Takeoff
Takeoff speed of an airplane
Author:
Title 4
Learning objectives :
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.
Concepts covered
Linear acceleration; Speed calculation by integration; Forces during takeoff; Kinematics of accelerated movement; Measurement accuracy
What students will do :
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.
What is required :
Smartphone with the FizziQ application; A plane flight; An armrest or stable surface to place the smartphone; FizziQ experience notebook
Scientific background :
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.