Two Models for Essay #1 (Summer 1998)


"The Great American Scream Machine"

by Yashi Chaudhari

In 1884 the steam turbine, the fountain pen, and cocaine used as a local anesthetic were among the breakthroughs that changed the world for the better. One can add to that list yet another contribution to mankind. It demonstrates some of the fundamental principles of physics -- without being boring or beyond comprehension. Still scratching your head? It's that machinery that brings out the daredevil in all of us: the roller coaster. Changed the world for the better? maybe for the scarier. But that's the entire point. If you pay money, good money, to be scared to death, while being sure you are not going to die, maybe you should know what you are depending upon to save you.

Roller coasters were originally made of wood and rode on steel wheels. Later versions followed paths of steel and rolled on air-filled tires. But through all the variations, these rides work on the same principle: gravity. The park charges you to take you to the top of the hill, and gravity gives you the rest of the ride for free. Of course, the park also ensures that you get safely back to the starting point -- or you, or a surviving relative, may exercise your option to litigate.

Besides gravity, a roller coaster works because of another physics principle: the conservation of energy. For those who have forgotten, this law states that energy can change from one form to another, but cannot be created or destroyed. With respect to roller coasters, this energy is twofold. It involves potential energy and kinetic energy. Potential energy is stored energy that can be used later, like the anticipation attacks you get when you're mounting the first hill. Kinetic energy is energy that is being used, the energy caused by motion that gives you that sullen pale look.

Riding a roller coaster is similar to a slide except that you ride in a train car rather than by the seat of your pants! Unlike riding a slide, you don't have to climb to the top of the first hill on the roller coaster. A motor does the work. Once you're at the pinnacle, you start with potential energy. As you're plummeting with 60 mph winds roaring at your face, that potential energy is changed into kinetic energy, which you feel as speed. That's when all the shrieking and squawking begins. Just when you thought you lived through your 50+ mph nightmare, the ride goes even faster at the bottom of the hill (60-75mph) because all the potential energy has been converted to kinetic energy.

As you go up to the next hill, and start having palpitations again, kinetic energy is changed back into potential energy and the ride slows down (whew). This conversion of kinetic to potential and vice versa continues as you go up and down hills for the rest of the ride. The total energy does not increase or decrease; it just changes from one form to another.

However, some of the energy is changed into friction. Wind resistance, the rolling of the wheels -- even your weight -- and other factors all use some of the energy. Coaster designers know that friction plays a part in the ride. Therefore, they make each successive hill lower so that the coaster will be able to make it over each peak. How thoughtful of them.

Of course, besides the physics, the designers assure the passengers that they won't go spinning into orbit by providing other measures. There are harnesses outfitted for your torso as well as lap bars that keep you nailed to your seat. The wheels under your train car have little legs or hooked prongs that grip the track below it. Though tracks may vary, they are usually made from steel pipes that are tubular and have a radius of about five inches. Any less and perhaps you shouldn't ride. Steel tracks cannot rival the scariness of creaky wooden frames that seem to always be on the verge of disintegrating below you, but it makes up for this deficiency with new kinds of thrills.

Much of the excitement around roller coaster rides centers on the ones that turn sharply, loop, or go through a corkscrew action. The force that you feel when the coaster makes a turn is called centripetal force. This is the force that causes an object ot move in a circle. Gravity is the force that makes you do down in a straight line, but because the track curves, centripetal force makes you roll along the curve. Making a turn feels as though you are being thrown to the outside of the train car.

The roller coaster somersaults. Ever remember looking at the shape of the curve in a looping roller coaster and wished you hadn't? You may have noticed the teardrop shape. That shape, by the way, is called a clothoid loop. Before the idea to use a teardrop shape came, designers had no success with what seemed to be the logical choice for a loop, a 360 circle. Simple physics doomed that shape. All rides moving in a vertical circle generate centripetal force that presses riders into their seats. At the top of the loop, when the coaster and its occupants are upside down gasping for air, the centripetal force must be greater than the gravitational force or...

