I'd always been a chicken when it came to roller coasters. I hated the gut-wrenching drops. I hated the disorienting loops. I hated the scary speed. But as a kid, I loved going to amusement parks even though I spent most of the time waiting for my friends to get off the rides. I waved as they screamed down mega-hills and looped the loops. On several occasions, friends dragged me onto a ride but, thankfully, I managed to escape with my life. So when David Wright, an expert on the physics of roller coasters, told me that lap bars and safety harnesses really aren't necessary on most coasters, I was confused. He said this just as I was about to take my first voluntary coaster ride at Busch Gardens Williamsburg. If not the safety devices, what would keep me from falling to my death? "Roller coasters seem scary without really being scary," said Wright, a professor of physics at Tidewater Community College in Virginia Beach. He said that in all but a few of the coasters that go upside down, the laws of physics keep passengers safely in their seats, no matter how wild -- or upside-down -- the ride. Not only does safety depend on physics, so does the thrill of the ride. I found that after Wright explained the science, roller coasters were less scary and I was prepared to take a ride. What I learned is that the two most important phenomena in coasters are inertia (the tendency of an object to keep doing whatever it already is doing -- moving or standing still) and acceleration. Although the popular definition of acceleration is an increase in speed, physicists consider acceleration to be any change in speed (faster or slower) or any change in direction. The resistance of the human body to those changes -- its inertia -- is what creates the sensation of being slammed back in the seat or flung to the side or lifted to near weightlessness as the coaster hurtles along. The concept of inertia is codified in Isaac Newton's first law of motion. It says that objects at rest tend to remain at rest, and objects in motion tend to remain in motion, unless acted upon by an external force. Newton's second law states that every change in speed or direction requires an outside force. And the third says that for every action or force, there is an equal and opposite reaction. In most roller coasters, all these phenomena come into play as a result of just one force -- gravity -- plus the shape of the track's path. All the other "forces" you feel -- being pushed back or even up -- are not genuine forces. They are what some physicists call "fictitious forces," the result of gravity plus the laws of motion. Wright explains that gravity works its effects through two types of energy: kinetic energy and potential energy. Potential energy is what the cars gain by moving up a hill. Poised at the top and ready for gravity to pull it down, the train has its maximum potential energy. As the train rolls down the slope, this energy becomes kinetic energy -- the energy of motion. This gives it momentum, or inertia, to climb the next hill. However, as the wheels roll, friction and wind resistance convert some of the energy to heat. This is why the following hills can never be taller than the first. The amount of energy the coaster has and the number and sharpness of turns or twists depend largely on the height of the first hill and the amount of potential energy the train acquires at the very beginning. Coasters are designed to work with nature in other ways, too, Wright told me. For example, most coasters have hills in the shape of a parabola -- the natural path of a thrown ball. If you toss a ball, it does not follow a straight line or even circular path. The ball curves -- arcing up, over and down in a shape that geometry calls a parabolic arc. Because coaster hills are designed with this natural curve, they are effective at prolonging the sense of weightlessness for a second or two, lifting you slightly from your seat at the top of some hills. Ever drive too fast over a hill and feel as if your car becomes airborne for a moment? It's the same phenomenon. Your body in motion on an upward trajectory tends to stay in motion as the car (or train, in the case of the coaster) drops below you, forced down by gravity and the road (or the track). The momentary separation, even if only partial, between you and your vehicle gives the sensation of partial weightlessness. Instead of landing you with a thud at the bottom of a hill, the coaster's track reverses the curve on the way down and gives you a similarly prolonged experience with the opposite of weightlessness. Your inertia "wants" to stay in motion -- downward -- while the track forces the train to level out and head up another hill. Once you hit the bottom of the valley, you can feel as much as 3.5 Gs. In other words, you feel as if gravity is three and a half times stronger than it really is. Wright explained that if you're a 100-pound person and you step on a bathroom scale at the moment you hit the bottom the hill, it would read 350 pounds. Learning this information was fascinating, but I still wasn't convinced that roller coasters would be the thrill of my life. I was still afraid that I'd fall out of my seat and plummet to the ground -- harness or no harness. After all, my definition of gravity has always been that when something is not already on the ground, it was forced to the ground. Not always, according to physics. If other phenomena are happening, the results can be dramatically different. The reason for not tumbling out of the coaster as the train turns upside down is what many people call centrifugal force -- something that seems to fling you toward the outside of the curved path you are following. Actually, this is a fictitious force. You feel pushed outward, but in reality you are being manipulated by a combination of forward speed and something called centripetal force. Centripetal force acts toward the center of the curve that you and the train are following. If the track were circular, centripetal force would tend to push you toward the center of the circle. The force is a result of the curvature of the track, which prevents you from traveling in a straight line. Newton's third law of motion, remember, says that for every action there is an equal and opposite reaction. The force holding you in your seat as the roller coaster goes upside down is the equal and opposite reaction to the centripetal force directed to the center of the curve. You can get a sense of how this works by swinging a bucket of water over your head. The faster you swing, the stronger the centripetal force (acting toward the center of the circle) and the stronger the fictitious centrifugal force acting in the equal and opposite direction. Roller coaster loops typically are designed so that the centrifugal "force" is about 2 Gs, or twice the pull of