by Tom Rogers
When it hits the shore, the giant 240-foot- (72.8-m-) high wave would again be far more devastating than depicted. By comparison the Indian Ocean tsunami on December 26, 2004, was as much as 115 feet (35 m) high as it rolled ashore in Sumatra near the epicenter of the earthquake that caused it, killing about 320,000 people. In Thailand the tsunami was down to at most 34.7 feet (10.6 m) high with a death total of 14,000 people. By the time it reached India, the tsunami was less than 8 feet (2.4 m) high—a mere shadow of its younger self—yet still caused about 22,000 deaths. Overall, more than 400,000 people died as a result of the tsunami’s devastating power. A 240-foot- (72.8-m-) high super-tsunami hitting New York City is going to make the December 2004 tsunami look mild in terms of death and destruction.
Static water pressure would be 7.25 atmospheres (atm) at the bottom of a 240-foot wave as compared to an estimated pressure of 4.1 atmospheres under the Hiroshima atomic bomb blast. Like the Statue of Liberty, a building would be unaffected by the static water
SUPER-TSUNAMI MATHEMATICS
Mathematically predicting the destructive potential of the super-tsunami would be extremely complex. 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 such as a wind or water flow is stopped, say, by running into a wall, the kinetic energy of the flowing fluid will be converted into 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:
Using the above relationship, a sedate water velocity of ten miles per hour will be equal to an air velocity of 290 miles per hour from a kinetic energy standpoint—the equivalent of the wind speed in a category F5 tornado. Ramp the water velocity up to thirty-five miles per hour and the available kinetic energy would be equivalent to a 1,000 miles per hour of wind, similar to the wind speed under the Hiroshima bomb blast, estimated at 980 miles per hour (1,580 kph)26. Since anyone attempting to measure it would likely be killed, good data for the velocity of a tsunami after coming ashore is hard to find; however, it’s typically estimated to be between ten and thirty-five miles per hour. A 240-foot-high wave would probably be faster.
pressure if the interior and exterior water levels rose at the same rate, but that’s unlikely. The first wall to be hit by the wave would be instantaneously submerged, while the wall on the opposite side of the building remained dry.This condition, however, would not last long. A wave traveling thirty-five miles per hour (56 kph) will cover a distance of 51 feet (15.5 m) in a second. With the exterior water level rising around the building’s entire perimeter in a matter of seconds, the resulting exterior water pressure would be more than enough to simultaneously implode windows and sections of walls. The water gushing in would act like a giant piston compressing air in the building into a high-pressure shock wave that would travel upward, blowing out windows and sections of wall as it progressed. It would be followed by a water hammer gushing upward though every possible path. The resulting structural damage could bring the building down, but that’s only part of the picture.
From a kinetic energy standpoint, a wall of water traveling 35 miles per hour would be equivalent to a 1,000-mile-per-hour (1600 kph) wind! Since the wind speed directly beneath the Hiroshima bomb blast was estimated to be 980 miles per hour (1,580 kph), it’s clear that a 240-foot-high super-tsunami would be horrendously destructive. By comparison, the highest tornado wind speed ever measured was 318 miles per hour (512 kph). Wind pressures act on almost the entire side of a building from top to bottom, while wave action will affect mostly the lower part, so comparisons of relative kinetic energy don’t necessarily correlate with damage. However, weakening a building’s support at its base is an invitation for collapse.
The combination of static pressure from the depth of water and dynamic pressure from the wave’s motion would likely cause structural failure in the affected high-rise buildings with the possibility of a domino-like collapse. Even if a building did not collapse into one of its neighbors, the collapse would cause a local tsunami as falling building materials slammed into the water. Few structures would be capable of withstanding the abuse of being hit by a super-tsunami followed by the wave action of local minitsunamis. New York City would largely lie in ruins.
Why Buildings Collapse
The collapse of the twin towers on 9-11 due to airplane impact and resulting fires, along with the destruction of the Alfred P. Murrah Federal Building in Oklahoma City from a truck bomb, have demonstrated to most people that modern buildings are not as indestructible as they seem. Yet conspiracy buffs seem convinced that only explosives planted on the inside can bring a modern building down. For the Murrah Building, conspiracy theories generally go something like this:
The buildings were constructed of such and such materials rated for thousands of pounds per square inch, how could an explosion outside the building with far less pounds per square inch demolish it? Obviously, explosives were planted inside.
