nearly instantaneous melting of Antarctic ice.

Not only does Antarctica hold about 90% of all ice on Earth but the ice rests on a land mass. Water produced by melting will raise ocean levels.

By contrast, North Pole ice is floating. Melting it would have little effect on ocean levels, although it might be disastrous for Santa Claus.

The storm surge in the movie eventually recedes but not to its previous level. Again, using the Statue of Liberty as a reference, and allowing for about 20 ft (6.07 m) of snow, the water level had to remain over 150 ft (45.5 m) higher than normal.

To raise ocean levels by 150 ft (45.5 m), about 75% of Antarctica's ice would have to melt.

We estimate this would take about 2.6 million years, assuming that all solar energy available to Earth went entirely into melting Antarctica's ice.

Even if global warming completely melted all the Antarctic ice we would likely never see a storm surge wave break over the face of the Statue of Liberty.

By the time Antarctica thawed, The Statue of Liberty would be corroded into oblivion.

On the other hand, maybe we're supposed to believe that the 150 ft (45.5 m) deep water did not recede because it was frozen all the way to the bottom in a few hours.

After all, the movie showed no flooding in Washington DC even though it's located in a coastal area.

According to the movie, the storm system over New York pulled extremely cold air from the upper troposphere down to ground level where it had a temperature of -151 (-102 ° C) ° F, over 20 ° F (11 ° C) colder than the coldest climatic temperature ever recorded on Earth.

Air in the upper troposphere is at roughly 1/10 as much pressure as air at the ground.

Increasing its pressure would tend to raise its temperature. If the air temperature at ground level were -151 ° F it would have to be even colder in the upper troposphere.

Furthermore, the volume of air would decrease by about a factor of 10 as it was lowered from the troposphere to the ground.

This means an enormous volume of air would have to be sucked out of the upper troposphere.

Getting it to move from a low to high pressure area, while not impossible, would be highly unlikely.

Lowering the temperature of water to its freezing point is not enough to cause it to freeze.

It's still necessary to remove the heat of fusion and that's substantial. This heat ends up in the air and it takes relatively little heat to elevate the air's temperature.

We calculate that freezing 1.0 cubic meter of water would require a minimum of 2,500 cubic meters of air at a temperature of -151 ° F.

But wait, we have assumed that the air is allowed to heat up to a temperature of 32 ° F or the freezing point of pure water.

Hence, it no longer can flash freeze people. (Note: For simplicity we have used fresh rather than salt water data.)

To match the movie's depiction we probably should assume that the air only heats up to say -149 ° F.

This means that we need 232,000 cubic meters of cold air at the ground level pressure of one atmosphere.

However, this air is from the upper troposphere where it occupies a much greater volume of around 2.3 million cubic meters due to the lower pressure.

Freezing all the water in New York harbor and the surrounding area to a depth of 150 ft would probably require most of the air in the upper troposphere for a radius on the order of 1500 miles (2400 km).

Getting all this air to New York Harbor in a few hours would require supersonic wind velocities.

In the movie, we learned about the -151 ° F temperature level when a group of U.K. helicopters encountered them and immediately crashed due to frozen fuel lines. The kerosene-type jet fuel commonly used in commercial jets and military aircraft freezes at -40 to -52.6 ° F ( -40 to -47 ° C)

Yet, these aircraft often fly at altitudes above 30,000 ft (9100 m) which is in the upper part of the troposphere where the super cold air supposedly came from.

Even aviation gasoline freezes at about -76 ° F ( 60 ° C) and so we're at a loss to explain what the helicopters were burning, let alone how the air got so cold.

It's highly doubtful that temperatures of -151 ° F could ever be attained near the ground by sucking super cold air out of the troposphere.

Even if it did happen, it's doubtful that seawater could be frozen to a depth of 150 ft in a matter of hours. This pretty much rules out the possibility that the storm surge remained high because it was frozen in place. Indeed, there's really no reasonable explanation for any part of the storm surge scenes.

If the 240 foot (72.8 m) storm surge had occurred it would have done far more damage than depicted, especially near the harbor.

If we assume that the surge behaves like a tsunami, we can use the following formula to calculate its velocity when it hit the shore:


v = Sqrt(gh)

Where:
v = wave velocity
g = acceleration of
gravity
h = water depth

Using h = 240 ft yields a velocity of 59.7 miles per hour (96.2 km/hr).

The 1960 Chilean tsunami, by comparison, had a maximum height of about 82.4 ft (25 m) giving a calculated velocity of 35 miles per hour (56.3 km/hr).

