Takeoff

This activity allows students to use acceleration measurements to calculate the speed of an airplane during takeoff. It concretely applies the principles of kinematics in a real and impressive situation.

The moment a commercial airliner begins its takeoff roll is one of the most physically intense experiences in everyday life. In less than 30 seconds, the aircraft accelerates from standstill to over 250 km/h, pressing passengers firmly into their seats with a sustained force they rarely experience elsewhere. The acceleration is not constant: it builds as the engines reach full thrust, then gradually decreases as aerodynamic drag increases with speed. Pioneering aviators like the Wright brothers had no instruments to measure this acceleration; they relied entirely on instinct and observation. Today, every smartphone contains a precision accelerometer capable of recording the entire acceleration profile of a takeoff with millimeter-per-second-squared precision. By integrating this acceleration data over time, students can reconstruct the velocity curve and determine the takeoff speed, a critical parameter in aviation safety that pilots calculate before every departure based on aircraft weight, wind conditions, and runway length.

Activity overview:

The student uses the FizziQ accelerometer to measure the horizontal acceleration of an airplane from the start of taxiing until takeoff. By recording the data and then analyzing it after the flight, the student performs an integration calculation to determine the final speed and compares its value to the typical takeoff speeds of airliners.

Level:

High school

FizziQ

Author:

Duration (minutes) :

25

What students will do :

- Record the horizontal acceleration during an aircraft takeoff using the smartphone accelerometer
- Integrate the acceleration data over time to calculate the aircraft's velocity at any moment
- Determine the takeoff speed and compare it with published values for the aircraft type
- Understand the relationship between acceleration, velocity, and displacement in kinematics
- Identify the different phases of the takeoff roll from the acceleration profile

Scientific concepts:

- Linear acceleration
- Speed calculation by integration
- Forces during takeoff
- Kinematics of accelerated movement
- Measurement accuracy

Sensors:

- Accelerometer (horizontal / X-axis linear acceleration)

Material needed:

- Smartphone with the FizziQ application
- A plane flight
- An armrest or stable surface to place the smartphone
- FizziQ experience notebook

Experimental procedure:

Before the flight, open FizziQ and select the Linear Acceleration X sensor (horizontal axis along the direction of travel).
Secure the smartphone on the armrest or tray table so the X-axis is aligned with the aircraft's direction of travel. Use a case or wedge to prevent sliding.
Before taxiing, start a test recording to verify the sensor reads approximately 0 m/s² when the aircraft is stationary.
When the aircraft lines up on the runway and begins the takeoff roll, start recording.
Record continuously until the aircraft is clearly airborne (you feel the nose lift and the ground vibrations stop). This typically takes 25-40 seconds.
Stop recording shortly after liftoff.
After the flight, examine the acceleration versus time graph. Identify the start of the roll (acceleration rises sharply from zero).
Identify the liftoff moment (acceleration drops as the aircraft becomes airborne and the rolling friction disappears).
To calculate the speed, perform a numerical integration: for each time interval Δt, calculate v += a × Δt. Start with v₀ = 0 at the beginning of the roll.
Plot the velocity versus time graph from your integrated data.
Read the takeoff speed from the graph at the moment of liftoff. Convert from m/s to km/h (×3.6) and to knots (×1.944).
Compare your result with typical takeoff speeds: 240-280 km/h (130-150 knots) for a medium-haul airliner like an A320 or B737.

Expected results:

The acceleration graph should show a sharp increase at the start of the takeoff roll, reaching 2-4 m/s² within the first few seconds as the engines reach full thrust. The acceleration then gradually decreases as aerodynamic drag increases with speed, typically falling to 1-2 m/s² by the time of liftoff. The integrated velocity should show an approximately linear increase (for roughly constant acceleration) reaching 65-80 m/s (235-290 km/h) at liftoff. The total takeoff roll duration is typically 25-40 seconds for a medium-haul airliner. Measurement precision depends on the phone's alignment with the direction of travel; a misalignment of 5° introduces about a 0.4% error, which is negligible.

Scientific questions:

- Why is the acceleration not constant during the takeoff roll? What forces change?
- How does the takeoff speed depend on the aircraft's weight and the wind conditions?
- What is the relationship between acceleration, velocity, and displacement? How are they connected mathematically?
- Why do pilots calculate V1 (decision speed) and VR (rotation speed) before every takeoff?
- How would the acceleration profile differ for a fighter jet compared to a commercial airliner?
- What sources of error might affect the integration of acceleration data to obtain velocity?

Scientific explanations:

A smartphone's accelerometer measures acceleration with an accuracy of approximately 0.01 m/s² at a high sampling rate (>100 Hz). During the takeoff phase of an aircraft, acceleration is not perfectly constant but varies depending on factors such as engine thrust, air resistance and contact with the runway.

To calculate speed from acceleration, we use integration: v = ∫a·dt. In practice, this integral can be approximated by the sum of the products (acceleration × time interval) for each measurement.

The takeoff speed depends on the type of aircraft: approximately 130-150 knots (240-280 km/h) for a medium airliner, 165-180 knots (305-330 km/h) for a large aircraft. This speed, called V2 (safe take-off speed), is greater than the minimum speed allowing the plane to fly.

Sources of error in this experiment include: (1) imperfect orientation of the smartphone relative to the axis of motion, (2) spurious vibrations from the aircraft, (3) variable inclination of the runway and aircraft, and (4) possible sensor drift. Despite these limitations, this method generally provides an estimate within ±10% of the actual speed, demonstrating the usefulness of smartphone sensors for approximate physical measurements.

Extension activities:

Frequently asked questions:

Q: The acceleration reading shows a lot of noise. How do I get a clean takeoff profile?
R: Ensure the phone is firmly secured and cannot vibrate independently of the aircraft. Use FizziQ's linear acceleration (which subtracts gravity) rather than absolute acceleration. Vibrations from the landing gear on the runway will add high-frequency noise that can be smoothed in post-processing.

Q: My calculated takeoff speed is much higher or lower than expected. What went wrong?
R: The most common error is axis misalignment. If the phone's X-axis is not perfectly aligned with the direction of travel, you may be measuring only a component of the acceleration. Also verify that you started the integration at the correct moment (when the roll begins).

Q: Can I do this experiment during landing instead of takeoff?
R: Yes, the landing deceleration (reverse thrust and braking) can be analyzed similarly. The deceleration is typically stronger and shorter than the takeoff acceleration.

Q: The acceleration shows negative values during the roll. Is this normal?
R: Brief negative values can occur due to bumps on the runway or vibrations. The overall trend should be positive (forward acceleration). If the values are consistently negative, the phone's X-axis may be pointing backward.