Barometric Altitude and Floor Signal-to-Noise

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

Barometric Altitude and Floor Signal-to-Noise

The chapter’s altitude calculator defaults to a measured pressure of 900 hPa against a sea-level reference of 1013.25 hPa, feeding the barometric formula h = 44330 × (1 − (P/P0)^0.1903). It then argues that because each floor of a building causes about 0.36 hPa of pressure change and the BMP280 holds ±0.12 hPa relative accuracy, a climbing sensor should see a clean 3:1 signal-to-noise ratio per floor. This audit asks the question those numbers invite: does the exponential altitude formula agree with the chapter’s simpler 12 Pa/m rule of thumb, and does the 0.36 hPa floor signal really clear the sensor’s noise by 3:1?

Companion to the chapter Lab: Motion and Environment — every number here comes from that chapter.

Ada: This chapter converts pressure to altitude two ways and then argues a floor is detectable. Both deserve full precision, because the barometric exponent hides how far the rule of thumb drifts. The formula is h = 44330 x (1 - (P/P0)^0.1903) with P0 = 1013.25 hPa.

Altitude at a measured P = 900 hPa:

  • Ratio: 900 / 1013.25 = 0.888231.
  • Raised to the exponent: 0.888231^0.1903 = 0.977697.
  • h = 44330 x (1 - 0.977697) = 44330 x 0.022303 = 988.7 m, which rounds to the chapter’s ~989 m.

Cross-check with the 12 Pa/m rule of thumb:

  • (1013.25 - 900) hPa x 100 Pa/hPa / 12 Pa/m = 11325 / 12 = 943.75 m, about 944 m.
  • The ~45 m gap is expected, not an error: 12 Pa/m holds near sea level, but at ~900 hPa the thinner air drops less pressure per meter, so the exponential result sits higher and is the trustworthy one.

Floor detection (each floor ~0.36 hPa, sensor relative accuracy 0.12 hPa):

  • Signal-to-noise 0.36 / 0.12 = 3.0, a clean 3:1 margin – and a 0.01 deg/s gyro bias would meanwhile drift 0.01 x 60 = 0.6 deg per minute, which is why orientation cannot lean on integration alone.

The audit shows the linear shortcut and the exponential formula disagree by tens of meters on purpose: a design that reports absolute altitude must use the exponential form, while floor detection needs only the 3:1 relative margin that survives the daily +/-30 hPa weather swing.

Every number above is taken from the chapter’s own material and re-derived step by step.