Where the 6-Microtesla Threshold Sits

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

ADA · CALCULATION AUDIT

Where the 6-Microtesla Threshold Sits

A parking sensor calibrated to a 50 microtesla baseline sees a 12 microtesla swing when a car parks directly over it, but only a 3 microtesla swing from a truck in the next bay. The chapter sets the occupancy threshold at 6 microtesla and claims it both catches the real occupant and rejects the neighbour. So does 6 really do both jobs — and why is that the number the threshold sits at?

Companion to the chapter Smart Parking Sensor Contracts — every number here comes from that chapter.

Ada: The cross-detection worked example gives four numbers — a 50 microtesla baseline, a 12 microtesla swing from the car in the bay, a 3 microtesla swing from a truck next door, and a 6 microtesla occupancy threshold — and claims that threshold “catches the real occupant and rejects the neighbour.” Let me check it does both, then work out why 6 was the number chosen.

• Catch the occupant: the direct car swings the field 12 uT, and 12 > 6, so it clears the threshold — detected.
• Reject the neighbour: the adjacent truck swings it 3 uT, and 3 < 6, so it stays below — rejected.
• Reject margin: 6 - 3 = 3 uT of headroom above the worst crosstalk.
• Detect margin: 12 - 6 = 6 uT of headroom below the true occupant.

The threshold is not arbitrary. It sits at 6 / 3 = 2x the neighbour’s shift and 12 / 6 = 2x below the occupant’s — an equal multiplicative margin on each side. That is exactly the geometric mean of the two swings: sqrt(3 x 12) = sqrt(36) = 6 uT.

The design meaning is that centering the threshold on the geometric mean of the crosstalk swing and the true-occupant swing buys the widest balanced safety factor — 2x either way — from a single magnetometer. It also shows exactly where the method fails: if tight bays or huge vehicles push the neighbour’s 3 uT up toward the occupant’s 12 uT, that 2x margin collapses and no single threshold can separate them, which is precisely when the chapter says to add a second sensing mode or fuse two magnetic axes.

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