(combined with previous
chapter: dropping food without parachuttes, on 3-17-02)
© 2001, 2002, Richard A. Muller
Last Tuesday, terrorists attacked the World Trade Center in New York, and the Pentagon in Washington D.C. In the spirit of this course, I'm going to describe what happened with emphasis on understanding the relevant physics. This should give you a somewhat deeper appreciation of the problems involved in countering terrorism, and in finding the solutions.
The terrorists chose to use the fuel of the airplane as their weapon. They chose transcontinental flights since these flights would have full fuel tanks. The airplanes probably contained 60 tons of fuel each, maybe more. Airplane fuel contains 10x the energy, gram per gram, as TNT. Thus the energy was equivalent to about 600 tons of TNT, more than half a kiloton. However, fuel doesn't explode unless it is well mixed with air. We'll describe what happened in the impact in a later paragraph.
The terrorists chose early-morning flights. This was possibly because, in the U.S., such flights have the best on-time records. The terrorists wanted to have several attacks take place almost simultaneously. Their scheme would work only if the flights left on time.
The planned attack took advantage of basic knowledge of airport security. But this was not a deep knowledge; it was known to almost any technically-competent person.
When you board an airplane, your carry-on luggage is passed through an x-ray machine. It can spot many objects from their shapes, although they don't have good enough resolution to see an object which is camouflaged. I suspect no camouflage was used, because if caught, that would suggest that a terrorist attack was underway, and might alert the security people. Rather than use camouflage, the terrorists probably took advantage of the fact that security regulations allowed the passenger to carry on knives if the blade was less than 4 inches in length. A passenger reported on an airline telephone (or possibly on a cell phone) that a terrorist was using a package knife. This is a knife with a short blade that can be retracted. It is almost as sharp as a razor blade.
In the United States, passengers are not x-rayed. They walk through a metal detector that responds to large metal objects and other conductors. Since humans are somewhat conductive, the detector can't be too sensitive. There are some weapons available that are not conductive and would pass through such a detector. The most obvious is a knife made out of ceramic material. There are also guns available that contain very little metal; they are mostly ceramic.
If there is some suspicion (e.g. the x-ray operator sees something unfamiliar in the x-ray picture of the computer) then they may send you to the sniffer. They take a cotton-tipped swab and rub it on our computer or your luggage. It is placed in a box that has a chemical system for recognizing the most common explosives. If you have built a bomb, then the vapors from explosive will probably be found on your luggage.
The terrorists, knowing all this, planned an attack that would not require using explosives, or a detectable weapon.
After the flights took off, the terrorists took control of the airplanes. We don't have the information to know exactly how they did this, so we can only guess. The terrorists undoubtedly planned to take advantage of the U.S. policy that the airline pilots are expected to cooperate with hijackers. This policy was based on the past success of such cooperation. The best way to maximize the safety of the passengers, in the past, was to cooperate. Do what the terrorists say, and let the experts on the ground negotiate with them. The result is that the terrorists could count on cooperation.
It is not clear that they got such cooperation. Some terrorist reports suggested that some of the crew had been attacked with knives. It could be that the terrorists did not want the pilots to send the "secret code" (the code is not so secret) that alerts the ground that they are being hijacked. If that is the case, then the terrorists would go into the cockpit and kill the pilots with their knives.
In most airplanes they could do this by walking in. If you have flown recently, you know that the door to the cockpit is usually left open. Why not? If terrorists take over the airplane, the pilots are supposed to cooperate anyway.
In the airplane, the terrorists had sufficient training to fly the planes. It does not take much training to do this. Most airplane training consists of learning how to land the plane, how to take off, how to make sure nothing goes wrong, and what to do if something does go wrong. Navigation and flying a plane level is relatively simple. (You already knew this if you watched any of the airplane disaster movies. Keeping an airplane in relatively level flight, even aiming it at an airport runway, is not difficult. Landing is.)
Navigation is likewise relatively easy, at least for the World Trade Center. Even to fly a small airplane, you must learn how to use the navigation equipment. It is also possible that the terrorists used simple GPS systems in the cockpit. These can be purchased for less than $200. They will tell you where you are, how fast you are going, what direction you are traveling, and the distance to your goal (the WTC towers, keyed in ahead of time).
