The Weather-Station Battery Budget

The Weather-Station Battery Budget

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

foundations
math-foundations
calculation-audit
sensors
Ada ADA · CALCULATION AUDIT

The Weather-Station Battery Budget

The chapter’s Weather Station Power Analysis puts an ESP32 and BME280 sensor through a 15-minute cycle: a 30 mA sensor read for 3 seconds, a 170 mA Wi-Fi transmit for 2 seconds, and 895 seconds of 10 µA deep sleep, 96 cycles a day. It claims that cycle stretches a 2000 mAh battery to about 171 days. This audit asks the question that headline number invites: do the three per-cycle energies actually sum to a battery life of 171 days when carried out to full precision?

Companion to the chapter Low-Power Sensor Networks — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is fifteen-minute cycles. The middle card applies this page's rule. The green card is 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 fifteen-minute cycles, so the numeric fixture does not switch without explanation.

Fifteen-minute cycles changes daily charge An input card leads through the rule charge = 0.1219306 mAh/cycle x cycles per day to the daily charge result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. More reporting cycles repeat the same sensor, radio, and sleep ledger each day.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 96 cycles/day.

  2. 2

    Name the relationship. charge = 0.1219306 mAh/cycle x cycles per day

  3. 3

    Substitute with units. 0.1219306 x 96 = 11.705 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 fifteen-minute cycles

Try Predict the direction of charge = 0.1219306 mAh/cycle x cycles per day. Test another fifteen-minute cycles, then compare daily charge.

96 cycles/day
Chapter baseline
Daily charge

Observe More reporting cycles repeat the same sensor, radio, and sleep ledger each day. Reset fifteen-minute cycles to 96 and compare daily charge.

Explain More reporting cycles repeat the same sensor, radio, and sleep ledger each day.

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 fifteen-minute cycles moves here. Field effects named in the technical boundary stay fixed.
Try

Use Sensor read at 30 mA for 3 s and Wi-Fi transmit at 170 mA for 2 s with 96 cycles/day, then click Check audit.

Observe

Per-cycle charge totals 0.121931 mAh, daily use becomes 11.705 mAh, and the 2000 mAh battery estimate settles near 170.9 days.

Explain

Wi-Fi occupies only 2 seconds but consumes 77% of cycle charge, so buffering transmissions changes runtime far more than trimming the tiny sleep term.

Ada: The headline claim is that a 2000 mAh battery runs this node for about 171 days. That number rests on three per-cycle energies, so let me rebuild each one from the current-and-duration table before trusting the total. Energy in mAh is current (mA) times duration in hours, and one 15-minute cycle is 900 seconds split across sensing, transmitting, and sleep.

  • Sensor read: 30 mA x (3 / 3600) h = 0.025000 mAh
  • Wi-Fi transmit: 170 mA x (2 / 3600) h = 0.094444 mAh
  • Deep sleep: 0.01 mA x (895 / 3600) h = 0.002486 mAh
  • Per-cycle total: 0.025000 + 0.094444 + 0.002486 = 0.121931 mAh

With 96 cycles per day, 96 x 0.121931 = 11.705 mAh/day, and 2000 / 11.705 = 170.9 days, which rounds to the chapter’s 171 days (about 5.6 months). The chapter’s alternate split reconciles cleanly: the active pair is (0.025000 + 0.094444) x 96 = 11.47 mAh and sleep is 0.002486 x 96 = 0.239 mAh, and 11.47 + 0.239 = 11.71 – the same total by a different grouping.

Carrying full precision matters here because the Wi-Fi term is 0.094444 / 0.121931 = 77% of every cycle. The design-meaningful takeaway is that battery life is set almost entirely by how often the radio transmits, which is exactly why buffering transmissions – not shrinking the already-tiny sleep current – is the lever that multiplies runtime.

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

Technical boundaries: The mAh division assumes constant currents and full nominal capacity; it omits regulator efficiency, Wi-Fi association and retries, battery voltage sag, temperature, self-discharge, ageing, and sleep leakage outside the listed loads.

Ready: work the ledger before checking it.