How to Destroy the Universe (2 page)

Conservation of energy is a concept that applies right across the whole of physics. It is an important principle in wave theory, thermodynamics, quantum mechanics and relativity. In 1918, German physicist Emmy
Noether proved that the conservation of energy is a direct consequence of the laws of physics being “time invariant”: meaning that if I drop a stone out of my bedroom window today, then it will fall to the ground in exactly the same way if I repeat the experiment tomorrow.

Of course, not every rollercoaster relies on gravity. Some of the newer designs incorporate launchers to provide the initial boost to gets things moving. These employ mechanical catapults, electromagnets or hydraulic systems that make use of compressed liquid to give the cars a kick down the track. For example, the hydraulic launcher used on the Stealth rollercoaster at Thorpe Park, England, accelerates the cars from 0 to 130 km/h (80 mph) in just two seconds. That's an average acceleration of 18 m/s (60 ft/s) every second, roughly twice the rate you would accelerate by if falling freely under gravity. Physicists call this an acceleration of 2G. It creates a force pushing you back into your seat that is twice as powerful as the gravitational force on your buttocks as you sit reading this. G-forces such as this are an essential part of any rollercoaster experience. You feel them when the rollercoaster is accelerating forward (in the case of launched rollercoasters), accelerating backward (i.e. during braking—this
normally only happens at the end of the ride) or changing direction.

Changes in direction can take place in the vertical plane (passing over a crest or through a dip) or in the horizontal plane (turning a corner). The G-forces you experience in each case will vary according to what it's safe for the human body to experience. The highest permissible forces are those pushing you into your seat at the bottom of a dip. These can briefly reach up to 6G. By comparison, astronauts on the Space Shuttle rarely experience more than 3G. (Although, admittedly, astronauts must endure high G-forces for many minutes during the trip into orbit, whereas on a rollercoaster they last just a split second.) The opposite forces, which lift you out of your seat as you pass over a peak, are typically much lower, at around 2G. The weakest forces are those experienced on rounding a horizontal bend. These should not exceed 1.8G, owing to the weakness of the muscles in the side of the human neck. Most rollercoasters try to ease these lateral forces by banking the track on bends so that some of the cornering force is transmitted down through the body and into your seat rather than pulling sideways on the neck.

The forces you feel when you go round corners are all
down to Newton's laws of motion. These are three laws of physics that English physicist and mathematician Isaac Newton first published in his book
Mathematical Principles of Natural Philosophy
in 1687. The first law of motion says that an object will either remain stationary or carry on moving in a straight line at constant speed unless a force acts on it. This is sometimes also known as the law of “inertia.” It means that a rollercoaster on a straight and level track will carry on moving forever (assuming there's no friction). If the track turns, however, the rollercoaster turns with it. The passengers—which Newton's laws apply equally well to—have their own inertia and their own natural tendency to want to keep moving in a straight line. But instead they feel a force exerted on them by the side of the rollercoaster car as it turns.

Newton's second law of motion explains how the force makes the passengers turn the corner. It draws a distinction between forces and accelerations, and asserts that a force acting on an object causes the object to accelerate in the same direction as the force. If I push a toy car on a tabletop then I exert a force on the car, which makes it accelerate. Similarly, the passengers on a rollercoaster feel the force exerted on them by the car as it turns and as a result of it they are accelerated in a sideways direction.

Sideways acceleration is also what enables a rollercoaster to loop-the-loop without you falling out of your seat. (All rollercoasters have restraints to hold you in, but in all but the slowest loop-the-loops these are unnecessary.) Here, the acceleration acts at right angles to the track, toward the center of the loop, making the rollercoaster and the passengers move in a circle. At the top of the loop, where you are in the most danger of falling out of your seat, the acceleration pushes the seat into your bottom faster than gravity can pull your bottom out of the seat. As a result you stick to the seat. It's a similar effect that makes your washing stick to
the sides of the spin dryer. Physicists refer to the force that causes this acceleration as “centripetal force.” The strength of the centripetal force is determined by the radius of the loop and the speed at which the rollercoaster whizzes round it. The speed is lowest right at the top of the loop, but this is where the force needs to be strongest to stop you falling out. That's why the loops on some rollercoasters aren't circular but teardrop shaped, with a section of tight curvature at the very top to give maximum centripetal force where it is most needed.

Although physicists prefer to talk in terms of centripetal force, most people are more familiar with “centrifugal force”—a force acting in the opposite direction that seems to be pushing them down into the floor of the rollercoaster as it loops. Centrifugal force is a consequence of Newton's third and final law of motion, which states that for every action (that is, every force) there is an equal and opposite reaction (a force pushing in the opposite direction). So, for example, when I sit on a chair, the chair pushes back to support my weight and stop me crashing into the floor. You can also think of centrifugal force in terms of inertia—each passenger's inertia makes them want to keep moving forward in a straight line at a tangent to the loop, in keeping with Newton's first law. As the rollercoaster car turns inwards, following the path of the loop, this inertia pushes the passengers down into the floor.
Considering the centrifugal force also makes it slightly easier to visualize the physics of looping the loop. At the bottom of the loop, both gravity and centrifugal force act in the same direction, making passengers feel extremely heavy in their seats. But at the top, the two forces practically cancel one another out, making the passengers feel almost weightless. It's up to the engineers designing the ride to make sure the centrifugal force at this point is just bigger than the force of gravity to keep people in their seats. Going over a crest in the track, passengers experience the opposite effect to looping the loop. It's rather like being on the outside of the spin dryer—the rollercoaster car drops away from under you faster than gravity can carry you after it, and you rise up out of your seat. Many rollercoaster junkies argue that these “negative G-force” moments are some of the best parts of the entire ride.

