Why the Battery Numbers Overturn the Range Guess

Why the Battery Numbers Overturn the Range Guess

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

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Ada ADA · CALCULATION AUDIT

Why the Battery Numbers Overturn the Range Guess

A smart beehive monitoring project needs to reach 50 beehives from a gateway about 200 m away — a distance the chapter itself calls an awkward tweener: too far for BLE or Zigbee, overkill for LPWAN. Its own battery-life model then runs Wi-Fi, LoRaWAN, and Zigbee mesh through the same 2000 mAh capacity and 24 reads-a-day workload, each using its own transmit time and sleep current. This audit asks the question that comparison invites: does the 200 m tweener distance actually decide the protocol, or does the daily battery budget settle it first?

Companion to the chapter Protocol Selector Wizard — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is wi-fi reports. The middle card applies this page's rule. The green card is wi-fi daily charge. 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 wi-fi reports, so the numeric fixture does not switch without explanation.

Wi-Fi reports changes wi-fi daily charge An input card leads through the rule charge = 3.6 mAh sleep + reports x 5 mA x 10 s / 3,600 to the wi-fi daily charge result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Sleep sets the floor while every additional Wi-Fi report adds the same transmit charge.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 24 reports/day.

  2. 2

    Name the relationship. charge = 3.6 mAh sleep + reports x 5 mA x 10 s / 3,600

  3. 3

    Substitute with units. 3.6 + 24 x 50 / 3,600 = 3.933 mAh/day

  4. 4

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

Predict, then change wi-fi reports

Try Predict the direction of charge = 3.6 mAh sleep + reports x 5 mA x 10 s / 3,600. Test another wi-fi reports, then compare wi-fi daily charge.

24 reports/day
Chapter baseline
Wi-Fi daily charge

Observe Sleep sets the floor while every additional Wi-Fi report adds the same transmit charge. Reset wi-fi reports to 24 and compare wi-fi daily charge.

Explain Sleep sets the floor while every additional Wi-Fi report adds the same transmit charge.

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 wi-fi reports moves here. Field effects named in the technical boundary stay fixed.
TryRecompute Wi-Fi transmit: 5 mA x 10 s = 50 mA·s, and 50 / 3600 = 0.013889 mAh per transmission. Over 24 reads: 0.013889 x 24 = 0.333333 mAh/day active. Sleep adds 0.15 mA x 24 h = 3.6 mAh/day.
ObserveTrack LoRaWAN transmit: 6 mA x 2 s = 12 mA·s = 0.003333 mAh; x 24 = 0.08 mAh/day active, plus 0.0015 mA x 24 h = 0.036 mAh/day sleep. Total 0.116 mAh/day.
ExplainExplain why Zigbee relaying for four neighbours adds 0.024 mAh/day and changes the energy comparison with Wi-Fi and LoRaWAN.

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

Ada: The 200 m “tweener” distance makes range look like the deciding factor, but the beehive comparison is really settled by the daily battery budget. Let me re-run each option’s mAh/day from the chapter’s own current and time figures, carrying full precision and rounding only at the end.

  • Wi-Fi transmit: 5 mA x 10 s = 50 mA·s, and 50 / 3600 = 0.013889 mAh per transmission. Over 24 reads: 0.013889 x 24 = 0.333333 mAh/day active. Sleep adds 0.15 mA x 24 h = 3.6 mAh/day. Total 0.333333 + 3.6 = 3.933 mAh/day.
  • LoRaWAN transmit: 6 mA x 2 s = 12 mA·s = 0.003333 mAh; x 24 = 0.08 mAh/day active, plus 0.0015 mA x 24 h = 0.036 mAh/day sleep. Total 0.116 mAh/day.
  • Zigbee mesh: own transmit 9 mA x 0.1 s = 0.9 mA·s = 0.00025 mAh; x 24 = 0.006 mAh/day, relaying for four neighbours adds 0.006 x 4 = 0.024 mAh/day, and sleep adds 0.003 mA x 24 h = 0.072 mAh/day. Total 0.102 mAh/day.

So the chapter’s 3.93, ~0.12, and ~0.10 mAh/day all reproduce exactly. The decisive ratio is 3.933 / 0.102 = 38.6: Wi-Fi burns almost forty times the daily charge of the Zigbee mesh, and its 3.6 mAh sleep floor — not its transmit cost — is what dominates that gap.

The audit conclusion is bounded: the arithmetic confirms battery, not raw range, breaks the tie at 200 m — but only for these illustrative current and duty-cycle figures. Re-measure the real sleep current and per-read radio time on the installed board before treating any years-of-life claim as a site commitment.

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

Technical boundaries. This battery ledger deliberately does not simulate retries, fading, changing mesh routes, or battery ageing. It integrates the stated transmit and sleep currents over fixed Wi-Fi, LoRaWAN, and Zigbee activity times, including four relayed neighbours.