ChatGPT says:
What you’re describing is partially correct in theory, but it runs into serious practical problems when you try to do it with a phone’s accelerometer.
Let’s break it down.
1. The theory
You’re using two standard kinematic equations:
- Distance
In an ideal world:
- You’d take acceleration data from the accelerometer.
- Integrate once to get velocity.
- Integrate again to get displacement.
That’s exactly what’s in your equations.
2. Why this breaks in real life
Phone accelerometers are noisy and measure total acceleration, which includes:
- Gravity (~9.81 m/s²) — which is huge compared to small motion changes.
- Sensor bias (a constant tiny offset error).
- Random noise.
When you integrate noisy acceleration:
- Even a 0.01 m/s² bias turns into a large velocity error in seconds.
- A small velocity error turns into a massive position error when integrated again.
That’s why:
- In practice, purely integrating accelerometer data without correction drifts like crazy.
- After just a few seconds, your “distance” can be completely wrong — sometimes by meters.
3. How variometer apps make it work
Variometers (used in paragliding, skydiving, etc.) do detect vertical speed from accelerometers, but:
- They don’t rely on just raw acceleration integration.
- They use sensor fusion with the barometer (altimeter) to correct drift.
- The barometer provides an absolute vertical position (pressure → altitude), while the accelerometer fills in short-term responsiveness.
- Some also use GPS as a correction source (slow, but drift-free over time).
Without a barometer, your vertical velocity estimate will drift almost immediately.
Bottom line
- Possible in principle: Yes, your physics equations are fine.
- Accurate with a phone accelerometer alone: No, because of noise, bias, and gravity removal issues.
- How apps do it: They combine an accelerometer, gyroscope, and barometer (and sometimes GPS).
- If you want to make a working vertical velocity sensor, Start by learning how to remove gravity via gyroscope data, then combine accelerometer with barometer readings to prevent drift.
