Let’s verify the Thread mesh network capacity and battery life claims for the 2,000 PIR motion sensors transmitting dimming commands.
Thread mesh capacity analysis: Each PIR sensor triggers ~4 times per night (pedestrian detected). Dimming command: 10 bytes CoAP message.
Time-on-air at 250 kbps (802.15.4) with compressed headers (6LoWPAN IPHC + NHC): \[T_{\text{airtime}} = \frac{8 \times (25 \text{ MAC} + 6 \text{ 6LoWPAN} + 4 \text{ UDP-NHC} + 10 \text{ CoAP})}{250{,}000} = \frac{360}{250{,}000} = 1.44 \text{ ms}\]
Total nightly airtime for 2,000 sensors: \[T_{\text{total}} = 2{,}000 \times 4 \times 1.44 \text{ ms} = 11.5 \text{ seconds/night}\]
With 8,000 mains-powered mesh routers (one per streetlight), each router handles: \[\text{Load per router} = \frac{2{,}000}{8{,}000} = 0.25 \text{ sensors}\]
Router channel time: \(0.25 \times 4 \times 1.44 = 1.44\) ms/night – negligible
PIR sensor battery life (2× AA lithium, 3000 mAh each @ 1.5V, 6000 mAh total): Energy per transmission at 17.4 mA TX: \[E_{\text{TX}} = 17.4 \text{ mA} \times 1.44 \text{ ms} = 0.025 \text{ mAs}\]
Sleep current (0.5 uA) over 24 hours: \[E_{\text{sleep}} = 0.0005 \text{ mA} \times 86{,}400 \text{ s} = 43.2 \text{ mAs}\]
Daily energy (4 transmissions): \[E_{\text{daily}} = (4 \times 0.025) + 43.2 = 43.3 \text{ mAs} = 0.012 \text{ mAh}\]
Battery life with 2x AA (6000 mAh): \[\text{Life} = \frac{6000 \text{ mAh}}{0.012 \times 365} = 1{,}370 \text{ days} = \mathbf{3.8 \text{ years}}\]
Problem: Target is 5 years, but calculation shows only 3.8 years!
Solution: Use 3x AA lithium batteries (9000 mAh total): \[\text{Life}_{3\text{AA}} = \frac{9000}{0.012 \times 365} = 2{,}055 \text{ days} = \mathbf{5.6 \text{ years}}\]
Meets 5-year requirement with 12% margin. ✓
TCO impact of battery sizing:
- 2x AA ($4): Replace at 3.8 years = 4 replacements x 2,000 sensors = $32K labor + $16K batteries
- 3x AA ($6): Replace at 5.6 years = 3 replacements x 2,000 sensors = $24K labor + $18K batteries
- Savings: $6K over 15 years in labor by upsizing battery ($2 extra per sensor = $4K upfront)
ROI: \(\frac{(\$48\text{K} - \$42\text{K}) - \$4\text{K}}{\$4\text{K}} = 50\%\) return on battery upsizing investment.
Key principle: Battery sizing calculations must account for both active and sleep energy. Sleep current (0.5 uA) over 24 hours consumes 99.7% of total energy – active transmissions are negligible in comparison. This is why ultra-low sleep current matters more than TX efficiency for infrequent-reporting IoT devices.