Does Halving the Payload Really Halve the Battery Cost?

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

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Ada ADA · CALCULATION AUDIT

Does Halving the Payload Really Halve the Battery Cost?

The chapter says an 8-byte binary message cuts radio energy “by roughly five to six times” versus a 47-byte CBOR message, on an SF12 link at 250 bits/s with a 44 mA radio. That is a battery claim, not just a byte claim, since airtime falls from about 1.5 s to 0.26 s. This audit traces the chain to answer directly: does halving the payload really halve the battery cost?

Companion to the chapter Choosing an IoT Data Format — every number here comes from that chapter.

Ada: The chapter says the 8-byte binary message cuts radio energy “by roughly five to six times” versus the 47-byte CBOR message. That is a claim about battery, not just bytes, so let me trace the whole chain on the chapter’s own SF12 numbers — 250 bits/s and a 44 mA radio — and find exactly where the ratio comes from.

Airtime first, from the chapter’s own airtime = payload_bytes x 8 / data_rate:

  • CBOR, 47 bytes: 47 x 8 / 250 = 376 / 250 = 1.504000 s (chapter: about 1.5 s)
  • Binary, 8 bytes: 8 x 8 / 250 = 64 / 250 = 0.256000 s (chapter: about 0.26 s)

Then energy, energy = radio_current x airtime, converting milliamp-seconds to microamp-hours with x 1000 / 3600:

  • CBOR: 44 x 1.504000 = 66.176000 mA-s, and 66.176000 x 1000 / 3600 = 18.382222 uAh — about 18 uAh
  • Binary: 44 x 0.256000 = 11.264000 mA-s, and 11.264000 x 1000 / 3600 = 3.128889 uAh — about 3 uAh

Both match the chapter. Now the ratio: 66.176000 / 11.264000 = 5.875000. That is not a coincidence — it is exactly the byte ratio 47 / 8 = 5.875000, because the shared factors (the x 8, the / 250, and the 44 mA) all cancel. On a constrained link where nothing but the payload changes, energy is linear in bytes, so the energy saving equals the byte saving.

The honest caveat is the one the chapter already flags: real LoRaWAN airtime also carries a fixed preamble and symbol overhead that does not shrink with the payload. That fixed floor makes the measured ratio smaller than 5.875x, so “five to six times” is the ceiling of the saving — and the format choice buys the most battery precisely when the payload dominates that fixed overhead.

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