Your Phone Has an Accelerometer. We Use It.

Every modern smartphone contains a MEMS (Micro-Electro-Mechanical Systems) accelerometer — a tiny sensor that measures acceleration forces along three axes (x, y, z). This sensor was designed for screen rotation and gaming, but it also measures gravity directly. And gravity is the key to measuring freefall.

When your phone sits flat on a table, the accelerometer reads approximately +9.8 m/s² on the z-axis — the force of gravity pushing into the sensor. When you drop the phone, that reading changes. That's the signal we use.

The Physics: Double Integration

Acceleration is the rate of change of velocity. Velocity is the rate of change of position. To get distance from acceleration, you integrate twice:

v(t) = ∫ a(t) dt

d = ∫ v(t) dt

In discrete terms, your phone takes acceleration readings every 10–20 milliseconds. We sum those readings to estimate velocity, then sum velocity to estimate distance. The key challenge is that small errors in each reading compound over time — this is called drift. A 1% error in acceleration reading becomes a larger error in the final distance number the longer the fall lasts.

Why Phone Accelerometers Are Actually Good at This

You might expect consumer accelerometers to be too imprecise for scientific measurement. Surprisingly, they're not bad:

  • Resolution: Most phone accelerometers resolve changes of 0.001–0.01 m/s². At 9.8 m/s² gravity, that's about 0.02% resolution — far finer than we need.
  • Sample rate: 50–100 Hz is standard. At 60 Hz, a 0.5-second fall gives you 30 data points — enough for a decent reconstruction.
  • Calibration: Phone accelerometers are factory-calibrated and temperature-compensated. Drift due to temperature changes during a 1-second fall is negligible.

The Floop Algorithm

Floop's measurement algorithm:

  1. Wait for release: Monitor the z-axis acceleration. When it drops below 0.5 m/s², the phone has entered freefall.
  2. Subtract gravity: During freefall, the z-axis reads near zero. We subtract the known gravity offset (9.80665 m/s²) to isolate the true acceleration signal.
  3. Integrate to velocity: Sum acceleration samples over time. The result is estimated velocity in m/s.
  4. Integrate to distance: Sum velocity samples. The result is estimated distance in meters.
  5. Detect impact: When the acceleration signal spikes (sudden stop), record the current accumulated distance.

Accuracy Factors

The measurement is most accurate when:

  • The phone falls screen-up or screen-down (z-axis dominant)
  • The drop is smooth — minimal rotation during fall
  • The phone doesn't bounce or slide after impact
  • The drop height is between 0.2 and 3 meters

For typical drops, Floop's measurements are within 10% of the actual freefall distance. Errors come from device rotation (mixing x/y components into the z-axis reading), sensor noise, and timing jitter in the sample clock.

Why Not Just Use a Formula?

The simple formula (d = ½gt²) assumes perfect conditions. Real-world drops have initial velocity (you're not always dropping from a dead stop), partial rotation, and sometimes the phone starts falling at an angle. The accelerometer-based approach adapts to these conditions automatically — as long as the z-axis is dominant, the measurement holds.

Floop is designed to be a measurement tool, not a crash simulator. For phones that slip from a hand, the accelerometer approach gives a practical, usable number.