Ada Audits the IMU Bandwidth Budget
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Ada Audits the IMU Bandwidth Budget
The chapter streams a 100 Hz IMU as 1,200 bytes/s — about 103.68 MB/day — against a LoRa ceiling of roughly 4.17 bytes/s, leaving the raw stream 288x over budget. Aggregating to nine summary values cuts it 67x, to 18 bytes/s. This audit works the IMU bandwidth budget to show that even a 67x cut is still 4.3x over the radio’s limit.
Companion to the chapter Edge Data Architecture — every number here comes from that chapter.
A six-axis IMU is a firehose. The arithmetic decides whether a battery node can ever put that stream on a 1% duty-cycle radio, or whether it has to summarise first.
1. The raw rate is a product of four numbers.
Over a day that is 1200 × 86,400 = 103,680,000 B = 103.68 MB/day. (The chapter's "101 MB/day" rounds the rate to 1.17 KB/s; carried at full precision it is 103.68 MB/day.)
2. The radio has a hard ceiling.
A 1% duty cycle at SF7 clears about 250 bytes per minute, so 250 ÷ 60 = 4.17 B/s. The raw stream is 1200 ÷ 4.17 = 288× over that ceiling (the chapter's "285×" rounds the ceiling up to 4.2 B/s).
3. Aggregation trades detail for fit.
Nine summary values (RMS + peak per accelerometer axis, RMS per gyroscope axis) × 2 B, once per second = 18 B/s.
| Quantity | Arithmetic | Result |
|---|---|---|
| Raw rate | 100 × 6 × 2 | 1200 B/s |
| Raw per day | 1200 × 86,400 | 103.68 MB/day |
| LoRa ceiling | 250 ÷ 60 | 4.17 B/s |
| Raw over budget | 1200 ÷ 4.17 | 288× |
| Aggregated rate | 9 × 2 ÷ 1 s | 18 B/s |
| Reduction | 1200 ÷ 18 | 66.7× ≈ 67× |
| Aggregated per day | 18 × 86,400 | 1.56 MB/day |
| Aggregated vs ceiling | 18 ÷ 4.17 | 4.3× (still over) |
What the audit buys you: even after a 67× cut the one-second summary at 18 B/s is still 4.3× over the 4.17 B/s ceiling — the numbers say a one-second window is not enough, so the aggregation window must stretch (or the value count shrink) before this node is legal on the radio.
Every number above is taken from the chapter’s own examples and re-derived step by step.