Designers can make the ride fast enough (yeah) and the circle big enough (yeah) to create just over 1 g of centripetal force to counteract the 1 g of gravitational force. (g is just a unit of force.) Unfortunately, in order to achieve 1 g of force at the top of the circle, riders would have to be subjected to over 8 g's when they first enter the circular loop. Let's put it in perspective. The space shuttle creates only about 3 g's. At 6 g's you get a nosebleed, and at 9 g's you're a vegetable (unconsciousness occurs). So the 8 g's circular loop is not a pursuable option. The clothoid loop allows for a somersault at a safe 3-4 g's because its circle has a radius that is continually decreasing on the upward swing. This creates a higher centripetal force at a slower speed.

The corkscrew loops are loops that are helical (think of DNA strands or wrestling worms). Only at two points are the passengers upside down: when they're entering and when they're exiting the corkscrew. The physics of this ride is similar to a regular loop. The difference lies in the direction of the centripetal force. With the regular loop, you are confined to a vertical (or up and down) plane whereas with the corkscrew you experience both the vertical and horiziontal (or side to side) planes. This added feature makes it popular among the coaster junkies.

Aside from that, there's no much else to a roller coaster. It's your preference as to what your adrenalin-of-choice may be -- the monolith hills or the seemingly 90 degree turns? (Theoretically, it's not possible at 50 plus mph.) Or is it the teeth-grinding, baby-clenching loops that make you feel sorry for even trying? How about the corkscrew? It might as well be called That Loop That Went Askew. It should be mentioned that the man who made all this possible was La Marcus Thompson, inventor and thrill-seeker. He built the first American roller coaster at Coney Island in 1884. Railcars were pushed up an artificial hill, and down they went. A far cry from the great American Scream Machines that we have today...

I think I'll have a sedative now.


Slutzker, Gary. "All Aboard," Forbes 140 (1987), 96-8.

Walker, Jearl. "The Amateur Scientist: Thinking About Physics While Scared to Death," Scientific American 249 (Oct 1983), 162-9.


"The Golden Gate Bridge"

by Karen Schrader

My sister and her husband used to live in Sausalito, which is on the northern side of the Golden Gate Bridge. My brother lived in San Francisco, and naturally, when visiting them, I would have to travel across the Golden Gate. My fascination with the bridge's architecture and appreciation of its beauty, would often lead me up into the highlands of Marin, where you can get the most spectacular view of the bridge. Sometimes it was so foggy that you could only catch a glimpse of the peaks of the two towers jutting through, but even then, with the sound of the foghorn, it was a sight to behold.

Unfortunately, I think the people who live there and commute across the bridge everyday and sit in traffic and have to pay tolls, probably have a absolutely no appreciation for the bridge. They more than likely have never even considered what it would have been like without the bridge or how many years of painstaking calculations, political battles, surveys, and experimentations actually took place in order for the bridge to be built.

In the early 1900's San Francisco was a fairly booming city that depended mainly on the service of ferry boats. On the weekends there would always be huge lines built up on both the Marin and San Francisco sides waiting to go across. There was no room for expansion. Connection to Northern California was non-existent and the city of San Franciso's population was stifled. Something had to be done.

The city engineer at the time, Michael O'Shaughnessy, used to go around asking prominent bridge builders how they would go about bridging the Golden Gate, kind of as a game. There were so many things to take into consideration. The tip of San Francisco was a little over a mile away from that of Marin. The depth of the water in the middle of the channel was 335 feet. High winds, ocean waves, and strong tidal currents had to be accounted for. Also the location of the Golden Gate was twelve miles from an earthquake fault that had caused severe damage in the past.

The feedback that O'Shaughnessy got on this problem, taking all of these things into consideration, was that the cost for constructing such a bridge would be $250 million. Joseph Strauss, a man with a patent on a bascule bridge (drawbridge) design told O'Shaughnessy that he could design and build the Golden Gate Bridge for under $25 million. He got the job.

What Strauss proposed was a part suspension, part cantilever (several triangles supporting a flat part between them) design. It was functional, but ugly. O'Shaughnessy felt that there would have to be changes made to the design in order to withstand forces of nature, but Strauss was the only one who had actually taken him seriously, and submitted a design at a price he could afford. Strauss was a slick businessman, more than he was an engineer, but he knew how to get the right people together to get the job done.

Strauss got in contact with Leon Moisseiff, the designer of the Manhattan Bridge, and a theoretician on suspension bridges. He asked Moisseiff to come up with a design for a suspension bridge based on the prices and specifications of this cantilever-suspension combination. The design very much resembled what was eventually built.

