The 20x Cut, and the 300x the Contract Forbids

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

ADA · CALCULATION AUDIT

The 20x Cut, and the 300x the Contract Forbids

The chapter promises about 20x less radio traffic from adaptive sampling plus gateway aggregation: sampling every 3 seconds gives 1,200 readings an hour, and sending roughly 60 keeps only 24 KB. A gateway could collapse the whole hour into one summary for a 300x cut — but that lone mean erases a one-minute 95 C spike. This audit works the numbers to show why the honest reduction stops at 20x, and the 300x the data-quality contract forbids.

Companion to the chapter Radio Gateway Aggregation — every number here comes from that chapter.

Ada: The chapter promises “~20x less radio traffic” from adaptive sampling plus gateway aggregation, and it is right to stop there. But a bigger number hides one step away, and the gap between them is the data-quality contract. Let me work the chapter’s own figures.

Sampling every 3 seconds means one hour holds 3600 / 3 = 1200 readings. The naive uplink sends all of them; the adaptive-plus-aggregate scheme sends “~60 transmitted items instead of 1,200,” so packets fall by 1200 / 60 = 20.0x.

That 20x holds in bytes too, not just packet count. At a 20-byte payload the naive hour is 1200 x 20 = 24,000 bytes, about 24,000 / 1000 = 24 KB. The kept path is roughly 60 change-triggered readings plus one rollup: 60 x 20 + 80 = 1,280 bytes, and 24,000 / 1,280 = 18.8x — the same ~20x the chapter quotes.

Now the temptation. If a gateway collapsed the whole hour into a single under-80-byte summary, the byte cut would be 24,000 / 80 = 300x, fifteen times the headline. So why not take it? Because that lone summary is only a mean. A bearing that sits at 40 C for 59 minutes and spikes to 95 C for one would report a harmless 40-ish average, and the maintenance signal is gone.

Design meaning: the honest reduction is set by what the downstream decision must still see, not by what the radio could compress to — the gateway stops near 20x, carrying the min, max, count, and event flags, precisely so the extremes survive the trip that a 300x single-mean summary would erase.

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