Experiment: Integrated acceleration

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Integrated acceleration
Experiment Integrated acceleration
Category Tools
Used sensors Accelerometer


The experiment "integrated acceleration" calculates the phone's velocity and position (relative to its starting position) by integrating the data from the accelerometer (Sensor: Acceleration (without g)).

This experiment has not been included in the phyphox installation as its use is limited and its interpretation difficult or misleading. The errors in the acceleration sum up in the velocity and hence have an even worse impact on the location. Usually, the noise of the sensors brings the results to absolutely unreasonable values within a short time.

Requirements

This is rather a tool or a demonstration of the acceleration data and its analysis than an actual experiment, so there are no specific requirements.

Setup

Again, as this is rather a tool than an experiment, there is not specific setup.

Analysis

For each sensor reading, the time step dt is calculated as the difference from the time of this reading to the previous one. The acceleration is multiplied with dt to get the change in velocity dv. All subsequent dt are added (integrated) to get the absolute velocity at the time of this reading. This velocity is again multiplied with dt to get the change in location, which again is subsequently added to get the absolute position.

Problems and resolutions

  • The position drifts without moving the phone. This is to be expected as wrong acceleration leads to a constant (wrong) speed, which leads to a drifting position. Let's assume, that your sensor reports an acceleration that is off by 0.1 m/s² (this is quite optimisitic!) on a single measurement at a rate of 50 samples per second. As the time between each sample is 20ms, this single sample leads to a drift velocity of 2 millimeters per second - and this is only a single sample. If the error is systematic, this will add up very quickly. You should also keep in mind that the physical accelerometer measures data containing the earth's acceleration and the data used here is a virtual sensor provided by the manufacturer of your phone. This means on one hand, that the result will depend on the device and on the other hand, that the error is very likely to be systematic.

phyphox file

File:Integrated_acceleration.phyphox