G-forces on a roller coaster
Record G-forces, angular velocity, and atmospheric pressure during a ride to analyze the physics of amusement parks.
Activity Summary
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.
Introduction
Amusement parks are open-air physics laboratories! Every roller coaster, Ferris wheel, and spinning ride illustrates fundamental principles of mechanics. By recording G-forces, angular velocity, and atmospheric pressure during a ride, you can reconstruct the altitude profile, identify moments of weightlessness, and calculate the centripetal acceleration in loops and turns. All you need is a smartphone securely stowed in a zipped pocket.
Learning Objectives
- 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
Instruments and sensors
Scientific instruments
- Absolute acceleration
- Angular velocity
- Altimeter
Sensors
- Accelerometer
- Gyroscope
- Barometer
Required Materials
- - Smartphone or tablet with FizziQ - A zipped pocket or armband to secure the phone - Access to a roller coaster or amusement park ride - Note: the protocol remains adaptable to any comparable multi-sensor data acquisition tool.
Experimental Protocol
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
- 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 Background
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.
Extensions
- Estimate the power dissipated by friction over the course of the ride
- Calculate the speed at the bottom of the first drop and compare with the theoretical value from energy conservation
- Study the angular velocity data to identify inversions and corkscrews
- Compare two different roller coasters and discuss which is more 'extreme' based on the data
Frequently Asked Questions
Is it dangerous for the smartphone?
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.
The barometer data seems noisy. Is the altitude reconstruction reliable?
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.
The G-force reading shows more than 1g even when standing still.
Verify the sensor calibration. The absolute accelerometer reads g (9.81 m/s²) at rest. Use the linear acceleration mode to subtract gravity.
Can I do this experiment on a playground swing instead?
Yes! A swing provides a simplified version with clear moments of weightlessness at the top and increased G-forces at the bottom.
Detailed Description
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 of loops and turns. FizziQ lets a single smartphone record the accelerometer, gyroscope, and barometer synchronously throughout the ride, then graph and analyze this multi-sensor data set afterward directly in the app.
Ready to start?
Download FizziQ and try this activity with your students.