Where a Store-Carry-Forward Collar Spends Its Charge

Where a Store-Carry-Forward Collar Spends Its Charge

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

foundations
math-foundations
calculation-audit
emerging-paradigms
Ada ADA · CALCULATION AUDIT

Where a Store-Carry-Forward Collar Spends Its Charge

An elephant’s GPS collar runs on a 19,000 mAh D-cell and spends only 0.446 mAh/day, which leaves a 38.9x safety margin across a three-year mission. The obvious worry is the DTN radio that carries every reading. This audit totals the daily charge state by state and asks whether that radio is really what drains the collar, or whether sensing — the GPS fixes at 89.8% of the budget — quietly dominates the ledger.

Companion to the chapter DTN Store-Carry-Forward — every number here comes from that chapter.

See the relationship before changing it

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

GPS active time changes gps charge An input card leads through the rule GPS charge = 40 mA x active seconds / 3,600 to the gps charge result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. The GPS fix time dominates the stated daily charge even though the DTN radio carries the data.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 36 s/day.

  2. 2

    Name the relationship. GPS charge = 40 mA x active seconds / 3,600

  3. 3

    Substitute with units. 40 x 36 / 3,600 = 0.400 mAh/day

  4. 4

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

Predict, then change gps active time

Try Predict the direction of GPS charge = 40 mA x active seconds / 3,600. Test another gps active time, then compare gps charge.

36 s/day
Chapter baseline
GPS charge

Observe The GPS fix time dominates the stated daily charge even though the DTN radio carries the data. Reset gps active time to 36 and compare gps charge.

Explain The GPS fix time dominates the stated daily charge even though the DTN radio carries the data.

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

Ada: This chapter’s reliability claim is that a DTN radio barely touches the battery — a 0.446 mAh/day budget that leaves a 38.9x margin on a 19,000 mAh D-cell over three years. That only holds if sensing, not the radio, dominates the ledger. Let me total the daily charge to the microamp-second and carry every digit to the end, using the chapter’s own per-state numbers.

  • TX: 1.3 contacts x 0.135 s x 10 mA = 1.755 mA-s
  • RX: 1.3 x 0.135 s x 6 mA = 1.053 mA-s
  • BLE beacons: 288/day x 0.01 mA-s = 2.88 mA-s
  • GPS fixes: 48 x 30 mA x 1 s = 1,440 mA-s
  • Sleep: 86,400 s x 0.001 mA = 86.4 mA-s
  • MCU wake: 48 x 3 mA x 0.5 s = 72 mA-s
  • Daily total: 1.755 + 1.053 + 2.88 + 1,440 + 86.4 + 72 = 1,604.088 mA-s/day
  • Convert: 1,604.088 / 3,600 = 0.445580 mAh/day, which rounds to the chapter’s 0.446.
  • Three years: 0.445580 mAh/day x 1,095 days = 487.9 mAh (488 mAh from the rounded daily figure).
  • Safety factor: 19,000 / 487.9 = 38.9x.
  • Where it goes: GPS is 1,440 / 1,604.088 = 89.8% of the charge; the entire radio stack (TX + RX + beacons) is only 5.688 / 1,604.088 = 0.35%.

The ledger confirms the counter-intuitive point: the DTN radio that carries the whole mission is not what drains the collar. Sensing outweighs communication by more than two hundred to one, which is exactly why store-carry-forward can afford to wait days for a contact — delayed delivery costs almost no energy.

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

TryRun Check audit on the daily state ledger before extending its 0.44558 mAh total over 3 years.
ObserveGPS accounts for 89.8% of daily use while radio activity contributes only 0.35%.
ExplainOptimizing the 0.35% radio slice cannot materially extend life until the dominant 89.8% GPS state is reduced.
Technical boundaries. The ledger assumes fixed daily event counts, durations, currents, and a 19000 mAh usable battery. It does not model self-discharge, temperature, ageing, regulator loss, failed fixes, contact variability, retransmissions, firmware growth, or battery voltage limits.
Audit result

The arithmetic yields 487.9 mAh over three years and a 38.9x nominal capacity margin, before omitted battery losses.