Finally, the terrorists could rely on visual flying. I suspect that they did this, after discovering that they were confused by the navigation systems. Even GPS sounds simpler than it is. As you approach the target, switching back and forth between the modes of the GPS can become confusing. I would guess that the terrorists switched to visual navigation. Flight 11 may have followed the Hudson River.
If you have flown over Washington DC, you may have noticed how difficult it is to pick out landmarks. Even the Washington monument is difficult to spot; from the air, it is very small. The White House is tiny and very tricky to spot. It is possible that the target for American Airlines flight 77 was the White House, but the terrorists couldn't spot it. In contrast, the Pentagon is huge and an easy target. They may have gone to this as a backup -- because they could spot it visually.
The airplane that hit the South Tower of the World Trade Center was steeply banked as it hit; this is evident from the movie taken from Battery Park. Some people have stated that this shows the pilots were highly trained. That is ridiculous. It shows that the pilot had aimed the airplane badly, and was trying a last-minute desperation maneuver to hit the building. Unfortunately, the maneuver succeeded.
As the airplane entered the World Trade Center building, it was torn apart, and the 60 tons of fuel, stored mostly in the wings, was released. Such fuel is highly explosive when mixed with air, but the mixing is not easy to accomplish. Only part of the fuel exploded. (Technically, it was not an explosion, but a conflagration. That's why the sound was muffled.) Most of the force of the explosion blew out several floors of the World Trade Center. The explosion passed around most of the columns, leaving them in place. (The only columns taken out immediately were probably those hit by the plane directly.) Much of the airplane passed through the building and emerged on the other side. This may be why debris from the airplane (including the passport of one terrorist) was found; it was not trapped in the building itself.
The buildings survived the impact. As you look at the films, note how little the upper parts of the buildings move. The antenna on the North Tower hardly shook. The upper part of the building remained vertical. Even the windows didn't break. Neither the impact, nor the subsequent explosion, destroyed the building.
The steel columns were covered with insulation, and were designed to maintain their strength for 2 to 3 hours of burning. However, the material that burned was not office furnature and paper documents. The wings, with their fuel load, probably remained in the building, where they provided fuel for the subsequent burning. The fierce burning that took place over the next hour was slowly fed by the fuel leaking out of the remains of the tanks.
At high temperatures, steel will melt. At much lower temperatures, it weakens. The jet fuel created a holocaust far hotter than planned for in the building. When the columns weakened, they became vulnerable to buckling. When buckling takes place, it takes place quickly. When one column buckles, it puts more weight on the others, and they buckle too. The columns for an entire floor (maybe for several floors) buckled at one time. The upper floors then slammed into the lower floors. The impact multiplied the force on these lower floors, and they buckled. The process continued as each lower floor continued to buckle in turn. In a few seconds, the entire building had collapsed.
Did the terrorists know this would happen. No. This was a new mode for the collapse of a tall building that was completely unanticipated. I can't rule out that some engineer, sometime, didn't write a memo pointing out this failure mode, but it was not well known. If it were, the building would not have had 300 firemen in the building at the time of collapse.
It is the fire that eventually caused the buildings to collapse. It was not the impact of the plane; it was not the explosion.
No. A commercial airplane will probably not be used as a weapon in the United States in the foreseeable future. The reason is simple: without the cooperation of the pilot, the attack is very difficult to accomplish. If the pilot keeps the cockpit door locked, the hijacking suddenly becomes much more difficult. Remember, the only weapon the hijacker had was a knife. In the past, this was sufficient: threaten a passenger, and the pilot will do whatever you ask. In the future, no airline pilot will let a hijacker take control of the plane.
Strengthening the cockpit doors can help. Arming the pilots can help (if they get training). Putting an armed guard on the plane can help, or it could hurt. Unless the armed guard is very experienced, he can be defeated, and that gives the terrorists a gun.
It is worthwhile noting that the terrorists probably did not even try to bring a gun or explosives on the plane. That is undoubtedly because they weren't sure they could accomplish that. They used only weapons that could reliably be smuggled on board.
