Roller coaster
Record G-forces, angular velocity, and atmospheric pressure during a ride to analyze the physics of amusement parks.
Activity overview:
The student records G-forces, angular velocity, and atmospheric pressure simultaneously during a roller coaster ride. Back in class, they analyze the data to reconstruct the ride's altitude profile, identify moments of weightlessness, and estimate the radii of curvature.
Level:
Author:
High school
FizziQ
Duration (minutes) :
45
What students will do :
- Record and analyze multi-sensor data during a complex motion
- Identify G-forces and relate bodily sensations to physical quantities
- Reconstruct an altitude profile from barometric data
- Calculate centripetal acceleration and estimate the radius of curvature
- Apply energy conservation to estimate speed at different points
Scientific concepts:
- Centripetal force and centripetal acceleration
- Weightlessness
- Potential and kinetic energy
- Conservation of mechanical energy
- Inertia
- Newton's laws
Sensors:
- Accelerometer (G-forces)
- Gyroscope (angular velocity)
- Barometer (atmospheric pressure)
Material needed:
- Smartphone or tablet with FizziQ
- A zipped pocket or armband to secure the phone
- Access to a roller coaster or amusement park ride
Experimental procedure:
Before the outing, configure FizziQ to record simultaneously: G-forces (accelerometer), angular velocity (gyroscope), and atmospheric pressure (barometer).
Secure your smartphone in a zipped pocket or tight armband. The phone must absolutely not fall! Verify it is firmly held.
Start the recording just before the ride begins.
Enjoy the ride! The recording runs automatically.
Stop the recording as soon as the ride ends.
Back in class, open the data and identify the different phases of the ride on the G-force graph.
Find the moments when the G-force exceeds 1g (bottom of loops, sharp turns) and when it drops below 1g (tops of hills, drops).
Look for instants where the G-force is close to 0g: these are moments of weightlessness, at the top of hills taken at high speed.
Use the barometer data to reconstruct the altitude profile of the ride. Compare it with a photo or diagram of the track.
For each loop or turn, calculate the centripetal acceleration and estimate the radius of curvature: R = v²/a, where v is estimated from energy conservation.
Expected results:
G-forces typically range from 0g to 3g on a standard roller coaster (up to 4-5g on extreme rides). Weightlessness moments (airtime, 0g) correspond to the tops of hills taken at high speed. The barometer shows pressure variations of 1-3 hPa corresponding to altitude changes of 10-25 m. The altitude profile reconstructed from the barometer matches the visual shape of the track.
Scientific questions:
- Why do you feel heavier at the bottom of a valley and lighter at the top of a hill?
- What is the minimum speed to pass the top of a vertical loop without falling?
- Why is the first drop always the tallest on a roller coaster?
- How can you estimate the radius of curvature of a loop from the G-force data?
- Why do clothoid-shaped loops produce less extreme G-forces than circular loops?
- At what point during the ride is the kinetic energy maximum?
Scientific explanations:
The G-forces measured by the accelerometer correspond to the ratio between the normal force (the force the seat exerts on the rider) and the rider's weight. A reading of 1g means you feel your normal weight; 2g means you feel twice as heavy.
At the top of a vertical loop, centripetal acceleration is directed downward. For the rider not to fall, gravity alone must provide at least the centripetal acceleration: v² ≥ gR, where R is the loop radius.
The clothoid shape reduces G-forces at the top while maintaining safety. The radius of curvature decreases gradually, avoiding sudden transitions.
Conservation of mechanical energy (neglecting friction) allows estimating the speed at any point: ½mv² + mgh = constant. The speed is highest at the lowest points.
This is why the first drop is always the tallest: it sets the total energy of the system. Each subsequent hill must be shorter than the first.
The gyroscope measures the rider's rotation speed, which is particularly interesting in rides with corkscrews or inversions.
The sensation of heaviness in valleys is explained by the seat needing to push upward with a force greater than the weight to provide centripetal acceleration.
Conversely, at the top of a hill, gravity already provides part of the centripetal acceleration, and the seat pushes less: you feel lighter or even weightless.
Extension activities:
- Why do you feel heavier at the bottom of a valley and lighter at the top of a hill?
- What is the minimum speed to pass the top of a vertical loop without falling?
- Why is the first drop always the tallest on a roller coaster?
- How can you estimate the radius of curvature of a loop from the G-force data?
- Why do clothoid-shaped loops produce less extreme G-forces than circular loops?
- At what point during the ride is the kinetic energy maximum?
Frequently asked questions:
Q: Is it dangerous for the smartphone?
R: No, if the phone is properly secured in a zipped pocket or armband. The G-forces are within the phone's tolerance. Never hold the phone in your hand during a ride.
Q: The barometer data seems noisy. Is the altitude reconstruction reliable?
R: The barometer has a resolution of about 0.01 hPa (≈ 10 cm), but wind and pressure waves from the ride create noise. Smoothing the data over 1-2 seconds improves the altitude profile.
Q: The G-force reading shows more than 1g even when standing still.
R: Verify the sensor calibration. The absolute accelerometer reads g (9.81 m/s²) at rest. Use the linear acceleration mode to subtract gravity.
Q: Can I do this experiment on a playground swing instead?
R: Yes! A swing provides a simplified version with clear moments of weightlessness at the top and increased G-forces at the bottom.