TTL and Relay Density

Ada audits TTL and relay density — hop count, flooding budget, and sizing checks

ADA · CALCULATION AUDIT

Foundations · optional mathematics and physics

TTL and Relay Density

The BLE-Mesh calculator’s default run takes an 80 m node distance and 10 m relay spacing to ceil(80 / 10) = 8 hops, then a 2.0 safety multiplier lifts the TTL to 16 and the settling delay to 160 ms. The tighter office example measures 50 m corner-to-corner at 8 m spacing for a TTL of 9 and a 90 ms window. This audit re-derives each figure and the 100-200-relay building estimate, asking whether the chapter’s hop, TTL, and density numbers all hold.

Companion to the chapter BLE Mesh Networking — every number here comes from that chapter.

Hop count, flooding budget, and sizing checks

A BLE Mesh TTL is a physics-and-traffic budget, not a magic reliability knob. The number must cover the physical hop count, leave a margin for alternate paths, and avoid flooding every relay longer than necessary.

Calculator default

The interactive default uses an 80 m maximum node distance, 10 m relay spacing, 10 ms per hop, and a 2.0 safety multiplier.

ceil(80 / 10) = 8 hops

TTL = ceil(8 x 2.0) = 16

delay = 16 x 10 ms = 160 ms

Office worked example

The office example is tighter because the measured corner-to-corner distance is 50 m and relay spacing is 8 m.

50 / 8 = 6.25, so round up to 7 hops

TTL = 7 + 2 = 9

settling window = 9 x 10 ms = 90 ms

Relay density check

The quick-reference ranges translate directly into relay counts before field testing.

home: 50 x 10-20% = 5-10 relays

office: 200 x 15-25% = 30-50 relays

building: 1000 x 10-20% = 100-200 relays

Every number above is taken from the chapter's own TTL and relay-density example and re-derived step by step.