Audit the Battery-Life Ledger

Audit the Battery-Life Ledger

Ada turns each measured state into charge, then into two lifetime estimates with the rounding shown

foundations
math-foundations
energy
average-current
intermediate
Ada ADA · CALCULATION AUDIT

Audit the Battery-Life Ledger

The chapter’s worked cycle reports every 10 minutes (600 s): sleep at 0.008 mA, a 42 mA radio burst, and other states summing to 146.736 mA-s — an average of about 245 uA that a derated 1680 mAh gives about 286 days. Add two weak-signal retries and it falls to about 105 days. This audit treats the lifetime as an auditable battery-life ledger, row by row.

Companion to the chapter Energy-Aware Design Basics — every number here comes from that chapter.

Treat the lifetime number as an auditable ledger, not a guess. Every row below comes from the measured trace in the worked example, then the rounding is shown before the battery-life claim is accepted.

See the relationship before changing it

The figure reads from left to right. The blue card is radio-active time. The middle card applies this page's rule. The green card is cycle-average current. 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 radio-active time, so the numeric fixture does not switch without explanation.

Radio-active time changes cycle-average current An input card leads through the rule average = (20.736 mA-s fixed states + 42 mA x radio time) / 600 s to the cycle-average current result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A longer radio state raises the cycle average far faster than the low-current sleep term.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 3 s.

  2. 2

    Name the relationship. average = (20.736 mA-s fixed states + 42 mA x radio time) / 600 s

  3. 3

    Substitute with units. (20.736 + 42 x 3) / 600 = 0.245 mA

  4. 4

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

Predict, then change radio-active time

Try Predict the direction of average = (20.736 mA-s fixed states + 42 mA x radio time) / 600 s. Test another radio-active time, then compare cycle-average current.

3 s
Chapter baseline
Cycle-average current

Observe A longer radio state raises the cycle average far faster than the low-current sleep term. Reset radio-active time to 3 and compare cycle-average current.

Explain A longer radio state raises the cycle average far faster than the low-current sleep term.

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 radio-active time moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only radio-active time. It is not a field prediction.

TryThe chapter’s worked cycle reports every 10 minutes ( 600 s ): sleep at 0.008 mA , a 42 mA radio burst, and other states summing to 146.736 mA-s — an average of about 245 uA that a derated 1680 mAh gives about 286 days . Use Check derivation.
ObserveThe displayed ledger resolves 10 minutes, 600 s, 0.008 mA, 42 mA, 146.736 mA-s at full precision. This audit treats the lifetime as an auditable battery-life ledger, row by row. Check derivation shows this.
ExplainReview rule: accept the lifetime claim only when the state durations, usable-capacity derating, rounding choice, and retry assumption are recorded with the trace. Check derivation confirms it.

1. Turn each measured state into charge

Current multiplied by duration gives charge in mA*s for one 600-second reporting cycle.

Qcycle = sum(Istate x tstate)
State Trace value Charge arithmetic Result
Sleep 0.008 mA for 592 s 592 x 0.008 4.736 mA*s
Sensor warm-up 2 mA for 3 s 3 x 2 6 mA*s
Compute 6 mA for 1 s 1 x 6 6 mA*s
Radio transmit/receive 42 mA for 3 s 3 x 42 126 mA*s
Storage plus shutdown 4 mA for 1 s 1 x 4 4 mA*s
Total One cycle 4.736 + 6 + 6 + 126 + 4 146.736 mA*s verified

2. Convert cycle charge into average current

The exact division is 146.736 / 600 = 0.24456 mA. The paragraph rounds that to 0.2446 mA, which is 0.24456 x 1000 = 244.56 uA, or about 245 uA.

3. Convert usable capacity into baseline lifetime

Derating the source gives 2400 x 0.70 = 1680 mAh. Using the displayed rounded current gives 1680 / 0.2446 = 6868.4 h, and 6868.4 / 24 = 286.2 days, so the text's "about 286 days" is consistent.

4. Audit weak-signal retries

Two extra attempts at 3 seconds and 42 mA add 2 x 3 x 42 = 252 mA*s. The new cycle charge is 146.736 + 252 = 398.736 mA*s, so 398.736 / 600 = 0.66456 mA, rounded to 0.6646 mA. The lifetime becomes 1680 / 0.6646 = 2527.8 h, and 2527.8 / 24 = 105.3 days. That is 105.3 / 286.2 = 0.368 of the baseline, or about a 63 percent lifetime loss.

Review rule: accept the lifetime claim only when the state durations, usable-capacity derating, rounding choice, and retry assumption are recorded with the trace.

Technical boundaries
The battery ledger deliberately does not simulate voltage sag, regulator loss, self-discharge, temperature, capacity fade, or a distribution of retry counts; it integrates the stated cycle states and one explicit retry scenario.

Work the audit first, then check the displayed derivation.

Every number above is taken from this chapter's own worked example and re-derived step by step.