The Wild Cat
Y. Korang-Beheshti, D. Tedeschi
University of South Carolina

Introduction:
The Wild Cat is a rollercoaster at Midway Physics Day in which the rider is in a cart that goes up and down hills and around in horizontal loops.  The cart starts going up a hill at 17^o angle to a height of about 14 meters.  After reaching the top, the car rolls down the hill and back up another.  At the bottom of the first drop, the riders feel a large force on them that is on the scale of 3.5 times the riderÕs weight.  The ride goes through about 4 more drops before starting to do horizontal loops and coming to an end.  The ride lasts about 1 minute and 30 seconds.  The data is taken with an accelerometer which has a set of axes shown below in Figure A, B, and C.  A barometer is used to measure the change in pressure on the ride, and with a conversion factor of 0.0864 mm-Hg/m, and the reference pressure is 751.56 mm-Hg.

The accelerometer's axes are shown in Figure A with the vertical axis, z, being down towards the ground of the cart.  The x-axis is in the direction that the ride is moving in, and the y-axis is positive to the right.  The axes shown in Figure B are rotated 90 degrees about the x-axis.  Figure C shows the cart, and how it is going up and down a hill affect the axes.  y is always to the right, while x is always in the direction of the ride, and z is always pointing down into the tracks.

Ride Data:

On the Wildcat, data is taken with a barometer.  A barometer is a device that measures the pressure, force per unit of area, being exerted on it.  The average pressure (atmospheric pressure) before the ride is in motion, which is about at 10 seconds to 15 seconds, as seen in Chart A, is used and found to be 751 mm-Hg.  On an average day, the pressure is approximately 760 mm-Hg.  On the day the data was taken, the average pressure was lower than the normal pressure.   The height change is calculated from finding the change in pressure from the atmospheric pressure, and using a conversion factor of 0.0864 mm-Hg/m.  In Chart A the pressure and height are shown with respect to time, and shows the direct relationship the pressure and change in height have in common.

The next set of data taken on the Wildcat is from an accelerometer.  The accelerometer measures the acceleration that the cart is experiencing.  Acceleration is the rate of change of velocity.  In Chart B, the acceleration vector components are shown for the ride.  Using this information, the axes can be determined to how they are facing.  First, by looking at the acceleration that is measured along the z-axis, it is noted to be about 10 m/s², or g.  Since it is positive, that means that the z-axis is pointing to the floor of the cart.  At around 16 seconds, the x-axis after a sudden start shows an increase in acceleration, and looking at Chart A, the cart is moving up the first hill.  Seeing that the y-axis is still approximately zero, this means that the z-axis and x-axis are feeling the effects of gravity.  Since x is negative, it must be pointing away from the Earth, and since it is feeling a portion of gravity on a hill, and the x-axis is at a right angle with the z-axis and the y-axis, then the x-axis must be pointing to the front of the cart.  This leaves the y-axis to be to the left and right of the cart.  In Chart F below, it can be noted that the y-axis and z-axis both experience gravitational acceleration, and the y-axis is given a positive acceleration, so it must be toward the Earth, or to the right. 

In Chart C, the height and resultant acceleration show the relationships between the height and the acceleration when there are large changes in each.  The resultant acceleration is calculated by the following:

At around 17 seconds the cart starts to climb the hill, with a huge spike in the acceleration at first, due to the sudden jerk that would be accompanied by the cart initially being pulled up the hill.  At around 40 seconds, the cart drops down the first hill, and at the bottom of the hill the acceleration is the greatest because of a sudden change in the directions of the acceleration.  Soon after the first drop, the cart goes up another hill, and down it, continuing this cycle 3 more times.

In Chart D, the three acceleration components are shown with the height from 15 seconds to 30 seconds to see the effects the acceleration while going up the first hill.  The average acceleration was calculated in the x-direction from about 20 seconds to 25 seconds, and this was used to find the angle that the hill is at. 

The equation tells the relationship between a_x, g, and the angle of the hill. 

When this calculation is ran, θ is approximately 17^o.  With the height known to be at 14 meters, and the angle 17^o, the length of the track and velocity the car is traveling at can be calculated.  Figure D is an example of the hill, where the length of the track is X, the height known is h (which is 14 meters), and the θ is 17^o.  With the formula h/sin(θ) = x, we can calculate the trackÕs distance to be about 48 meters. 

Knowing , the distance is 48 meters, and the time to be about 8 seconds, the speed of the car is 6 m/s, or approximately 13.5 mph. 

Future Analysis:

At around 70 seconds the ride starts to do horizontal loops till the end of the ride, and on Chart E and F the increase in acceleration with little change in height displays this.  Both charts show the centripetal acceleration from the view of the resultant and height and the acceleration components and height.  Future analysis will need to be done on the centripetal acceleration to find information out about the radius, velocity, or the angle that the track is tilted at.