The oldest roller coasters were the “Russian Mountains” which were essentially mountains of ice often reinforced by wooden supports. They were popular in 17th century Russia mainly among the Upper Class. The slides were built to a height of 70 – 80 feet and consisted of a 50 degree drop. Catherine the Great herself was a fan of these constructions and many of these can be found in her palaces. The first roller coaster in the United States was constructed by a mining company in Summit Hill, Pennsylvania – The Mauch Chunk gravity railroad of 1827. A major breakthrough for roller coaster came with LaMarcus Adna Thompson’s 1884 Gravity Switchback railway in New York. This track design was soon replaced with oval complete circuit.
In 1885, Phillip Hinkle introduced the first complete-circuit coaster with a lift hill, the Gravity Pleasure Road, which was soon the most popular attraction at Coney Island. In response, LaMarcus Adna Thompson patented in 1886 his design of roller coaster that included dark tunnels with painted scenery. “Scenic Railways” were to be found in amusement parks across the county. The concept of Vertical Loop was explored for the first time in 1895 with the Brooklyn “Flip Flap”. The best known historical roller coasters, The Cyclone, was opened at Coney Island in 1927. The coastersso far were all made with wood and the first departure from this practice came with Disneyland’s introduction of Steel Roller Coasters with the “Matterhorn Bobsleds” designed jointly by Arrow Development and WED Imagineering. Modern coasters have many notable design improvement including catapult lifts, Ferris wheel lifts, cork screw turns etc. Computer aided design has changed the face of coaster engineering with engineers rapidly challenging conventional limits of technology.
The Mechanics of Roller Coasters and Safety Considerations
Roller Coasters are operated by basic inertial, gravitational and centripetal forces. It must be made clear at the very beginning of this discussion that a coaster does not have any engine at all but is driven by gravity and momentum. The cars are pulled to the top of a tall hill so that it acquires sufficient potential energy for the rest of the ride. The pulling mechanism employed is usually the “Chain lift” or “Catapult Launch Lift”. The chain lift is a long length of chain running up under the track. This is fastened in a loop, which is wound around two gears – one at the top and another one at the bottom of the hill. Their function is to pull the train like a conveyor belt. Upon descending the hill, the reservoir of potential energy is converted to kinetic energy causing an increase in the velocity of the train. On ascending the second hill, this is once again converted to potential energy.
The loop in a roller coaster acts like a centrifuge. While executing a loop, the cars and the inhabitants are pressed against the tracks counterbalancing the force of gravity. Originally, roller-coaster designers made circle-shaped loops with constant angle of turn. In order to build an acceleration force strong enough to push the train into the track at the top of the loop, the trains were sent into the loop with at a fairly high speed. But nowadays, a tear drop shaped design is used to more easily balance the forces. Inertial forces are responsible for the inducing the “thrill factor” in roller coaster design. A passenger in a forward cruising coaster feels thrust back into his seat due to his inertia of motion. Similarly, when falling down through a loop, the body feels pushed up effectively counteracting the force of gravity – thereby creating the exciting feeling of “weightlessness”. The internal organs of the human body face no physical load at all resulting in an exhilarating sinking feeling.
Data Sheet
To illustrate the mathematics involved in designing roller coasters, the actual working data from five different theme parks in America has been tabulated below. Three of these are from California while the other two – The Carolina Cyclone and The Cedar Creek Mine Ride has been selected due to their historic importance. At 35 m, the Buena park Boomerang is the highest ride of them all while Disney’s California Adventure holds the record for the longest ride with an amazing 1850.66 m. Both the speeds as well as the acceleration represented are average values due to their continuous variation during operation. If the total distance travelled is represented by ‘s’, time of travel by ‘t’, average speed by ‘v’ and acceleration by ‘a’, then Newton’s laws of Motion relates them as:
And
Name of the Park
Location
Roller coaster
Height
(m)
Length
(m)
Speed (m/s)
Duration (sec)
Avg Acc (m/s2)
Carowinds
Charlotte, North Carolina
Carolina
Cyclone
28.95
640.05
7.11
90
0.15
Cedar Point
Sandusky, Ohio
Cedar Creek Mine Ride
14.63
774.15
4.78
162
0.05
Disney’s California Adventure
Anaheim, California
California
Screamin
32.92
1850.66
11.86
156
0.15
Knott’s Berry Farm
Buena Park, California
Boomerang
35.54
284.97
2.64
108
0.04
Batman
The Ride
Valencia, California
Six Flags Magic mt
32.00
822.92
6.86
120
0.11
Roller Coaster Design
As per the given instructions, three simulated rides were attempted through the web portal located at http://www.learner.org/exhibits/parkphysics/coaster/. The three schemes are given below:
For the best performance of a coaster, the initial hill must be as high as possible as this creates a vast pool of potential energy which subsequently translates to enhanced kinetic energy upon descent. For example, the coaster in consideration attains a velocity of 39.6 m/s if it descents from a hill of 80 m height which is greater than that for the small hill of fig 3. It will have the optimum velocity for the rest of the ride and give riders the feeling of “weightlessness” for the maximum amount of time. A roller coaster follows the path of a projectile in free fall and the exit path should therefore merge smoothly with the next hill. A linear fall followed by an abrupt shift in the horizontal axis (fig 1) is disastrous as it leads to the creation of unbalanced momentum and force vectors which can even derail the cars.
The coaster at this point is travelling very fast and can easily travel over the second hill, provided it is smaller than the first hill. To provide a long and flat path, a gentle slope is preferred. It should be noted that the second hill can never be as high as the first one as some of the potential energy accumulated has been lost to friction. Loops are a necessity to induce the element of thrill but it has been found that an elliptical loop is preferred to a circular loop. As has already been explained, in this shape, the forces are more easily balanced providing a safer trajectory capable of enhanced “thrill factor”.
Conclusion
Roller Coasters have become established as an integral part of American life and Culture. Infact, the extent to which they have become established in our society can be judged by the fact that many things that show unpredictable ups and downs are now described as “Roller Coasters”. Despite their apparent complexity, the fundamental physics of the coasters are given by basic physical principles. The technology of their operation, creation and maintenance is however very complicated and requires an interdisciplinary mastery of skills. The design of Steel roller coasters revolutionized coaster design enabling greater conceptual manipulations. Computer aided design and electromagnetic levitation principles are latest introductions to this field pushing the limit of thrill to stratospheric levels.