It was one of the most destructive tsunamis on record and is credited with killing 333 to 2000 people along the Peru/Chile coast.

When it hit Hilo Hawaii 14.8 hours later, the maximum wave height reached 35.3 ft (10.7 m) giving a calculated velocity of 22.9 miles per hour (36.9 km/hr). It devastated downtown Hilo and killed 61 Hawaiians. Parking meters were bent to the ground.

It would be very difficult to mathematically predict the exact damage done by the high velocity storm surge in “The Day After Tomorrow”.

However, we can get a rough idea of its destructive potential by comparing it to a wind with similar kinetic energy.

The famous Bernoulli equation indicates that when a moving fluid like a wind or water flow is stopped, say by running into a wall, the kinetic energy of the flowing fluid will be converted into a pressure acting on the wall. Obviously if the pressure is too high the wall collapses.

To approximate how the pressure created by flowing water compares with wind, we can use the kinetic energy term from Bernouli's equation and solve for the velocity of air as follows:

1/2 (density water)(velocity water)2 = 1/2 (density air)(velocity air)2

1/2 (1027 kg/m3)(96.2 km/hr)2 = 1/2 (1.25 kg/m3)(velocity air)2

velocity air = 2760 km/hr

This means that from a kinetic energy standpoint the 240 ft high storm surge is comparable to a 1710 mile per hour (2760 km/hr) wind!

To put this into perspective, the wind at ground zero underneath the Hiroshima nuclear bomb blast was estimated to be about 920 mile per hour.

The 1960 Chilean tsunami had the kinetic energy equivalent of a 252 miles per hour (406 km/hr) wind when it hit Hilo. The highest tornado wind ever measured was 318 mile per hour (512 km/hr)

Again, our analysis is very simplistic, but within reason. It indicates that damage caused by a tsunami should be comparable to damage caused by a major tornado and, indeed, both do pretty much wreak havoc on anything in their path. Clearly a 240 ft. high storm surge would be even more devastating.

Note, that we deliberately ignored the gravitational potential energy term in the Bernoulli equation for the sake of simplicity.

This term accounts for the considerable static pressure created on a wall by the weight of water standing against it and is far from trivial. Static pressure would be 7.25 atm at the bottom of a 240 ft storm surge. A pressure this high acting on one side of a wall could easily cause it to collapse.

While it looks solid, the Statue of Liberty is merely 0.09375 inch (0.237 cm) thick copper sheet metal covering a skeletal support structure.

If the water outside it quickly rose to a level of 240 ft without simultaneously flooding the interior to the same depth, the statue would be crushed like a giant soda pop can just from static pressure due to the weight of water around it.

The statue's designers clearly did not envision that it would have to resist the static pressure caused by submersion or the dynamic pressure of having a gigantic wave break against it.

Wind tends to create its maximum pressure on the upper portion of buildings while flood water creates it on the lower part. This also tends to complicate a comparison between the two.

However, it does not indicate that flowing water is less likely to destroy a structure. The columns at the bottom of skyscrapers have to carry the buildings' weight. Take out a number of these and the whole structure collapses.

Horizontal force on a column with a high vertical load is a prescription for disaster and this is exactly what a swiftly flowing flood would create.

To illustrate, cut a three-inch piece of soda straw and hold it as though it were a column between your thumb and index finger.

Your thumb is like the floor and your index finger like the ceiling of a building. Squeeze so that the straw is compressed (but not bent) similar to the way a column in a building would be compressed by the weight of the floors above it.

Push lightly on the middle of the straw in a direction perpendicular to the simulated weight and the straw will immediately buckle.

Obviously a column holding up a skyscraper is much stronger but it will still tend to fail if it's hit sideways with a wall of water.

The static and dynamic pressure of the water against buildings would immediately implode submerged windows as well as sections of wall.

If the water rose slowly, air inside the structures could escape through cracks and vents fast enough to keep the enclosure from over-pressuring.

However, slam a wall of high velocity water against a well sealed building and the imploding windows would likely create an air pressure shock wave similar to setting off a bomb.

While it's hard to estimate the potential damage, this pressure wave would at least blow out some windows on floors above the water line.

In the worst case, it would destroy the building.

All things considered, the huge storm surge would probably demolish the Statue of Liberty and knock over buildings near the harbor causing them to fall domino-like into other buildings. The effects would be devastating, especially where the wave initially came ashore.