Simply put, the “thousands of pounds per square inch” refers to the maximum internal stress the material can handle before failing catastrophically, not the maximum external pressure, pressure that might be caused by a bomb blast. Stress and pressure are very different quantities, although they use the same units (psi). Stresses are internal and depend on an object’s material and shape as well as the load applied to it. Pressure is a type of external load. Calculating stresses is too involved to describe in anything less than a text book, but suffice it to say that the internal stresses on the structural parts of buildings are usually far higher than the external pressures on them. For example, the maximum wind pressure loads buildings are designed to withstand are generally less than 0.74 pounds per square inch (0.05 atm). Although this load sounds miniscule, such a pressure would have created a sideways force of about 270,000 pounds on the vertical wall of each floor in the Murrah Building for a total force of over 2.4 million pounds on the building. To produce such pressures and forces with natural phenomenon would require something like a recordbreaking hurricane or a direct hit by a tornado. The Oklahoma bomb blast pressure was easily higher.
Elastic stability or buckling resistance of the columns supporting a building’s load is also a factor in collapse. Cut a soda straw about 3 inches long and compress it like a column running between your index finger and thumb. The straw will withstand a considerable force before it buckles. Repeat the experiment, only this time push lightly sideways on the straw as you compress it. The straw will quickly buckle. Sideways forces applied to support columns by explosions or walls of water are a very bad idea if the goal is to keep a building standing.
Similar conspiracy theories—multiple bombs planted by insiders—exist for the twin towers. According to conspiracy theorists, the fire inside the towers could not have melted the steel structure that supported the top floors, thereby leading to their collapse, and here the theorists are right. The steel support beams would not have melted, because they didn’t have to. At around 800 degrees Fahrenheit (430ºC) steel beams or trusses begin to significantly lose both their strength and stiffness.
In the twin towers most of the supporting steel columns were located in the outer walls and were connected together by long, light-weight steel trusses in the floors. With fire temperatures inside the towers easily exceeding 800 degrees Fahrenheit, the floor trusses sagged. Stiff trusses normally create little sideways force on the steel columns in the outer walls. But let the trusses sag, and they become more cable-like and capable of creating sideways forces many times the downward weight of forces acting on them. As a result of these forces, the outer wall’s columns were pulled inward until they snapped, sending the whole top of each tower careening down on the floors below in a chainreaction collapse.
Conspiracy buffs counter by claiming tha
t no modern building has collapsed due to fire. Maybe it has something to do with the fact that, except for the twin towers, no modern building has ever been hit at full speed by a fuel-laden jumbo jet that destroyed a significant part of the building’s support structure and caused parts of the floors in the impact zone to collapse on those below, not to mention leaving the weight of many jumbo jet parts scattered on the floor in the burning inferno. From the beginning, the floors and structures in the impact area were overloaded.
The conspiracy buffs continue by asking how a few collapsing floors could bring down an entire building. Of course, they fail to note that the “few” collapsing floors (thirty-three floors for tower two, and seventeen for tower one) would have been tall enough in themselves to be major buildings in many communities.
Floors are usually designed for higher-pressure loads (not including the weight of the floor itself) than walls, but the maximum pressure is still generally less than 0.05 atmospheres. Pile the concrete and steel debris from several collapsed floors atop a good one, and its pressure rating is easily exceeded. But, in the twin tower collapse, the chunks of debris were not just piled, they fell with considerable impact. The result was an almost instant failure of the floor being struck.
The floors might have simply pancaked to the bottom, leaving the walls standing like a huge hollow tube, except that the floors were firmly attached to the walls. Overloading a floor enough to make it sag and collapse would have produced a substantial sideways force on the walls, pulling them inward, similar to the effect of making the floors sag from high temperature only on a much faster time scale. The result: structural steel in the walls would have buckled and snapped as the floors failed.
Conspiracy theorists continue by asking how a building collapse could pulverize the structure’s concrete and give the appearance of a blast wave emanating outward. The answer is straightforward: Energy used to lift building materials over a construction period lasting years was stored in the buildings as potential energy—an amount roughly equal to 500,000 pounds of TNT (230,000 kg TNT) per tower, easily enough to pulverize much of the building’s concrete. When each tower collapsed, all the energy was released. As top floors fell they acted like a gigantic piston compressing the air in the floors below. This compressed air had no way to escape except by blasting outward and downward, taking anything loose with it, such as concrete dust. By the time the building approached the ground, the velocity of the escaping air was high enough to throw hapless victims violently sideways. Placing a few thousand pounds of explosives inside the building would have made little difference.
Since the super-tsunami in The Day After Tomorrow does relatively little damage to the Statue of Liberty, the statue once again provides a useful reference point when the water eventually recedes. Allowing for about 20 feet (6.07 m) of snow, the water level had to remain over 150 feet (45.5 m) higher than normal after the tsunami had receded. To raise ocean levels by 150 feet (45.5 m), about 75 percent of Antarctica’s ice would have to melt. That would take about 2.6 years, assuming that all solar energy available to Earth went entirely into melting Antarctica’s ice and that the ice was already warmed up to 0 degrees Celsius26 Obviously, this is only a fraction of the time required for melting, and so a super-tsunami with an immediate 150-foot increase in ocean level caused by melting ice is absurd.
