Duty-Cycle Battery Ledger Calculation Audit

Duty-Cycle Battery Ledger Calculation Audit

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

ADA · CALCULATION AUDIT

Duty-Cycle Battery Ledger Calculation Audit

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.

— average current, lifetime, and the 5× optimisation, ~4 minutes

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.

See the relationship before changing it

The figure reads from left to right. The blue card is measured average current. The middle card applies this page's rule. The green card is ideal pack lifetime. 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 measured average current, so the numeric fixture does not switch without explanation.

Walk the arrows. Lower measured average current lengthens ideal pack life before derating and self-discharge.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 0.55156 mA.

2. 2

   Name the relationship. lifetime = 2,500 mAh / average current / 24 h/day

3. 3

   Substitute with units. 2,500 / 0.55156 / 24 = 188.9 days

4. 4

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

Predict, then change measured average current

Try Predict the direction of lifetime = 2,500 mAh / average current / 24 h/day. Test another measured average current, then compare ideal pack lifetime.

Measured average current

0.55156 mA

Chapter baseline

Ideal pack lifetime

Observe Lower measured average current lengthens ideal pack life before derating and self-discharge. Reset measured average current to 0.55156 and compare ideal pack lifetime.

Explain Lower measured average current lengthens ideal pack life before derating and self-discharge.

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 measured average current moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only measured average current. It is not a field prediction.

TryThe 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 . Use Check derivation.

ObserveThe displayed ledger resolves 0.55 mA, 189 days, 2500 mAh, 2.56 years, 5x at full precision. This audit carries the duty-cycle battery ledger at full precision to show where the 5x comes from. Check derivation shows this.

Explaintransmit 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. Check derivation confirms it.

1. Average current is a weighted sum over one cycle.

I_avg = ( ∑ t_state × I_state ) ÷ t_cycle

Baseline hour (t_cycle = 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.

Technical boundaries
The state ledger deliberately does not simulate battery discharge curves, regulator loss, temperature, self-discharge, gateway receive load, or retry bursts; lifetime is capacity divided by the stated average current.

Work the audit first, then check the displayed derivation.

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