Math Bridge: HTTP Radio Time and Battery Energy

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Math BridgeApplication ProtocolsStruggle-friendly runway

What does 24 seconds less radio time buy from the battery?

Connect active radio seconds to supply energy, cell heat, voltage sag, and self-discharge.

Eddie, the electronics guideEddie guides
The one targetTurn daily active seconds into the chapter’s radio and cell-loss ledger.
The chapter caseHTTP/1.1 at 33.6 s/day versus HTTP/3 at 9.6 s/day on a 3.7 V cell.
What it buys youA visible separation between radio energy, internal heat, pulse sag, and shelf loss.

A field team faces an unresolved physical question: What does 24 seconds less radio time buy from the battery? They must answer it before changing active time 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 active time. The middle card applies this page's relationship. The green card is nameplate energy. 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.

Active time changes nameplate energy An input card leads through the page relationship to the nameplate energy result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Protocol setup time changes duration-dependent energy. Current and internal resistance set the depth of each pulse sag.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for active time is 33.6.

  2. 2

    Name the relationship. nameplate=3.7(2.000)=7.40 Wh HTTP/1.1 radio=3.7(0.300)(33.6)=37.3 J/day cell heat=0.300²(0.080)(33.6)=0.242 J/day sag=0.300(0.080)=24.0 mV remaining=2000(0.98)^12=1570 mAh

  3. 3

    Substitute the chapter fixture. Set active time to 33.6. The page ledger gives nameplate energy as 7.40 Wh.

  4. 4

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

Predict, then change active time

Try Predict the direction of nameplate energy. Move one control, calculate, then check your prediction.

33.6
Chapter baseline
Nameplate energy

Observe Protocol setup time changes duration-dependent energy. Current and internal resistance set the depth of each pulse sag. Reset the control to 33.6 and compare nameplate energy.

Explain Only active time 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 active time moves. Field effects named in the page's technical boundary stay fixed.

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

1. Start with the physical story

Shorter setup reduces how long the radio draws 300 mA. It saves supply energy and heat inside the cell, but it does not change the instant voltage sag caused by the same current pulse.

Eddie: Follow one quantity at a time; every displayed result comes from the same ledger.

2. Name every algebra move

1

Turn charge into nameplate energyMultiply 2.000 Ah by 3.7 V.

2

Find radio energyMultiply voltage, current, and active seconds.

3

Find internal heatMultiply I², internal resistance, and time.

4

Find pulse sagMultiply current by internal resistance; duration does not enter.

5

Apply shelf lossKeep 98% of charge once per month for 12 months.

3. Reproduce the chapter case

nameplate=3.7(2.000)=7.40 Wh
HTTP/1.1 radio=3.7(0.300)(33.6)=37.3 J/day
cell heat=0.300²(0.080)(33.6)=0.242 J/day
sag=0.300(0.080)=24.0 mV
remaining=2000(0.98)^12=1570 mAh

The arithmetic stays visible so that units and assumptions can be checked before the result is used.

4. Try one real input

TryMove active time from 33.6 seconds toward 9.6 seconds. Predict which terms change and which stay fixed.

Active time
Nameplate energy
Pulse sag
Loaded voltage
Radio energy
Cell heat
Time saved vs HTTP/1.1
Radio energy saved
Cell heat saved
Charge after 12 months
Shelf loss
Shelf loss share

ObserveAt 9.6 seconds, the radio term falls from 37.3 J/day to 10.7 J/day and cell heat falls from 0.242 J/day to 0.0691 J/day. Sag remains 24 mV.

ExplainProtocol setup time changes duration-dependent energy. Current and internal resistance set the depth of each pulse sag.

Technical boundaries.

This transparent ledger reproduces the named chapter case.

Traffic
The slider treats daily active time as measured input and does not model packets, RTT, loss, or retries.
Battery
Voltage, current, internal resistance, and monthly shelf loss are fixed illustrative values.
Accounting
Sleep, receive, regulator, quiescent, conversion, and application loads are outside it.

Correct, not complete: this ledger does not predict battery life or prove that one HTTP version is best for every IoT link.

5. Use the result in the design

Measure actual request timing and current on the target network; combine active, receive, idle, sleep, retry, conversion, and shelf-loss terms.

6. Record the evidence state

Record HTTP version, handshake mode, resumption success, RTT, packet loss, active seconds, current trace, cell state, retries, and daily request count.

7. Check yourself

Why does shorter active time not reduce the 24 mV sag?
Answer: Sag is IR for the same 300 mA pulse and 80 milliohm cell; duration affects energy, not the instant drop.
Is the 0.173 J/day heat saving already inside the 26.6 J/day radio-energy saving?
Answer: No. The first is heat inside the cell resistance; the second is the ideal supply-side VIt term used by the chapter calculator.
Does 2% monthly self-discharge predict a real deployment exactly?
Answer: No. Chemistry, temperature, age, state of charge, storage, and protection electronics change it.
Honesty boundary.

This transparent ledger reproduces the named chapter case.

Traffic
The slider treats daily active time as measured input and does not model packets, RTT, loss, or retries.
Battery
Voltage, current, internal resistance, and monthly shelf loss are fixed illustrative values.
Accounting
Sleep, receive, regulator, quiescent, conversion, and application loads are outside it.

Correct, not complete: this ledger does not predict battery life or prove that one HTTP version is best for every IoT link.

Return to Modern HTTP for IoT with the maths unpacked →