A repository of math-oriented projects that incorporate data from sensors found in typical cell phones. The projects are all rendered in jupyter notebooks that have markdown annotations. To use these, download the .zip file of the repository, load the .ipynb file into jupyter, modify to suit your needs. Please visit https://github.com/schuelaw/PhoneSensorMath for the latest version.
There are a couple of ways of getting access to jupyter. The Anaconda
distribution comes with a jupyter
interface. Download and install the software, run the Anaconda Navigator
and click the Launch button under the jupyter notebook icon. This
will create a window in your browser that contains a fully functioning jupyter
environment.
Alternatively, you can avoid installing software on your computer by creating a free account at CoCalc. Just login, create a project, upload the example files and run them in your browser.
Collaborations and ideas for projects are welcome. Message at SensorMath@gmail.com
(FILE: PSM GPS Fastest Mile Analysis) This notebook describes the collection and analysis of GPS data recorded during an exercise run/walk/bike. The analysis allows one to determine the fastest mile within the longer exercise course. The notebook is documented so that other lengths and units (i.e. kilometer) can be considered. Such an analysis might accompany an introductory calculus curriculum about time vs. distance.
(FILE: PSM GPS Plotly Mapping Example - Mapbox) This notebook accepts recorded GPS data and plots it on a map. The notebook uses the Plotly plotting library and the Mapbox mapping library. Both libraries are free for non-commercial use (with some minor limitations) and are suitable for use by students and instructors in academic data science applications.
(FILE: PSM Accelerometer Frequency Analysis) This notebook describes the collection and analysis of phone accelerometer data recorded while the phone rested on a clothes washer during its spin cycle. The rate of spin is determined by using the discrete Fourier transform and identifying the dominant frequency of vibration in the accelerometer data. This analysis might accompany an engineering math course as it discusses the discrete Fourier transform.
(FILE: PSM Calculating Height) This notebook describes the collection and analysis of accelerometer data recorded while a phone rose from the floor to the height of a person. Then the height is calculated using calculus and approximating the integral of the acceleration data to find velocity and then again approximating the integral of the velocity data to find the change in posiiton, or height of the person. This analysis could accompany a Calculus class at many levels as well as a Physics class.
(FILE: PSM Circular Motion) This notebook describes the collection and analysis of accelerometer data recorded while a phone was spinning on a turn table. This notebook uses a discrete Fourier transformation to find the dominant frequency of the motion. The angualr velocity is calculated as revolutions per minute using the dominant frequency. It reconciles with the speed of the turn table (33 and a third). This analysis could work in a variety of classes discussing the discrete Fourier transform or circular motion.
(FILE: PSM Inclinometer Height) This notebook describes the collection and analysis of inclinometer data recorded while a phone slanted from pointing to the ground to the height of the object. There is a laser pointer attached to the phone. With simple trigonmetric analysis, we can find the the height of the object. This analysis would accompany a Geometry or Trigonometry class.
(FILE: PSM GPS Golf Tracking) This notebook describes the collection and analysis of GPS data recorded from a golf bag during a golf round. While this would be an informative activity for a high school or collegiate golf team, it can be easily modified for broader classroom applications. Students could be assigned to walk from their house or another point to the school and determine what the distance is as the bird flies using the same methods. This notebook uses the Haversine formula which takes into account the curvature of the Earth. This analyis could accompany a Geometry class and a discussion of Spherical Geometry.
(FILE: PSM GPS Crossing Paths) This notebook describes the collection and analysis of recording the GPS data of two people over the course of a few days. This allows the user to find the closest point of interaction throughout the time using the Haversine formula and then map the data. This analysis could accompany a variety of math courses.
(FILE: PSM Coefficient of Restitution) This notebook describes the collection and analysis of a microphone recording while a golf ball was bouncing on the floor. The notebook determines the time between bounces with help from the user and then calculates the coefficient of restitution to determine the energy lost while a ball bounces. This analysis could accompany a Physics class.
The examples in this repository use data collected with a free app called the Physics Toolbox Sensor Suite. There may be other apps out there that do the same thing, but this one is pretty good. That said, there are a few quirks some of which are discussed below. You are encouraged to do a lot of test recordings with different sensors before committing a lot of time to a long recording. The GPS sensor recording is particularly prone to failure unless you get things just right.
Tips about recording with the physics toolbox sensor suite. I use the app on a OnePlus 3T phone. A lot of phones, like mine, want to conserve battery power and aggressively try to put idle apps to sleep. This may cause your recordings of various sensors either to fail to start, or to shutdown prematurely. The behavior is highly dependent on the phone. Make sure you understand your phone quirks before you go out on a long recording only to find that the recording stopped halfway through the effort. Here are a few things that I've learned about my own phone. My knowledge of iPhone behavior in this area is practically zero. (Note: if you have tips you'd like to add to this list, please send them to me.)
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Lots of Android phones have a battery optimization section in the settings. This provides an app-by-app listing of battery optimization. It's wise to disable all battery optimization on whatever app you're using to record sensors.
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GPS recording, go to the GPS sensor page in the app, go into "advanced stats" wait until GPS lock, go back to the initial GPS screen, hit record, then recording is happening. On my phone, it is necessary to keep that screen selected and to keep the screen on during the entire recording. Fortunately, there is a setting to "Keep the screen on". Keeping the screen on and carefully putting the phone into a waistband or armband carrier has yielded the most reliable recordings.
Sometimes, if the GPS signal is lost during the recording, the recording will stop without notice.
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Accelerometer (an other sensor) recording seems to work pretty robustly by just hitting the record button, note that it generates a lot of readings since the sample rate is around 200Hz (at least on my phone).
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Multirecording, works as expected for most sensor combinations. I have not been able to add GPS to a multirecording.
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In general, most of the issues seem to center around getting the GPS to lock and stay locked. Getting the GPS going, bringing up the GPS screen, and keeping the phone screen on during recording seems to be the most reliable recording method. Your results may vary.