The super-tsunami depicted in the movie could have been a storm surge brought on by high winds, but that’s also ridiculous. At 240 feet (72.8 m) high, the super-tsunami is about 215 feet (65.2 m) higher than the unusually high storm surge that occurred in Louisiana during hurricane Camille (1969). That surge was caused by maximum wind speeds near 200 miles per hour (322 kph)27. A 240-foot- (72.8-m-) high storm surge would be virtually impossible without help from a catastrophic event such as an asteroid strike or massive land slide. Even then it’s unlikely that New York City would be inundated while Washington, D.C., was left untouched (as depicted in the movie).
On the one hand, the giant wave produced far less damage in the movie than would have been experienced in reality had such a wave existed. On the other hand, there were no conditions in the movie that could have caused the wave in the first place. It’s classical Hollywood logic: two conflicting mistakes equal perfection. Serious as it is, global-warming effects are not going to make the same dramatic entrance on the world’s stage as they did in The Day After Tomorrow. The behemoth globalwarming-induced wave is nothing more than a global-sized exaggeration; the potential long-term dangers of global warming are not.
THE ULTIMATE ANTI-CHAOS THEORY
The biggest surprise in The Day After Tomorrow is the total lack of reference to chaos theory. The theory had its roots in meteorology, and while far too rich to explain in a few paragraphs it can be partly understood by defining the “butterfly effect,” a term coined in the 1960s by Edward Lorenz28. According to Lorenz, chaotic systems such as the weather are extremely sensitive to initial conditions, and even slight changes in initial conditions can radically change such a system’s behavior over time. Weather is so sensitive that, theoretically, air currents caused by a butterfly flapping its wings in Beijing could eventually cause a tornado in Kansas. Imagine what a radical change such as global warming could do.
It’s not as though Hollywood is unaware of chaos theory— in Jurassic Park [PGP-13] (1993) Malcolm (Jeff Goldblum) babbles endlessly about it. Although his arguments were muddled, they indicated that dinosaurs brought back to life in the movie would eventually become able to reproduce in spite of precautions to the contrary. Sure enough they did, but big deal. If humanity could wipe out everything from the woolly mammoth to the carrier pigeon, then surely a few hundred dinosaurs couldn’t be all that hard to annihilate. It’s not like they would be hard to find.
Although The Day After Tomorrow does offer some explanation for how global warming can trigger an ice age, the paradox doesn’t make sense at a gut level. That’s not to say the concept is wrong, but rather an ice age would have seemed more plausible in the context of chaos theory. In that setting, unexpected or even opposite results seem reasonable. But referring to chaos theory would have made the magical weather predictions of the movie’s climatologist hero look silly. Weather accuracy is very sensitive to data available at the time a weather forecast is made—the greater the amount and accuracy of data, the greater the accuracy of the prediction, but only up to a point. Lorenz claimed that weather predictions could never be accurately made more than about two weeks ahead because that was the limit of humanity’s ability to collect and analyze the required data. Extending beyond that time span would quickly require a forecaster to know the condition of every atom in the universe, he claimed. Nevertheless, the movie’s climatologist nailed his forecast of a deadly ice-age-producing storm days ahead of time by using a computer simulation based on a few ice samples from Antarctica—what a guy.
With such a dire prediction in hand, what can be done? Why, of course, evacuate the entire southern United States to Mexico— northerners are doomed, but they may actually be the lucky ones. Imagine this joy: being trapped for endless days in a traffic-snarl hundreds of miles long during a major blizzard. What a great problem-solving idea: the ultimate antichaos theory—death.
Summary of Movie Physics Rating Rubrics
The following is a summary of the key points discussed in this chapter that affect a movie’s physics quality rating. These are ranked according to the seriousness of the problem. Minuses [–] rank from 1 to 3, 3 being the worst. However, when a movie gets something right that sets it apart, it gets the equivalent of a get-out-of-jail-free card. These are ranked with pluses [+] from 1 to 3, 3 being the best.
[–] [–] Highly exaggerated storm conditions.
[–] [–] Seriously underestimating the damage that would be caused by highly exaggerated storm conditions.
[–] [–] Seriously overestimating or underestimating damage done to structures by natural phenomena or acts of terrorism. (Movies should use computer simulations
and engineering studies to make these estimations.)
[–] Scientists spouting dramatic and authoritativesounding solutions or pronouncements that make no sense from a logical or scientific perspective (such as evacuating vast territories in the middle of a blizzard).
[–] Evacuating vast territories in the midst of foul weather. (Please, didn’t hurricane Katrina teach us anything?)
[–] Incredible computerbased predictions of chaotic systems, such as weather systems or the stock market, made in ridiculously short periods of time and based on flimsy amounts of data.
CHAPTER 18
THE MOVIEMAKER’S COOKBOOK:
Cigarettes as Lighters, Exploding Cars, Burning Bugs, and Other Recipes for Foolishness
