| | Category | PH | P27 | Comparing Methods of Determining the Acceleration of a Roller |
| | Coaster |
| | Abstract | This experiment was created to compare the acceleration found on a |
| | computer simulation (the NoLimits Roller Coaster Simulation) and the |
| | acceleration calculated from a mathematical formula. Using this program, a |
| | model of the Serpent, a roller coaster in Saginaw, Michigan, was |
| | constructed. A mathematical equation was also created based on the |
| | measurements of the first hill of this roller coaster. It was hypothesized |
| | that if a mathematical calculation of the acceleration on a roller coaster is |
| | computed, then the acceleration found by the simulator will be accurate |
| | within a factor of 10%. |
| | The simulated method was tested on the simulator by measuring the |
| | acceleration that riders experienced during the first hill of the Serpent for |
| | every tenth of a second. The calculated method was developed by |
| | identifying the times when the roller coaster was parallel to the ground as |
| | roots on the first hill, and then creating a velocity graph using these roots. |
| | This velocity graph was converted into a position graph to emulate the |
| | vertical position of the roller coaster over time. Then, the derivative of this |
| | equation was taken twice to find a function modeling the acceleration of |
| | the roller coaster. |
| | The simulated roller coaster showed that the acceleration decreased |
| | slightly during the first 0.5 seconds, and then increased dramatically as the |
| | roller coaster reached the bottom of the hill. Then, when the roller coaster |
| | traveled upwards, the acceleration decreased again. The calculated |
| | function showed similar data, but did not show the leveling out of the |
| | acceleration at either end. Therefore, while the percent error was within |
| | 10% during a central interval, the error ranged from 20% to 800% |
| | everywhere else. In conclusion, the mathematical equation derived only |
| | from the maximum and minimum vertical altitudes of a hill on a roller coaster |
| | did not describe the acceleration experienced throughout the hill with a |
| | 10% margin of error when compared to acceleration determined by a |
| | computer simulation. |
| | Bibliography | Marden, Duane, comp. "Serpent." Roller Coaster Data Base. Web. 25 Sept. |
| | 2009. <http://www.rcdb.com/4054.htm>. |
| | |
| | NoLimits Roller Coaster Simulation - The Ultimate Roller Coasters Simulator |
| | for PC and Mac. Web. 19 Sept. 2009. <http://www.nolimitscoaster.com/>. |
| | |
| | |
| | "Roller Coaster physics." Encyclopedia - Britannica Online Encyclopedia. |
| | Web. 25 Sept. 2009. <http://www.britannica.com/coasters/ride.html>. |
| | |
| | Tack, Steve. "Interview with Math Teacher." Personal interview. 11 Jan. |
| | 2010. |
| | |
| | Wagner, William. "Interview with Grandpa." Telephone interview. Winter |
| | 2009. |