TTL and Relay Density
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.
See the relationship before changing it
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 source-to-destination distance, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 80 m.
- 2
Name the relationship. TTL = ceil(distance / 10 m spacing) x 2
- 3
Substitute with units. ceil(80 / 10) x 2 = 16 hops
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change source-to-destination distance
Try Predict the direction of TTL = ceil(distance / 10 m spacing) x 2. Test another source-to-destination distance, then compare safety-scaled ttl.
Observe Distance and relay spacing set a hop estimate before the safety multiplier expands TTL. Reset source-to-destination distance to 80 and compare safety-scaled ttl.
Explain Dividing distance into relay-sized crossings and rounding up gives a whole-hop estimate, so this model's allowance rises in steps.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
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 . Calculate this case.
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. Check shows this.
Use TTL to bound hop reach and relay density to bound flooding load; neither number alone proves field reliability, so the calculated relay range is a starting point for measured coverage and congestion tests. Check confirms it.
Technical boundaries
The hop estimate assumes 10 m relay spacing and doubles the rounded-up hop count. It does not simulate flooding collisions, relay queues, retransmissions, cached messages for sleeping nodes, radio propagation, or changes in the mesh topology.
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.
Office worked example
The office example is tighter because the measured corner-to-corner distance is 50 m and relay spacing is 8 m.
Relay density check
The quick-reference ranges translate directly into relay counts before field testing.
Every number above is taken from the chapter's own TTL and relay-density example and re-derived step by step.