The Profile Energy Budget

The Profile Energy Budget

Ada audits the profile energy budget — payload rate, packets, duty cycle, and battery life

foundations
math-foundations
bluetooth
ble
intermediate
Ada ADA · CALCULATION AUDIT

Bluetooth · optional mathematics and physics

The Profile Energy Budget

A 100 Hz, three-axis sensor packing 16 bits per axis produces 6 bytes a sample and a 4,800 bps stream that both Classic Bluetooth SPP and BLE GATT can carry. Yet their battery lives split hard: SPP’s always-active link lasts 3.1 days while duty-cycled BLE reaches 46.8 days. This audit rebuilds the packing, packet, and current ledgers and asks whether that gap is magic, or simply the radio sleep time BLE wins between connection events.

Companion to the chapter Profiles for Interoperability — every number here comes from that chapter.

Payload rate, packets, duty cycle, and battery life, ~4 minutes

A profile choice is a physics choice once the radio has to wake, send bytes, and return to sleep. Keep the payload arithmetic visible before comparing Classic Bluetooth SPP with BLE GATT.

Try

A 100 Hz , three-axis sensor packing 16 bits per axis produces 6 bytes a sample and a 4,800 bps stream that both Classic Bluetooth SPP and BLE GATT can carry. Calculate this case.

Observe

This audit rebuilds the packing, packet, and current ledgers and asks whether that gap is magic, or simply the radio sleep time BLE wins between connection events. Check shows this.

Explain

BLE lasts 46.8 days instead of SPP's 3.1 days because its connection interval leaves the radio asleep between short GATT events, whereas the SPP ledger keeps the link at its active-current floor. Check confirms it.

See the relationship before changing it

The figure reads from left to right. The blue input is sample rate. The middle card names the page’s rule. The green output is sensor payload rate. The arrow matters: change the input, apply the rule once, then read the result with its unit.

Sample Rate changes sensor payload rate A three-part teaching diagram connects sample rate, the rule rate = samples/s x 6 bytes/sample x 8 bits/byte, and sensor payload rate. INPUT Sample rate APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrow. The payload rate grows in direct proportion to the sample rate.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 100 samples/s.

  2. 2

    Name the relationship. rate = samples/s x 6 bytes/sample x 8 bits/byte

  3. 3

    Substitute with units. 100 x 6 x 8 = 4,800 bit/s

  4. 4

    Read the result. Keep the unit beside the value, then use the result only inside the technical boundary below.

Predict, then change sample rate

Try Predict how sensor payload rate responds when sample rate moves. Calculate sample rate; compare sensor payload rate with that prediction.

100 samples/s
Chapter baseline
Sensor payload rate

Observe Return to 100 samples/s. Recheck sensor payload rate with sample rate at its chapter value.

Explain The payload rate grows in direct proportion to the sample rate.

Check yourself

What should you do before trusting a moved-slider result?
Answer: Predict its direction, apply the displayed relationship, keep the units, and compare the reset value with the chapter’s worked baseline.
What does this small model leave out?
Answer: Only sample rate moves here. The sensor payload rate calculation excludes field effects listed below.

Honesty note. The sensor payload rate result holds sample rate as the only changing input. It is not a field prediction.

Technical boundaries

Not represented by “The Profile Energy Budget” are connection-event overhead, retransmissions, PHY changes, controller sleep transitions, battery ageing, or regulator efficiency; “The Profile Energy Budget” therefore reports only its named fixtures.

Ada audits the profile energy budget

Audit step Arithmetic from the scenario Design implication
Sensor payload rate 3 axes x 16 bits = 48 bits = 6 bytes/sample; 6 bytes x 100 Hz = 600 bytes/s = 4,800 bps Both SPP and BLE GATT have enough throughput for this 100 Hz stream.
SPP packing 990-byte MTU / 6 bytes = 165 samples/packet; 100 / 165 = 0.606 packets/s; 990 / (990 + 27) = 97.3% Classic Bluetooth has large throughput margin, but the connection stays comparatively active.
BLE default MTU 23 - 3 = 20 bytes payload; floor(20 / 6) = 3 samples; 100 / 3 = 33.4 notifications/s; 1 / 0.0075 s = 133 events/s The default MTU can carry the stream, but it spends many connection events.
BLE negotiated MTU 185 - 3 = 182 bytes payload; floor(182 / 6) = 30 samples; 100 / 30 = 3.34 notifications/s A larger MTU reduces notification count and leaves more scheduling margin.
Battery comparison SPP: 40 mA x 8 h = 320 mAh/day; 1000 / 320 = 3.125 days. BLE: 2 / 7.5 = 0.267 duty; 10 mA x 0.267 + 0.002 mA x 0.733 = 2.671 mA; 2.671 x 8 = 21.37 mAh/day; 1000 / 21.37 = 46.8 days. The chapter's BLE result is not magic; it follows from radio sleep time between connection events.

Use this audit before generalizing the verdict. If the sample rate, MTU, active current, sleep current, or connection interval changes, rerun the same ledger with measured values.

Every number above is taken from the chapter's own profile energy-budget example and re-derived step by step.