Motion Marley guidesA technician must decide whether three-year alarm energy is safe before changing pir alarms per week on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is pir alarms per week. The middle card applies this page's rule. The green card is three-year alarm energy. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only pir alarms per week, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 18 alarms/week.
- 2
Name the relationship. energy = alarms/week x 156 weeks x 1.80 mJ / 3,600
- 3
Substitute with units. 18 x 156 x 1.80 / 3,600 = 1.40 mWh
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change pir alarms per week
Try Predict the direction of energy = alarms/week x 156 weeks x 1.80 mJ / 3,600. Test another pir alarms per week, then compare three-year alarm energy.
Observe More false alarms add event energy to the same sleep-dominated budget. Reset pir alarms per week to 18 and compare three-year alarm energy.
Explain More false alarms add event energy to the same sleep-dominated budget.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Start with the physical story
A PIR element responds to changing infrared flux, not a still temperature. Each accepted event can trigger a brief radio burst, but quiescent electronics draw current continuously. A large percentage reduction in events can therefore produce a small lifetime change.
2. Name every algebra move
Derate chargeApply three years of 99% retention and keep a 20% reserve.
Price one alarmMultiply 15 mA by 3.0 V by 0.040 s.
Price all alarmsMultiply burst energy by alarms per week and 156 weeks.
Price quiet timeMultiply 0.002 mA by voltage and 26,280 hours.
Average event currentSpread each alarm's milliamp-seconds across a week.
Find lifeDivide usable mAh by total average mA.
3. Reproduce the chapter case
Eburst=15 mA×3.0 V×0.040 s=1.80 mJ
Esleep,3y=0.002 mA×3.0 V×26,280 h=157.7 mWh
Ealarms,18/wk=18×156×1.80/3600=1.40 mWh
Iavg≈2.02 µA; ideal runtime≈9.7 years
Alarm reduction improves nuisance behavior and radio traffic, but quiet current owns most of this ideal charge ledger.
4. Try one real input
TryChange alarms per week and predict the ideal runtime before reading it.
ObserveAt 18 alarms/week, event energy is well under 1% of usable energy and runtime stays near the sleep-dominated value.
ExplainThe radio is expensive while on, but it is on for only fractions of a second per week. Two microamps flows through every hour.
This is an ideal fixed-current comparison.
- PIR
- Pyroelectric amplitude depends on optics, motion, geometry, temperature change, and analogue filtering.
- Radio
- Join, retry, receive, and acknowledgement states can cost more than one fixed burst.
- Cell
- Self-discharge, pulse sag, temperature, cutoff, and ageing vary over the full runtime.
Correct, not complete: a small charge saving does not make false-alarm reduction unimportant, nor prove field battery life.
5. Use the result in the design
Optimise false alarms for trust and service first, then measure the complete current trace to identify whether sleep, sensing, processing, or radio dominates energy.
6. Record the evidence state
Keep alarm cause, threshold, optics, room temperature, accepted and rejected events, radio states, current trace, retry count, sleep current, cell voltage, firmware, and user outcome.
7. Check yourself
Why does one report cost 1.80 mJ?
Why does an 87% event reduction add only weeks?
Does the small energy share make false alarms harmless?
The arithmetic reproduces the chapter's illustrative alarm rates and catalog-style PIR constants.
- PIR
- Pyroelectric amplitude depends on optics, motion, geometry, temperature change, and analogue filtering.
- Radio
- Join, retry, receive, and acknowledgement states can cost more than one fixed burst.
- Cell
- Self-discharge, pulse sag, temperature, cutoff, and ageing vary over the full runtime.
Correct, not complete: a small charge saving does not make false-alarm reduction unimportant, nor prove field battery life.