Amusement Park Physics/Precalculus

World of Fun Amusement Park, Kansas City, MO

After getting off of the bus and taking a quick photo, if was time to get off to work. However, the first order of business is to check the calibration of the equipment or calibrate the equipment if it has no been done. The equipment is calibrated using the program ACCALIB. When using a triple axis accelerometer, the accelerometer must be calibrated in all three planes of motion. Run the program and enter the channel to be calibrated. Normally the x-axis is plugged into channel 1, y into channel 2 and z into channel 3. For each channel, turn the appropriate axis down, hold or position the accelerometer in a stable position and press [ENTER] on the calculator. Enter the desired value of -9.8 (m/s^2) for the calibration in this position. Now, turn the axis up, press [ENTER] and enter the calibration value of 9.8 (m/s^2). Repeat this process for the remaining axes.

Even if the equipment is already calibrated, it is a good idea to check the calibration. Running the program ACC3AXIS and positioning the accelerometer in each of the 6 possible orientations with one of the axes pointed vertically upward or downward should produce the graph of a constant acceleration of 9.8 m/s^2 or -9.8 m/s^2. Checking the calibration is of great importance and often neglected. A properly configured graph will appear as one of the following graphs. The graph above shows the channel1 graph with the axis pointed down. The graph is close to the accepted value of -9.8 m/s^2. The graph above shows the channel1 graph with the axis pointed up. Note the value is close to the accepted value of 9.8 m/s^2. Failure to properly calibrate each axis of the CBL and properly test the calibration could lead to difficult if not impossible analysis of the data.

The Mamba is a coster with an out and back design. According to park literature, it features a first drop of 205 feet, a second hill 184 feet above the ground follows with nearly the same velocity as the first. A 580 degree rotation reaches speeds in excess of 60 miles per hour before entering five "camelback" humps, including an unusual "double up" bump.

The park opened this ride early to allow only physics students to ride the attraction. To give you a flavor for the data that can be collected, here are a couple of sample graphs. The data is available for downloading and more information and data can be found in the followup section where students analyzed the data they collected.

The graph at the right shows the first 30 seconds of the ride after being towed to the top of the first hill. Note the starting acceleration is 9.8 m/s^2. The plunge down the first incline results in accelerations close to 0 m/s^2 and then approaches 40 m/s^2 in the first valley. The rider returns up and over the second hill where the acceleration once again approaches 0 m/s^2 followed by the drop into the second valley with accelerations approaching 45 m/s^2 before falling into the second valley. The accelerations then gradually increase as one enters the 580 degree turn.The data file mamba30 is available in text format, TI-83 format and Vernier Graphical Analysis format (configure your browser to download and save a *.dat file extension). The data shows each axis of the 3-axis accelerometer as well as the modulus (all 3 axis combined.)

The graph at the left shows the acceleration as the rider proceeds into the 580 degree turn from the top of the third hill. The maximal acceleration occurs at about 10 seconds into this data set which corresponds to about 28 seconds in the data set above. Due to the memory limitations of the equipment available, we were not able to record the entire ride in one data set. (We hope to have the equipment to accomplish this next year.) The local maximum acceleration at about 21 seconds is a set of brakes applied to slow the rider down before entering the camel back humps. This data is also available as mamba580 in text file format, TI-83 format or Vernier Graphical Analysis format.

The final portion of the ride is the "camel back" humps at the conclusion of the ride. The ride image on the left above shows the "small" humps at the conclusion of the ride. Like the other data sets, these are available as mambahum in text file, TI-83 format and Vernier Graphical Analysis format. Note the clearly defined regions of the graph where the acceleration is around 2 m/s^2. These are at the top of each of the camel humps. Because the accelerometer is attached in a fanny pack and not directly attached to the car, there is some motion in the pack. On this particular ride, the rider experiences the sensation of rising out of their seat and being quickly forced back down. The swing of the accelerometer is responsible for the exceptionally large values on the graph.

Ripcord

The Ripcord is an attraction where 1 to 3 riders are hoisted to the tower in the background of the image at the right. When one of the riders pulls the "ripcord" they swing through the twin towers in the foreground. The ride continues as they swing back and forth like a pendulum, gradually slowing until they can grab a rope from the attendents and swing to a stop. The image at the right shows the students at the top of the tower preparing the equipment. The two individuals on the left wore the CBL's on their backs. The two on the right triggered the CBL of on the individual to their right as shown below.

Further images, data and discussion of the RIPCORD is available here.

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