The Sleep Floor Sets the Battery Life

The Sleep Floor Sets the Battery Life

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

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

The Sleep Floor Sets the Battery Life

A battery-powered ESP32 environmental-monitor node sends a reading every 300 s, drawing 160 mA during the 0.2 s WiFi transmit but only 0.8 mA asleep the rest of the time. On its 3000 mAh pack that averages 0.92 mA and lasts about 136 days, clearing the 7-day target by 19x. This audit rebuilds the average current term by term and asks whether the headline 160 mA transmit peak or the 0.8 mA sleep floor really sets that battery life.

Companion to the chapter Capstone Projects — every number here comes from that chapter.

Try

A battery-powered ESP32 environmental-monitor node sends a reading every 300 s , drawing 160 mA during the 0.2 s WiFi transmit but only 0.8 mA asleep the rest of the time. Calculate this case.

Observe

This audit rebuilds the average current term by term and asks whether the headline 160 mA transmit peak or the 0.8 mA sleep floor really sets that battery life. Check shows this.

Explain

Now the part worth noticing: the sleep term is 0.79946667 / 0.91946667 = 86.9% of the average, while the headline 160 mA transmit peak is only 0.10666667 / 0.91946667 = 11.6%. Because the radio is awake just 0.067% of the time, battery life is governed almost entirely by the 0.8 mA sleep floor, not the transmit peak, so on this device shaving the deep-sleep current buys farmore than reducing the brief transmit peak. Check confirms it.

See the relationship before changing it

Change the input, apply the rule once, then read the result with its unit.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 300 s.

  2. 2

    Name the relationship. average current = 160 x 0.2/interval + 0.8 x (1 - 0.2/interval) + 20 x 0.2/interval; life = 3000/average/24

  3. 3

    Substitute with units. at 300 s, average = 0.9195 mA and life = 135.9 days

  4. 4

    Read the result. Keep the unit beside the value, then use the result only inside the technical boundary below.

Predict, then change report interval

Try Predict how ideal battery life responds when report interval moves. Calculate report interval; compare ideal battery life with that prediction.

300 s
Chapter baseline
Ideal battery life

Observe Return to 300 s. Recheck ideal battery life with report interval at its chapter value.

Explain Longer intervals cut burst cost until the sleep floor dominates.

Check yourself

What should you do before trusting a moved-slider result?
Answer: Predict its direction, apply the displayed relationship, keep the units, and compare the reset value with the chapter’s worked baseline.
What does this small model leave out?
Answer: Only report interval moves here. The ideal battery life calculation excludes field effects listed below.

Honesty note. The ideal battery life result holds report interval as the only changing input. It is not a field prediction.

Technical boundaries

The report interval changes while the 3000 mAh battery, burst currents and duration, and 0.8 mA sleep current stay fixed. The lifetime estimate leaves out self-discharge, regulator losses, temperature, radio retries, sensor warm-up, and sleep current changing with age.

Ada: The panel above headlines a 160 mA transmit current, but I want to check which term actually decides the 136-day battery life. I will rebuild the average current from the chapter’s own duty cycle: the radio transmits 0.2 s out of every 300 s.

  • Active duty cycle: 0.2 / 300 = 0.00066667 (about 0.067% of the time)
  • Transmit contribution: 160 mA x 0.00066667 = 0.10666667 mA
  • Sleep contribution: 0.8 mA x (1 - 0.00066667) = 0.8 x 0.99933333 = 0.79946667 mA
  • Sensor contribution: 20 mA x 0.00066667 = 0.01333333 mA
  • Average current: 0.10666667 + 0.79946667 + 0.01333333 = 0.91946667 mA, which rounds to 0.92 mA

Feeding that into the 3000 mAh pack: 3000 / 0.92 = 3260.9 hours, and 3260.9 / 24 = 135.9, so about 136 days, clearing the 7-day target by 136 / 7 = 19x.

Now the part worth noticing: the sleep term is 0.79946667 / 0.91946667 = 86.9% of the average, while the headline 160 mA transmit peak is only 0.10666667 / 0.91946667 = 11.6%. Because the radio is awake just 0.067% of the time, battery life is governed almost entirely by the 0.8 mA sleep floor, not the transmit peak, so on this device shaving the deep-sleep current buys far more runtime than a faster or lower-power transmitter ever could.

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