Math Bridge: CoAP Observe Wake-Event Energy

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Math BridgeCoAPStruggle-friendly runway

Why do event savings and byte savings disagree?

Count radio wake events separately from transferred bytes, then turn one measured wake cost into daily joules.

Eddie, the electronics guideEddie guides
The one targetUse wake-event count—not byte count alone—to estimate radio-cycle energy.
The chapter case1,440 polling events versus 241 Observe events and a 3.00 mJ wake cycle.
What it buys youSeparate, honest bandwidth and energy claims for the same traffic trace.

A field team faces an unresolved physical question: Why do event savings and byte savings disagree? They must answer it before changing wake energy on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is wake energy. The middle card applies this page's relationship. The green card is observe events. 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Wake energy changes observe events An input card leads through the page relationship to the observe events result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The ratio depends on event counts; the absolute joules depend on a measured energy per event.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for wake energy is 3.

  2. 2

    Name the relationship. Observe events = 1 + 240 = 241 event saving = 1-241/1,440 = 83.3% byte saving = 1-6,764/63,360 = 89.3% polling = 1,440(3.00 mJ) = 4.32 J/day Observe = 241(3.00 mJ) = 0.723 J/day

  3. 3

    Substitute the chapter fixture. Set wake energy to 3. The page ledger gives observe events as 241.

  4. 4

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

Predict, then change wake energy

Try Predict the direction of observe events. Move one control, calculate, then check your prediction.

3
Chapter baseline
Observe events

Observe The ratio depends on event counts; the absolute joules depend on a measured energy per event. Reset the control to 3 and compare observe events.

Explain Only wake energy moves here. The other chapter fixtures remain fixed.

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 wake energy moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only wake energy. It replays the chapter fixture; it is not a field prediction.

1. Start with the physical story

A constrained radio often pays a setup cost each time it wakes, synchronises, transmits, and sleeps. Two small packets with different byte counts can therefore cost almost the same wake energy. Observe reduces both events and bytes, but by different percentages.

Eddie: First count wake cycles. Only then multiply by the measured energy of one cycle.

2. Name every algebra move

1

Count Observe eventsAdd one registration to 240 notifications.

2

Find event savingsSubtract the ratio 241/1,440 from one.

3

Find byte savingsRepeat with 6,764/63,360 bytes and keep the result separate.

4

Find daily energyMultiply each event count by 3.00 mJ and divide by 1,000 for joules.

5

Find idealised daysConvert 225 mAh at 3.0 V into 2,430 J and divide by daily joules.

3. Reproduce the chapter case

Observe events = 1 + 240 = 241
event saving = 1−241/1,440 = 83.3%
byte saving = 1−6,764/63,360 = 89.3%
polling = 1,440(3.00 mJ) = 4.32 J/day
Observe = 241(3.00 mJ) = 0.723 J/day

The energy and bandwidth percentages disagree because this teaching model gives every small radio wake the same fixed cost.

4. Try one real input

TryMove the measured wake-cycle cost from 3.00 mJ. Daily joules and idealised days change, while both traffic-saving percentages stay fixed.

Wake energy
Observe events
Event-energy saving
Bandwidth saving
Polling energy
Observe energy
Cell energy
Polling-only days
Observe-only days
Ideal life multiple

ObserveDoubling per-wake energy doubles both daily energy figures and halves both idealised lifetimes, but the 83.3% event saving remains the same.

ExplainThe ratio depends on event counts; the absolute joules depend on a measured energy per event.

Technical boundaries.

This is a fixed-cost wake-event model for the chapter's 24-hour trace.

Radio
Packet length, receive windows, retries, contention, data rate, and sleep transition costs may change each event.
Traffic
The polling and notification counts are fixed chapter scenarios.
Cell
The idealised days omit background load, self-discharge, derating, voltage cutoff, and ageing.

Correct, not complete: this ledger does not predict field life or prove Observe best for every resource.

5. Use the result in the design

Count actual wakes and bytes from a trace, then measure energy per state transition. Report bandwidth, radio-cycle energy, and total device energy as separate claims.

6. Record the evidence state

Record registration lifetime, notification rule, polling interval, event counts, bytes, losses, retries, radio state trace, per-event energy distribution, background current, and cell conditions.

7. Check yourself

Why are 83.3% and 89.3% both correct?
Answer: They describe different quantities: radio events and transferred bytes.
What measurement turns an event count into joules?
Answer: A current-and-voltage trace integrated over the wake, transmit or receive, and return-to-sleep cycle.
Why is the 3,361-day Observe result not a deployment promise?
Answer: It assigns the entire ideal cell energy to radio wakes and omits every other load and cell limit.
Honesty boundary.

This is a fixed-cost wake-event model for the chapter's 24-hour trace.

Radio
Packet length, receive windows, retries, contention, data rate, and sleep transition costs may change each event.
Traffic
The polling and notification counts are fixed chapter scenarios.
Cell
The idealised days omit background load, self-discharge, derating, voltage cutoff, and ageing.

Correct, not complete: this ledger does not predict field life or prove Observe best for every resource.

Return to CoAP Observe Extension with the maths unpacked →