The near destruction of LA by numerous giant tornados is possibly the second best special effect and is about as scientifically sound as the Statue of Liberty scene.

According to NOAA data, there has never been a tornado in California rated higher than an F1 on an F1 to F5 scale. Furthermore, there has never been a single recorded tornado-caused fatality.

Obviously, California does not have the terrain required for producing large violent tornados. The tornado scene would have been bizarre even in Kansas but in LA it's positively, um... overblown.

During its more scientific moments, the tornado scene teaches us important moral lessons.

For example, never attempt acts of extramarital sex, take frivolous pictures, nor work as a news correspondent during big storms, unless you have a death wish.

Before leaving on his rescue mission Jack is finally asked to advise the president. Of course, Jack must suggest something dramatic. Forget northerners. They're doomed. Evacuate the southern half of the United States to Mexico.

Having once been through an evacuation from Lake Jackson Texas to Houston (a distance of about 60 miles) when a hurricane loomed in the Gulf, we can imagine how an evacuation to Mexico would work.

In our experience, cars were bumper to bumper and moved 20 miles per hour, that is when they moved.

This was several thousand people leaving in sunny weather a few days ahead of the hurricane. The evacuation to Mexico would have involved tens of millions of people traveling hundreds of miles through a raging snow storm.

After giving the evacuation order, the president and his motorcade leave and end up frozen to death in a traffic jam. Oops, maybe there was a reason for not listening to brilliant but tortured scientists.

Here's a thought: if Jack's computer program really could accurately predict future weather and he knew that the storm was only going to last 10 days, why not simply tell people to bundle up and wait it out?

Surely riding out a storm trapped in one's home is a lot better than riding it out trapped in one's car.

Sam along with a small group of friends is eventually forced to leave the library's safety in a quest for medicine.

As they do so they're attacked by a group of vicious wolves escaped from the zoo. In a city with millions of people and corpses everywhere, the wolves are unable to find a meal and so attempt to dine on Sam and friends. Evidently, all the hot dog and pretzel carts washed away in the earlier flood.

Just when he thinks he's safe from the wolves, Sam looks up and realizes that he and his friends must run for their lives.

They're in the eye of the storm and it's about to turn nasty cold. As he runs back to the library's haven he is chased by a sinister cold wave which frosts everything behind him.

It was supposed to be a serious moment but between the wolves and the sinister frost, people in the theater (along with us) were giggling out loud.

The temperature had been at arctic levels for days. How in the world could there be enough moisture in the air to form frost?

Even if there were, why would frost suddenly form on solid surfaces? With a sudden dramatic air temperature drop, solid surfaces would initially be warmer than the air. Any moisture in the air would condense into a frozen version of fog.

By now, Jack has already lost one friend and is dragging the other, who's unconscious. Jack also looks up and is likewise horrified to discover that he's in the eye of the storm and about to be flash frozen.

He pushes his remaining friend through an opening into a hamburger joint, then dives in afterwards. They survive by turning all the gas burners to high.

We are mystified. How did he get into the eye unless he walked through the storm and why would one side of it be that much more dangerous than the other?

Jack eventually makes it through the storm and is reunited with Sam. We can't help wondering why he bothered to make the trip.

Once there, he simply radios back and a helicopter arrives just in time for the quintessential Hollywood ending. Why didn't he merely stay home, not get his friend killed, and helicopter out to the library when the storm ended?

But wait. The helicopters are in Mexico over 2000 miles from New York City and even the venerable Chinook helicopter only has a range of 1250 miles. Blackhawks are even worse with a range of a mere 373 miles. Where are they going to refuel?

The population of the United States is about 290 million. If half were trapped in the storm and a whopping 90% died, there would still be 14.5 million people in need of rescue.

At best, a Chinook can only carry 44 people and a Blackhawk only 14. A helicopter evacuation works out to around 330 thousand Chinook rides.

The logistical problems of evacuating survivors to Mexico would be a nightmare. Even with around-the-clock effort, we estimate it could take over 18 months.

The Hollywood ending did rescue us from having to endure more hackneyed disaster movie dialog.

Okay, at least the special effects were reasonably entertaining, even though they were based on badly flawed science.

Sadly, however, it looks like the world will run out of fossil fuels long before Hollywood runs out of inane scripts and special effects portraying smoke and mirror physics.

Intuitor rating: RP (Retch)

© Intuitor.com. Used with permission.

Find more offbeat sci-tech in the July 2004 issue of "Arte Six"