IMU Bandwidth Budget Calculation Audit

IMU Bandwidth Budget Calculation Audit

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

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Ada ADA · CALCULATION AUDIT

IMU Bandwidth Budget Calculation Audit

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.

— raw rate, LoRa ceiling, and the aggregation ratio, ~4 minutes

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.

See the relationship before changing it

The figure reads from left to right. The blue card is imu sample rate. The middle card applies this page's rule. The green card is raw imu rate. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only imu sample rate, so the numeric fixture does not switch without explanation.

IMU sample rate changes raw imu rate An input card leads through the rule rate = sample rate x 6 axes x 2 bytes to the raw imu rate result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A faster six-axis stream grows linearly and quickly outruns the LoRa ceiling.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 100 Hz.

  2. 2

    Name the relationship. rate = sample rate x 6 axes x 2 bytes

  3. 3

    Substitute with units. 100 x 6 x 2 = 1,200 B/s

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change imu sample rate

Try Predict the direction of rate = sample rate x 6 axes x 2 bytes. Test another imu sample rate, then compare raw imu rate.

100 Hz
Chapter baseline
Raw IMU rate

Observe A faster six-axis stream grows linearly and quickly outruns the LoRa ceiling. Reset imu sample rate to 100 and compare raw imu rate.

Explain A faster six-axis stream grows linearly and quickly outruns the LoRa ceiling.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only imu sample rate moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only imu sample rate. It is not a field prediction.

TryUse Check derivation to compare the 100 Hz, 6-axis, 2-byte IMU stream with the 4.17 B/s LoRa payload ceiling.
ObserveRaw acquisition produces 1,200 B/s or 103.68 MB/day, which is 288× the radio budget; a 9-value summary still needs 18 B/s.
ExplainEven a 67× reduction remains 4.3× over the ceiling. The aggregation window must lengthen, or the summary must shrink, before average payload rate fits.

1. The raw rate is a product of four numbers.

raw = fsample × axes × bytes = 100 Hz × 6 × 2 B = 1200 B/s

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.

Technical boundaries
The IMU byte-rate model deliberately does not simulate LoRa headers, retransmissions, channel contention, compression compute, or information lost by the nine-value summary; it tests payload rate against the stated airtime ceiling only.

Work the audit first, then check the displayed derivation.

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