Whoever is responsible for the attack may well be planning another. "Let me show the United States that it is not over!" What will come next?
All other terrorist attacks that I am able to imagine require much more sophistication than the recent attack showed. Perhaps the most frightening attack would involve biological agents, perhaps anthrax. Such an attack could cause many deaths, but they would not yield the kinds of photos that we have been seeing.
A great worry in the U.S. has been a nuclear attack. News stories today surfaced claiming that Osama bin Laden's organization attempted to buy the components needed for a nuclear weapon. This is not surprising. Such a weapon can be small, and it could yield the kind of devastation that the terrorist might find appealing. The weapon would likely be smuggled into the United States on a small boat, and set off in the harbor. The organization and planning required would be much greater than for the hijacking, but it can not be ruled out. The main argument against this attack is that it is very difficult to accomplish without something going wrong. The terrorist will not have the opportunity to test the nuclear device, and so it may not work.
The United States response to the terrorist threat may include action to minimize the nuclear danger. This could involve US attacks on plants that we feel are designed for nuclear weapon purposes. The United Nations has been prevented from inspecting suspected facilities for this purpose in Iraq, so I imagine that Iraq is expecting an imminent attack of many of its facilities. North Korea is suspected of similar activity. Both Pakistan and India have produced nuclear explosions. The nuclear weapons inherited by Ukraine, Kazakhstan, and Belarus, have supposedly all been removed to Russia. For information, see the Federation of American Scientists website at www.fas.org/nuke/hew/Nwfaq/Nfaq7.html.
As I mentioned above, it probably will not be another hijacked US airplane. It could be a much smaller attack, such as the destruction of one or more airplanes. The easiest way to do this is to ship an explosive in a commercial package that will be detonated when a sensor indicates it is at high altitude. To anticipate this, the US is now prohibiting the shipping of commercial packages on passenger aircraft. A plane may explode, but it will not contain passengers.
Most of the measures being taken by the US government are in anticipation of these alternative attacks. So when the actions being taken don't seem to make sense, consider whether you are thinking about the kind of attack that the government is considering.
Suppose they had hit a nuclear power plant? Most nuclear power plants are designed to take a hit from a fully-loaded airplane. The outer concrete vessel would have absorbed the blow and the inner reactor would not have been affected. No radiation would have leaked.
This was a remarkably simple attack. It required virtually no infrastructure in the United States. It required very little in the way of timing and logistics. The terrorists did not have to obtain explosives. There were not large numbers of people to coordinate. All they had to do was get their people to the airports on time. There was almost no way that it could fail. The attack was characterized by its simplicity and its understanding of the vulnerability of the United States.
Dropping food from airplanes -- without parachutes?
(minor changes made 10/21/01)
© 2001 Richard A. Muller
Early in the Afghanistan war, the U.S. began dropping food and medicine from airplanes, from altitudes perhaps as high as 30,000 feet. And they didn't use parachutes! Isn't the food crushed from the tremendous speed of the impact?
Why not use parachutes? It is a completely new idea to drop humanitarian aid into an area controlled by your enemy. In the past, the danger has always been that the enemy military will take the food and medicine, and use it to help their soldiers. Thus, instead of helping the people, we wind up helping the oppressors.
The prior method of dropping food has been to put it into big containers, and air drop those into the cities and towns using a big parachute. But the military does not want to do that if the town is controlled by the enemy. They see the parachute, and send some soldiers to follow it until it lands. If, instead, you break the aid up into small individual packages, and disperse them widely, then the military will not have the resources to go out and retrieve the packages. In contrast, a poor family will go out and spend an hour, if necessary, to retrieve a pound of flour from down in a ravine. It is a better return on their effort than the same amount of time spent farming. Once they have that food, then the military can try to take it from them, but will usually not succeed. (The people will hide the food.)
Isn't the food crushed? The answer, which seems to surprise many reporters, is "not necessarily." The physics behind this is very interesting, and has important implications for other issues, such as the gasoline efficiency of automobiles. So let's look at the physics.
