Audit the Battery-Life Ledger

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

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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.

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.

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