Ada Audits the Duty-Cycle Battery Ledger
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Ada Audits the Duty-Cycle Battery Ledger
The chapter builds a battery ledger for a gateway node: a baseline hour averages 0.55 mA, giving about 189 days on a 2500 mAh cell, while an optimised schedule that shrinks active-plus-transmit time reaches 2.56 years. That is a roughly 5x jump, and it rests entirely on cutting airtime, not battery size. This audit carries the duty-cycle battery ledger at full precision to show where the 5x comes from.
Companion to the chapter Edge Power and Gateways — every number here comes from that chapter.
Battery life is not a datasheet promise; it is a state-weighted average of current. Here is the ledger carried at full precision, then rounded, so the "189 days" and "5×" claims are auditable.
1. Average current is a weighted sum over one cycle.
Baseline hour (tcycle = 3600 s): (30×25) + (10×120) + (3560×0.01) = 750 + 1200 + 35.6 = 1985.6 mA·s. Divide by 3600: 0.55156 mA (the chapter rounds to 0.55 mA).
2. Lifetime is capacity over that average.
2500 ÷ 0.55156 = 4533 h = 188.9 days ≈ 189 days. (Using the rounded 0.55 mA gives the chapter's 4545 h.)
3. The optimised design shrinks the active seconds.
Active 5 s, transmit 2 s: (5×25) + (2×120) + (3593×0.01) = 125 + 240 + 35.93 = 400.93 mA·s ÷ 3600 = 0.11137 mA, so 2500 ÷ 0.11137 = 22,448 h = 2.56 years.
| Design | Charge/hour | Iavg | Lifetime |
|---|---|---|---|
| Baseline | 1985.6 mA·s | 0.55156 mA | 4533 h (189 d) |
| Optimised | 400.93 mA·s | 0.11137 mA | 22,448 h (2.56 y) |
| Improvement | — | 0.55156 ÷ 0.11137 | 4.95× ≈ 5× |
What the audit buys you: transmit current (120 mA) is 4.8× the sensing current, so the entire 5× lifetime jump comes from cutting active-plus-transmit time from 40 to 7 seconds per hour — sleep at 0.01 mA barely moves the ledger, which is why the design lever is airtime, not a bigger battery.
Every number above is taken from the chapter’s own examples and re-derived step by step.