Six Flags Ride Analysis

Six Flags Rides

Acrophobia

Batman the Ride

The Great American Scream Machine

The Georgia Cyclone

The Georgia Scorcher

The Mind Bender

The Ninja

Superman Ultimate Flight

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This data was collected by Dr. David Tedeschi and Dr. Ralf Gothe at Six Flags Over Georgia on April 4 2003. The acceleration and pressure were measured using Pasco's three-axes accelerometer and barometer. Pasco's Xplorer was also used to record the data measured by these devices. Pasco's Data Studio was used to analyze the data. All the graphs for the Six Flags rides were made using Data Studio.

Determining Ride Height By Pressure Measurement

Atmospheric pressure decreases exponentially with height above the earth’s surface. Near the surface the rate of change of pressure (P) with height (z) is given by

DP/Dz = – (mg/kT)P,

where :

m is the average molecular mass for air = 4.80 x 10–26 kg,
g is the gravitational acceleration = 9.81 m/s2,
k is Boltzmann’s constant = 1.38 x 10–23 J/K,
T is absolute temperature ~ 300 K,
P is the sea level pressure ~ 760 mm-Hg.

Entering these numbers into the computation yields

DP/Dz = – 0.0864 mm-Hg/m.

Thus for an increase in height of 10 m, the atmospheric pressure changes by – 0.864 mm-Hg or approximately 1 mm-Hg per 10 meter of height.

This pressure difference is just within the capability of the handheld measuring devices. Consequently, you may be able to measure the height of the roller coaster and the giant Ferris wheel from measurements of air pressure as a function of position on the ride.

Determining Resultant Acceleration

All data was collected using Pasco’s three-axes accelerometers. This means that the acceleration is measured in the x, y, and z-axes. The acceleration graphs however, plot the resultant acceleration. The resultant acceleration is the total contribution of the accelerations in the x, y, and z-axes. To determine to the resultant acceleration, the following formula was used:

where:

aR= resultant acceleration,
ax = acceleration in the x-axis,
ay = acceleration in the y-axis,
az = acceleration in the z-axis.

Notice that before and after the ride, the resultant acceleration is 9.8 m/s^2. This is the value for the acceleration due to gravity. This means that the rider is either at rest or moving at a constant velocity.

When a cart is moving up the first hill on a ride, it is being pulled (for our purposes) at a constant velocity. This can be seen from comparing the height and acceleration graphs. In all the graphs, except one, the acceleration does not change until the cart has gone over the first hill. In Acrophobia, which is a free fall ride, the acceleration does not change until the rider is dropped.