Suddenly you lurch forward. The brakes are on and the ride is over almost as quickly as it began. As you disembark you try not to look too disheveled in front of the people queuing up for their turn. But in reality, your internal organs feel like they've been through a food mixer, your head is pounding and you could swear you have bruised ribs from strapping yourself in too tightly. You vow to have another go before the day is out.

• Weather watching

• How to read a weather map

• Predicting the weather

• Number crunching

• Climate modeling

• Chaos theory

• Strange attractors

• Super crunchers

On the night of October 15, 1987, the worst storm in 284 years tore across the south of England, battering homes and property and causing damage totaling £2 billion. Winds reached hurricane force and downed an estimated 15 million trees. And yet, just 24 hours before it struck, weathermen were laughing off suggestions that we might be in for a rough night. They predicted that the storm would fail to make landfall, and would bluster harmlessly up the English Channel. Way-off weather forecasting seems an all-too-common occurrence. But why is it so hard? And what can be done to improve it?

Human beings are obsessed with the weather. It dominates our small talk, stops us getting to work in the winter and regularly ruins public holidays in the summer. Hardly surprising then that our best brains have been trying to distinguish the makings of a balmy Sunday from those of a wet weekend for thousands of years.

In 1835, US scientist Joseph Henry used the newly invented long-distance electronic telegraph to set up a network of weather-monitoring stations across the United States, the readings from which were wired instantaneously to a central office at the Smithsonian Institution in Washington DC. Weather-monitoring stations use a variety of instruments to gather data such as temperature, air pressure, wind speed, humidity and rainfall. Today, the findings of ground stations are supplemented by ships, together with a host of eyes in the sky such as weather balloons, aircraft and satellites, which scan the state of the planet's atmosphere from all angles to get a handle on what the weather is doing now—and what it's going to do next.

Sometimes it is easy to draw up a basic picture of how the weather is going to behave. For example, if a ground station in Florida is registering low pressure
and a ship off the coast in the Atlantic is reading high pressure, it's a good bet that Florida is due for strong winds as air rushes from the area of high pressure to the low. (Over larger scales winds are deflected by the Coriolis effect, caused by the planet's rotation—see
How to stop a hurricane.
)

Lines of constant pressure on a weather map are called isobars. They can be thought of as rather like contour lines on the 3D landscape you get by graphing the pressure at every point on Earth's surface. Pressure differences can sometimes be predicted from thermal effects. Hot air rises and the updrafts act to lower the pressure over warm regions, while cool downdrafts tend to create regions of high pressure. Warm updrafts carry with them moisture that forms clouds as it condenses at high altitude. Temperature differences sometimes appear on weather maps as warm fronts, denoted by a line of red semicircles, and cold fronts, marked out by blue triangles. The arrival of a cold front can cause rainfall—or “precipitation,” as meteorologists like to call it. Warm, moist air rises up above the advancing cold front where it condenses into clouds and then drops back to the ground as rain. When conditions are exceptionally cold the water can fall instead as snow or hail.

This broad-brush analysis is fairly straightforward, and allows forecasters to provide the public with a very general impression of the weather along the lines of “tomorrow's going to be windy.” But what if we need more details—such as how fast the gusts will be in each area, what time of day they'll be at their worst, or indeed whether hurricane-force winds will plow up the English Channel or veer inland to wreak havoc? Predicting the weather in this much detail means solving the mathematical equations that govern the physics of the planet's atmosphere. These equations are fiendishly complicated, coupling together processes such as the fluid dynamics of the air and oceans, heat transfer, atmospheric chemistry and the physics describing the radiation arriving from the sun. In fact, they are so abstruse they're nigh on impossible to solve—at least by the conventional methods most of us used to solve equations in math classes at school. Worse still, the equations are highly non-linear, meaning that small variations in the input variables can bring about wholesale shifts in the outputs, which makes it hard to even solve them approximately.

Physicists attack mathematical problems such as this using the only option left at their disposal: brute force. Or in other words, solving the equations “numerically.”
This works by shoving best-guess numbers into the formulae and then tweaking their values by trial and error until the equations all balance up. The first person to suggest doing this for the weather was the British physicist and mathematician Lewis Fry Richardson. In 1922, he published a book called
Weather Prediction by Numerical Process
. In it, he imagined a vast hall filled with “human computers”: people armed with pen and paper all busily grinding out numerical solutions to the equations describing the weather. A central “conductor” would collate their results and then issue them with new instructions. There was just one snag. Richardson calculated that keeping up with the world's weather in real time would require 64,000 of these mathematical drones—equivalent to the entire population of Palo Alto, California. It seemed the only way to realize Richardson's vision was to come up with a machine that could carry out the calculations automatically. And so it was that numerical weather prediction was put on hold for 20 years, pending the invention of the electronic computer.