Energy-Neutral Sizing Calculation Audit

Energy-Neutral Sizing Calculation Audit

Ada checks hourly load, storage reserve, and winter harvest against the same rounded inputs

foundations
math-foundations
energy
harvesting
intermediate
Ada ADA · CALCULATION AUDIT

Energy-Neutral Sizing Calculation Audit

The chapter sizes an outdoor harvesting node: a daily load of about 2.02 mAh (6.7 mWh), a storage reserve of about 26 mAh for seven low-harvest days, and a panel that must deliver at least 4.2 mW in a winter window. The radio event alone is 72.7% of the daily charge. This audit works the energy-neutral sizing to show the load, reserve, and panel must all be checked in the same units.

Companion to the chapter Energy Harvesting Design — every number here comes from that chapter.

The outdoor sensor closes only if the hourly load, storage reserve, and winter harvest window are all checked with the same units. The chapter rounds the daily load energy to 6.7 mWh before the storage and panel sizing steps, so the audit names that rounding point.

See the relationship before changing it

The figure reads from left to right. The blue card is useful harvest window. The middle card applies the page rule. The green card is required panel power. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Useful harvest window changes required panel power An input card leads through the rule power = 6.7 mWh / (hours x 0.8) to the required panel power result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A shorter winter window demands more panel power for the same daily load.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 2 h/day.

  2. 2

    Name the relationship. power = 6.7 mWh / (hours x 0.8)

  3. 3

    Substitute with units. 6.7 / (2 x 0.8) = 4.19 mW

  4. 4

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

Predict, then change useful harvest window

Try Predict the direction of power = 6.7 mWh / (hours x 0.8). Test another useful harvest window, then compare required panel power.

2 h/day
Chapter baseline
Required panel power

Observe A shorter winter window demands more panel power for the same daily load. Reset useful harvest window to 2 and compare required panel power.

Explain A shorter winter window demands more panel power for the same daily load.

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 useful harvest window moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only useful harvest window. It is not a field prediction.

TryPress Check derivation and follow the outdoor node from its 2.02 mAh daily demand through a seven-day reserve to the winter panel target.
ObserveThe storage allowance rises to about 26 mAh and the short harvest window demands at least 4.2 mW. The radio event alone accounts for 72.7% of daily charge.
ExplainEnergy neutrality requires harvested energy to cover the complete daily load, conversion margin, and low-harvest reserve. Because radio airtime dominates this profile, reducing transmissions changes both required storage and panel power more than trimming the sensing interval.

Load, reserve, panel power, and rounded inputs

Quantity Arithmetic shown Audit result
Sleep charge 0.018 mA x 24 h 0.432 mAh/day.
Sensing charge 6 mA x 3 s x 24 / 3600 0.120 mAh/day.
Radio charge 110 mA x 2 s x 24 / 3600 1.4667 mAh/day.
Daily load 0.432 + 0.120 + 1.4667 2.0187 mAh/day, reported as about 2.02 mAh/day.
Daily energy 2.0187 mAh x 3.3 V 6.6616 mWh/day, rounded in the chapter to 6.7 mWh/day.
Seven-day load 6.7 mWh/day x 7 46.9 mWh after the stated daily-energy rounding.
Storage reserve 46.9 / 0.8 / 0.7 83.75 mWh, rounded to 83.8 mWh.
Storage capacity 83.75 mWh / 3.2 V 26.17 mAh, so about 26 mAh before temperature and aging margin.
Panel power 6.7 mWh / (2 h x 0.8) 4.1875 mW, rounded to 4.2 mW during useful winter harvest hours.

Engineering consequence: the radio event contributes 1.4667 / 2.0187 = 72.7% of the daily charge. If the field panel misses the 4.2 mW winter target, lowering radio time or transmit retries helps the ledger more than shaving a small sensing interval.

Technical boundaries
The energy-neutral sizing deliberately does not simulate weather distributions, shading, converter and MPPT efficiency curves, battery aging, leakage, or harvest timing within the day; it balances stated daily load against a fixed winter window.

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.