Where the 6-Microtesla Threshold Sits

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.

See the relationship before changing it

The figure reads from left to right. The blue card is occupancy threshold. The middle card applies the page rule. The green card is balanced safety factor. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Walk the arrows. The factor peaks at the geometric mean between neighbour and occupant swings.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 6 uT.

2. 2

   Name the relationship. factor = smaller of threshold / 3 and 12 / threshold

3. 3

   Substitute with units. min(6 / 3, 12 / 6) = 2.00 times

4. 4

   Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change occupancy threshold

Try Predict the direction of factor = smaller of threshold / 3 and 12 / threshold. Test another occupancy threshold, then compare balanced safety factor.

Occupancy threshold

6 uT

Chapter baseline

Balanced safety factor

Observe The factor peaks at the geometric mean between neighbour and occupant swings. Reset occupancy threshold to 6 and compare balanced safety factor.

Explain The factor peaks at the geometric mean between neighbour and occupant swings.

Check yourself

What should you do before trusting a moved-control result?

Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.

What does this small model leave out?

Answer: Only occupancy threshold moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only occupancy threshold. It is not a field prediction.

TryAt Check derivation, compare the 12 microtesla occupied-bay swing and 3 microtesla neighbour swing with a 6 microtesla threshold.

ObserveThe 6 microtesla line leaves 6 microtesla of detect margin and 3 microtesla of reject margin while classifying both fixtures correctly.

ExplainSix is the geometric mean of 3 and 12, giving a balanced 2x multiplicative separation from neighbour crosstalk and true occupancy.

Ready: use the stated baseline inputs, then compare each displayed result.

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.

Technical boundaries. Magnetic-field geometry, vehicle orientation, temperature drift, street interference, and sensor ageing are excluded; the check compares only fixed 3, 6, and 12 microtesla evidence.