When an object falls, the force of gravity accelerates it, so it falls faster and faster. The force of gravity is called the "weight." It is typically measured in pounds, or in kilograms. But there is another force on the falling object: that of the air resistance. The force of the air becomes greater and greater as the object moves faster and faster. You can measure this yourself by putting your hand outside of the window of a car. The faster you go, the stronger is the force. Not only that, but the force increases with the square of the velocity. So if you double your speed, the force of the air increases by a factor of 4.
For physics majors only: In the MKS system, a kilogram is a unit of mass. However, in common usage, we say the "weight" of a kilogram of mass is also a kilogram. Even physics professors do this. In Europe, if you buy a kilogram of potatoes, you get potatoes that have a mass of a kilogram, which weighs 2.2 lb. The force that this kilogram exerts on the table that is holding it is, technically speaking, 9.8 "Newtons".
As an object falls faster and faster, the force of air resistance continues to increase, until it matches that of the weight. When that happens, there is no longer any net force on the object. Of course, it doesn't come to a stop. When there is no force on it, it just continues on at a constant speed.
What is that speed? We can measure it, or we can calculate it. The answer depends on how big the object is, but for small packages of food, it is about 100 miles per hour. This is called the terminal velocity.
Isn't that enough to crush food? It would certainly smash an egg. But with a little bit of careful packaging, most food would survive. A strong bag of flour would survive. 100 mph is a little faster than a baseball pitch, and a little slower than a tennis serve (when done by professionals). You can imagine a person catching something thrown at that speed, and not breaking it open, if the bag is made out of tough canvas. (And maybe the canvas bag is surounded by a little bit of padding.)
Why not use small parachutes? You could, and then the velocity of the fall would be even less. But why bother?
Unrequired calculation. For those who are interested, I'll calculate the terminal velocity for a sphere that has a radius of 10 cm. I'll assume the sphere has a density of 1 gm per cubic centimeter, i.e. it is similar to that of water. The physics equation for the force on an object depends on the shape of the object, and so we pick the sphere because the shape has a simple equation. For the sphere, the force is given by
F = (1/2)A r v2
In this equation, F is the force, A is the area of a circle (that's what the sphere looks like to the wind: A =p r2), r is the density of air = 0.001 gm per cubic cm, and v is the velocity.
The force of gravity is given by F = mg, where m is the mass and g is the gravitational constant. For typical physics units, we will use A in square centimeters, p in grams per cubic centimeter, v in centimeters per second. For these units, g = 980 = 1000 (approximately). The object falls faster and faster until the force of gravity equals that of the air. So we take the equation above and set it equal to F = mg. This gives
(1/2)A r v2 = mg
Now we substitute m = (volume)*(density), take the density of food = 1 gram per cubic centimeter, and use volume of sphere = (4/3)pr3. This gives the following equation:
(1/2)(p r2)r v2 = (4/3)pr3g
Plugging in the numbers, and solving for the velocity v, gives v = 5000 cm/sec. Using the fact that there are 3600 seconds in an hour, 100000 cm in a kilometer, and 1.6 km in a mile, we convert this velocity, and get that it is approximately equal to 100 miles per hour.
That's fast, but not too fast. If there air weren't there, an object falling from a height of 30,000 ft would reach a velocity close to 1000 miles per hour, i.e. ten times faster. (And at 10x the speed, it would carry 100x the energy. And if the ground is hard, most of that energy will go into crushing the food.)
How does a parachute work? A parachute is light, so it doesn't add much weight. But when it opens, it is very big. So it has a very large air resistance. The air resistance is proportional to the area. So even at a relatively slow fall velocity, the air resistance is equal to that of the weight of the person using it. The person then falls at that slower velocity. (A person also falls more slowly because of his shape, which is usually not a sphere.)
Another unrequired calculation. How big a parachute do you need to fall at a velocity of 3 meters per second? If you followed the previous unrequired calculation, you realize that you just use the same equations. But now the mass is the same (the object hanging on the parachute), and the area is larger (the area of the parachute). See if you can do it, and whether the answer seems reasonable.
Nice cartoon. This was sent to me by one of our students.