Math Bridge: DTLS Bytes and Battery Charge

A field team faces an unresolved physical question: How do 53 secured bytes become a daily battery cost? They must answer it before changing secured bytes 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 secured bytes. The middle card applies this page's relationship. The green card is transmit time. 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.

Walk the arrows. The same byte count drives the same airtime and charge formulas, while derating and self-discharge stay separate cell assumptions.

Derive the baseline in four named moves

1
Name the input. The chapter baseline for secured bytes is 53.
2
Name the relationship. 53 B x 8 = 424 bit 424/250,000 = 0.001696 s = 1.696 ms 20 mA x 0.001696/3,600 = 0.00000942 mAh 1,440 x 0.00000942 + 0.000064 = 0.01363 mAh/day usable charge = 220(1-0.20) = 176 mAh
3
Substitute the chapter fixture. Set secured bytes to 53. The page ledger gives transmit time as 1.70 ms.
4
Read the result. Keep ms beside the value. Use it only inside the technical boundary on this page.

Predict, then change secured bytes

Try Predict the direction of transmit time. Move one control, calculate, then check your prediction.

Observe The same byte count drives the same airtime and charge formulas, while derating and self-discharge stay separate cell assumptions. Reset the control to 53 and compare transmit time.

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

1. Start with the physical story

A radio sends bits, not an abstract message. More bytes mean more bits, more time with the transmitter on, and more charge taken from the cell. The one-time handshake belongs in the daily total once, not once per reading.

Eddie: Keep the chain in order: bytes → bits → seconds → milliamp-hours → daily charge.

2. Name every algebra move

Count bitsMultiply bytes by 8 because one byte contains eight bits.

Find airtimeDivide the bit count by 250,000 bits per second.

Find message chargeMultiply transmit current by seconds, then divide by 3,600 to change mA·s into mAh.

Build the dayMultiply by 1,440 readings and add the handshake charge once.

Bound the yearsApply the reserve, then divide usable charge by annual active use plus the stated annual self-discharge term.

3. Reproduce the chapter case

53 B × 8 = 424 bit
424/250,000 = 0.001696 s = 1.696 ms
20 mA × 0.001696/3,600 = 0.00000942 mAh
1,440 × 0.00000942 + 0.000064 = 0.01363 mAh/day
usable charge = 220(1−0.20) = 176 mAh

The 53/20 = 2.65 byte ratio explains the message-charge ratio. The daily ratio is slightly different because only the secured path includes the one-time handshake term.

4. Try one real input

TryMove the secured record from 53 bytes toward 70 bytes. Watch airtime, message charge, daily charge, annual use, tax, and bounded life move together.

ObserveAt 53 bytes, airtime is 1.696 ms and daily charge is about 0.01363 mAh. Increasing bytes raises every active-use result, but usable charge stays fixed.

ExplainThe same byte count drives the same airtime and charge formulas, while derating and self-discharge stay separate cell assumptions.

Technical boundaries.

This ledger isolates the chapter's fixed-rate transmit arithmetic.

Radio: Receive time, retries, channel access, CPU work, and changing current are outside the fixed 20 mA model.
Security: Record length and handshake charge are chapter values, not universal DTLS sizes.
Cell: The linear annual self-discharge term and 20% reserve do not model chemistry, pulse sag, temperature, or cutoff curves.

Correct, not complete: this ledger does not size a secure deployment or predict field battery life.

5. Use the result in the design

Measure real secured records and radio current, retain sessions where the security design permits, and report record overhead separately from retries, receive windows, processor work, and the cell qualification.

6. Record the evidence state

Record cipher suite, record bytes, handshake bytes and frequency, data rate, current trace, messages per day, retry rate, temperature, cell chemistry, reserve, and the exact lifetime model used.

7. Check yourself

Why multiply bytes by eight?

Answer: The radio rate is in bits per second, while the record length is counted in bytes.

Why is the handshake added only once here?

Answer: This chapter case reuses one session across the day's 1,440 readings; a reconnecting design needs a different handshake count.

Does a 2.65x message-charge ratio prove a 2.65x field-life penalty?

Answer: No. Sleep current, receive work, retries, self-discharge, derating, pulse voltage, temperature, and cutoff also consume or restrict the cell.

Honesty boundary.

This ledger isolates the chapter's fixed-rate transmit arithmetic.

Radio: Receive time, retries, channel access, CPU work, and changing current are outside the fixed 20 mA model.
Security: Record length and handshake charge are chapter values, not universal DTLS sizes.
Cell: The linear annual self-discharge term and 20% reserve do not model chemistry, pulse sag, temperature, or cutoff curves.

Correct, not complete: this ledger does not size a secure deployment or predict field battery life.