gravity. Since gravity is still pulling down toward Earth at 1 G, passengers feel pushed to their seats with a force equal to the difference -- a comfortable 1 G. After hearing Wright's explanations and watching the coaster fly by several times, I finally mustered enough nerve to try it out. This time, instead of feeling pure fear, I focused on experiencing the sensations induced by the ride. Wright sat next to me, coaching all the way. "Try to lift your foot," he yelled as we bottomed out in one valley. I tried. It was nearly impossible. My foot felt like it weighed a ton. Wright brought along a small weight hanging on the end of a string to show which way the forces would swing it. Although I missed the first demonstration because I kept my eyes shut when we went around a curve, he later explained that the weight stayed over his lap because the curve was banked -- sloped to allow the coaster to speed around the turn without flinging passengers to the outside of the curve. By the next curve, my fear had subsided, and I saw it for myself. The weight pulled the string toward the floor of the car, the same as if we were on a straight, level run. On another ride that did not have banked curves I saw the weight swing outward. While twisting and turning on an inverted coaster, where the train rides under the track, I felt free, as if I were flying and tumbling though the air. When I stepped off the coaster, it felt like my insides had gone through a workout, but surprisingly, I was ready to go again. The ride was truly a thrill, and I felt relieved to have conquered one of my childhood fears. But I still had two questions. The waiting lines for the first and last cars were always much longer than for middle cars. The whole train moves together, so what was the difference? Sitting in front had the obvious advantage that you can see what's ahead of you. But why would someone want to sit in the back, where the main view would be the head of the person in front of you. Turns out, parts of the ride are more exciting there, again thanks to physics. Think about the train cresting a hill. It doesn't begin to speed up on the downhill side until the center of mass -- usually near the middle of the train -- has crossed over. By the time the last car crests the hill, the train has speeded up. Thus, the last car is whipped over the top faster than were the cars ahead of it, giving passengers a stronger sense of weightlessness. My last concern was the whiplash feeling at the end of the ride. I was wondering if there was a way to avoid it. Unfortunately, physics again was responsible. When the train is slowed, by brakes or anything else, the passengers' inertia "tries" to keep them going. The bottom half of the body, in close contact with the train, stops first. The top of the body keeps moving forward until the middle of the body tugs it back into line. After learning these new concepts, I felt more secure in my ability to ride one of these monstrous contraptions. The rush I felt at the end my first ride was exhilarating, and although I was eager to tackle the next coaster of the day, I still had one last fear. I still hated the long, steep drops. So, of course, Wright wanted me to try the tallest coaster in the park, the Loch Ness Monster, which begins with a whopping 114-foot drop, akin to jumping off a ten-story building. As we reached the top of the first hill and started over the edge, I tensed up, clamped my hands to the harness handles, closed my eyes and screamed -- louder than I'd ever screamed before. When we reached the top of the second hill and zoomed down, I screamed again. By the end of the ride, I knew why the screams of coaster riders could be heard all over the park. It's a great way to express the excitement of being catapulted into weightlessness or driven downward to feel three times heavier than normal. The exhilaration also gave me a kind of psychological momentum: It's driving me to want to ride a coaster again, soon. Alicia Cypress is a news aide in The Post's Metro section. CAPTION: How Fictitious Forces Give Real Thrills
First, the concept of a fictitious force: Everyone has experienced it in a car. Floor the gas pedal, and it feels as if something has pushed you back in your seat. That's a fictitious force. What really is happening is that the seat back is pushing forward on you. Fictitious forces are felt to operate in a direction opposite to the real force. In a Car
Why do fictitious forces arise? All objects tend to resist changes in their motion or direction. That's Newton's first law of motion. When the car surges ahead, your body resists -- briefly. As the car accelerates forward, you feel a fictitious force pushing you back. At the same time, gravity pulls you straight down, gives you weight. When you accelerate forward, you feel as if you weigh more but are being pulled in a direction between that of gravity and that of the fictitious force backwards. On a Roller Coaster 1. When the car is at the top of the first hill and moving slowly, gravity pulls down and your apparent weight is equal to the pull of gravity. Everything feels normal. 2. When the car starts down, gravity pulls down the same as ever. The increase in speed produces a fictitious force pushing you back in your seat. The combination of the two forces reduces your apparent weight, making you feel partially weightless in your seat. 3. As your car enters the loop and starts up the slope, your apparent weight increases dramatically. Inertia makes your body "want" to continue down, but the change in track curvature prevents this. You feel your weight (downward as always) plus the fictitious downward force. They combine to produce a very high apparent weight -- two or three times normal. 4. Halfway up the loop, your horizontal motion is forced upward by the curving track, producing a fictitious force that points halfway between horizontal and the track. Since gravity pulls you down at the same time, what you feel is a combination of forces aimed directly at the track. 5. At the top of the loop, the car has slowed because it was climbing against the force of gravity. The fictitious outward, or centrifugal, force is still greater than the downward pull of gravity, leaving a difference just large enough to keep you and the car pressed safely against the track. Why does the last car in a train feel more weightlessness? 1. The train does not start to accelerate down until its center of mass (usually the middle of a fully loaded train) has started down. 2. By the time the last car crests the hill, it is moving upward faster than were the cars ahead at the same point on the track. CAPTION: At Busch Gardens' "Big Bad Wolf," coasting cars hang from a twisting steel track. CAPTION: The "Steel Phantom" at Pittsburgh's Kennywood is said to be the fastest continuous roller coaster in the world.