Where the 89% Saving and the 772-Day Battery Come From

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

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Ada ADA · CALCULATION AUDIT

Where the 89% Saving and the 772-Day Battery Come From

The chapter quotes two figures a reviewer must defend: CoAP Observe cuts monitoring traffic by about 89%, and a polling sensor lasts about 772 days on an 18650 cell. Both are reconstructable from the chapter’s own 44-byte and 28-byte messages and its 3000 mAh battery. This audit carries each end to end to show exactly where the 89% saving and the 772-day battery come from.

Companion to the chapter CoAP Observe Server Push — every number here comes from that chapter.

Ada: This chapter quotes two numbers a reviewer will be asked to defend: Observe cuts monitoring traffic by about 89%, and a polling sensor lasts about 772 days on an 18650 cell. Both are reconstructable from the chapter’s own message sizes and battery spec, so let me carry each through end to end.

  • Polling bandwidth (60 s interval, 24 h): 1440 exchanges x 44 bytes = 63360 bytes = 61.875 KB.
  • Observe bandwidth (1 registration + 240 notifications): 44 + 240 x 28 = 6764 bytes = 6.605 KB.
  • Saving: (63360 - 6764) / 63360 = 0.89324 = 89.3%, matching the chapter’s 89.3%.
  • Where “40 kJ” comes from: an 18650 at 3.7 V and 3000 mAh stores 3.7 V x 3.0 Ah x 3600 s = 39960 J, which the chapter rounds to 40 kJ.
  • Polling energy at 3.0 mJ per confirmed exchange, 17280 polls/day (every 5 s): 17280 x 3.0 = 51840 mJ = 51.84 J/day.
  • Battery life: 39960 / 51.84 = 770.8 days; using the rounded 40000 / 51.84 = 771.6, which is the chapter’s ~772 days.

The audit conclusion is that the two figures measure the same lever from two directions: Observe removes about nine of every ten messages, and since radio energy is proportional to messages sent, that same reduction is what turns a two-year polling battery into a shelf-life-limited one. The design meaning is that the saving is real only while the resource changes slowly – the 89% and the 772 days both assume roughly 10 notifications an hour, so a chattier resource must be rate-limited or the budget silently reverts to the polling case.

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