# The Physics of a Roller Coaster Loop

Each year millions of people will visit amusement parks in order to ride some of the fastest, highest, most extreme roller coasters. These machines thrill us because of their ability to accelerate us from a standstill to unbelievable speeds in a matter of seconds while changing from one direction to the next in an instant.

There is so much physics going on in the loop of a roller coaster. Angular velocity, centripetal acceleration, conservation of energy, force and motion, and more! In this Cool Demo, we are going to look at how we can collect the data by using a Hot Wheels track and by placing a PocketLab Voyager on the Hot Wheels car.

By placing magnets at each connecting section of the track you can now generate “gate” times with PocketLab’s magnetometer. When the car passes over these sections of the track you will be able to see a change in the magnetic field. Using this change and time we can come up with “timing gates” at each of these sections, and knowing the distance the car has traveled we can calculate the speed of the car.

The most obvious section of a roller coaster, or in this case, the Hot Wheels track is the loop. Although the loop of the Hot Wheel track is a circle, in reality, roller coaster loops have a tear-dropped shape that is geometrically referred to as a clothoid. As the car passes through the loop, you can see the track bends into a tear-dropped shape. Once the car passes through the loop we are able to measure the angular velocity or the rate of change of the angular rotations, as it’s moving through that loop using the PocketLab’s Gyroscope.

Roller coaster rides are notorious for creating g-forces. The PocketLab also has an accelerometer, so as the car passes through the loop you can also measure the g-forces a person would be experiencing if they were traveling in the car. Traveling around a circle creates a centripetal force that the rider experiences as a g-force. The force is a function of speed and radius.

The Flip Flap Railway (seen above) was built in 1895 and was the first roller coaster to have a loop. It was “famous” for its extreme g-forces that it produced on its riders of approximately 12 gs. The circular nature of the coaster’s loop along with its small diameter of 25 feet caused riders to experience neck injuries from whiplash. There are some interesting accounts where riders are hanging on for dear life in a death grip on the sides of the railcar and surviving a 12g ride, which is absolutely nuts! Modern looping roller coasters all use teardrop-shaped loops to reduce the g-forces. The Flip Flap Railway was the last coaster to use a truly circular loop.

Looking at the Data:

1. The time it took the car to travel through the loop = 0.34 seconds
2. The average angular velocity (gyroscope) through the loop = 1,170 degrees/seconds
3. The average acceleration through the loop = 3.7 g

Data analysis:
Looking at the angular velocity inside the loop can be done in two ways:

1. We can calculate the average loop velocity using our timing gates. (The time we exit the loop – the time we enter the loop and using the circumference of our track. Plugging in the geometry in our time we get 1.9 meters per second as our average velocity.
2. Using the (1.9 m/s) velocity we can calculate the average angular velocity of 18.5 radians per second or 1060 degrees per second.
To get the g-force we need to calculate the following:
3. Taking the timing gate data to calculate the G-Forces that would be felt inside the loop; (18.5 radians per second)²(0.1 meters per second) = 3.9 g.

The PocketLab Voyager has an array of sensors built into a small package. This allows you to quickly measure speed and acceleration in this Hot Wheels Loop track experiment. Simply connect it to your smartphone or tablet through Bluetooth and you will be able to see the data live in the palm of your hands. On-board memory is also included for when you the PocketLab Voyager is out of Bluetooth range. The best thing about PocketLab Voyager is that that it comes packaged with so many features compared to equipment that costs thousands more.

1. Click here to view – Energy on a Roller Coaster Activity
2. Click here to view – Potential Energy on a roller coaster track
3. Click here to view - Determine Roller Coaster Layout from Data Graphs

Explore the world around you with the sensors built into the PocketLab Voyager 2:

• Measure Acceleration
• Angular Velocity
• Magnetic Field
• Range Finder
• Altitude
• Barometric Pressure
• Ambient Temperature
• Humidity
• Light
• Dew Point
• Heat Index