The 20x Cut, and the 300x the Contract Forbids
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.
See the relationship before changing it
The figure reads from left to right. The blue card is kept readings. The middle card applies the page rule. The green card is byte reduction. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 60 readings/hour.
- 2
Name the relationship. reduction = 24,000 bytes / (kept x 20 bytes + 80 bytes)
- 3
Substitute with units. 24,000 / (60 x 20 + 80) = 18.75 times
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change kept readings
Try Predict the direction of reduction = 24,000 bytes / (kept x 20 bytes + 80 bytes). Test another kept readings, then compare byte reduction.
Observe Keeping fewer readings saves bytes, but the minimum, maximum, count, and event flags still need space. Reset kept readings to 60 and compare byte reduction.
Explain Keeping fewer readings saves bytes, but the minimum, maximum, count, and event flags still need space.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
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.
The reduction ratios deliberately do not simulate bursty anomalies, packet framing, retry traffic, downlinks, or whether aggregation preserves diagnostic fidelity; the 20x contract counts only the stated samples retained for radio delivery.
Work the audit first, then check the displayed derivation.
Every number above is taken from the chapter’s own material and re-derived step by step.