Many battles were fought. The site was at the entrance to one of the world's greatest harbors. The bridge would have to be high enough for the largest ship to be able to pass underneath at high tide. There were financial issues. Things were costing more money. Geological disputes broke out about whether the rock under the ground was sturdy enough to maintain tons of weight in place during an earthquake. At last the day came when plans could be made.

Two piers would be built. One in the strait, 1,100 feet off the San Francisco shore, and the other at the Marin shoreline. There would be two symmetrical side spans (the parts of the bridge stretching from shore to tower). They would use curved backstays because the heights of land on either side of the strait were uneven. The roadbed would be made of concrete slabs and wide enough to carry six 24-ton trucks abreast.

All of these decisions were made by Charles Ellis, a brilliant man, who was a professor of structural and bridge engineering at the University of Illinois. Ellis is fully responsible for the design of the bridge based on stress tests. He said a suspension bridge "behaves like a clothesline: it sways with the wind, expands in the sunshine, and contracts when it rains or grows cold" (3:106). He came up with thirty-three algebriac formulas to take into account not only the shape and structure of the bridge and the forces of heat, cold, and winds, but had to calculate, in advance, the amount of stress to be handled by each of the bridge's hundreds of suspender ropes. He did the calculations for the design of the towers, taking into consideration peak traffic time at the maximum load during a huge wind storm and how to account for the swaying action this would cause. He was extremely thorough in all of his calculations, but Strauss was an impatient man and time was of the essence. Ellis still wanted more tests done, but Strauss had a deadline. As a result, Ellis was fired. Even though Ellis was responsible for the design of the bridge, he never got the credit he deserved.

It took seven years for the bridge to be completed. On the Marin side things went smoothly. They built a cofferdam (a watertight enclosure constructed underwater and pumped dry to allow for easy construction) and put dynamite in the rock so they could set huge steel bars deep into the ground and then covered them with concrete to anchor them down and keep them from moving. The steel for the towers was manufactured in sections of 15-30 tons in Pennyslvania. These sections would come to San Francisco by boat by way of the Panama Canal. Huge cranes on barges would then lower the steel into place and the workers would rivet and seal each piece as it came down.

The San Francisco side was little delayed A ship had run into the trestle (a big metal-framed barrier on upside down A-frame legsaw) and caused a lot of damage. They decided to just build a fender (the size of a football stadium), pump it dry and use it like a cofferdam to do their building Once the anchorages, foundations and towers were built, they began the cabling. They tied one end of a 1 and 9/16 inch wire rope to the Marin anchorage and ferried 5,000 feet of it across to San Francisco. The rope was then hoisted to the tops of the towers by cranes in saddles they had built. Once they had 25 cables going across, they built foot bridges and catwalks for easier access. It was a long process after that to spin the two huge cables that would be the support of the entire bridge. These cables ended up being 36 inches in diameter, containing some 25,000 wires. They were camped off at every 50 feet where the suspenders would go.

All that was left was to build the roadway. They used copper expansion joints every fifty feet so the roadway would flex with heat expansion instead of buckling under stress. It was said enough concrete was poured for the bridge to lay a sidewalk 5 feet wide from San Francisco to New York.

The aesthetic aspect of the bridge came from an architect named Morrow who used to commute back and forth by ferry and take in the beauty of the place, the colors, the light, and the depths of the sky, the waters, and surrounding landscape. He designed large rectangular portals of varying sizes in the towers (imagine ladders) and on the spaces between the portals (rungs) he put vertical fluting (washboard design) which would capture and deflect the sunlight. The orange-red color we enjoy today, was his idea. He stated that "the magnitude of the structure and its crucial, definitely 'located' position in the landscape, suggests that it should be emphasized rather than played down" (3:219). Credit must go to him too, for the bridge's night illumination. He put in huge flood lights of a sulphuric yellow at the base of the towers that would bounce off each "rung" as they slowly ascended into the night. The San Francisco writer, Jon Carroll, observed of Morrow's architecture in 1981, "who, today, would care this much?"

My sentiments exactly. I am so impressed by the knowledge, intellect, vision, and determination that went into the construction of this bridge. It is a shame our every day hustle and bustle lives prevent us from looking at this creation of science and beauty, this poetry.


There then followed a three item bibliography which has, alas, been lost.
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