Ad-Hoc Link Calculation Audit

Ad-Hoc Link Calculation Audit

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

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Ada ADA · CALCULATION AUDIT

Ad-Hoc Link Calculation Audit

A factory ad-hoc link driven at 0 dBm over 50 m computes to -51.0 dBm, and the chapter’s practice link then reads 85% PDR, -73 dBm, and 30 ms latency — every check inside the GOOD band. It is tempting to promote that link to a production relay on the tier alone. This audit rebuilds the path-loss and threshold arithmetic and asks whether a matching GOOD tier settles the rollout, or whether backup-path and battery evidence must still clear first.

Companion to the chapter Ad-Hoc Deployment Framework — every number here comes from that chapter.

A routing graph is only as good as its radio evidence: the path-loss math, packet delivery tier, and latency threshold must all point to the same link decision.

See the relationship before changing it

The figure reads from left to right. The blue card is link distance. The middle card applies this page's rule. The green card is predicted rssi. 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 link distance, so the numeric fixture does not switch without explanation.

Link distance changes predicted rssi An input card leads through the rule RSSI = 0 dBm - 30 log10(distance in m) to the predicted rssi result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. The path-loss estimate weakens with distance but cannot replace measured backup and battery evidence.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 50 m.

  2. 2

    Name the relationship. RSSI = 0 dBm - 30 log10(distance in m)

  3. 3

    Substitute with units. 0 - 30 log10(50) = -51.0 dBm

  4. 4

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

Predict, then change link distance

Try Predict the direction of RSSI = 0 dBm - 30 log10(distance in m). Test another link distance, then compare predicted rssi.

50 m
Chapter baseline
Predicted RSSI

Observe The path-loss estimate weakens with distance but cannot replace measured backup and battery evidence. Reset link distance to 50 and compare predicted rssi.

Explain The path-loss estimate weakens with distance but cannot replace measured backup and battery evidence.

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 link distance moves here. Field effects named in the technical boundary stay fixed.
Try

Select Calculate for the 0 dBm, 50 m factory link, then Check its 85% PDR, -73 dBm RSSI, and 30 ms latency.

Observe

The path-loss line rounds to -51.0 dBm and all 3 practice measurements land inside the displayed GOOD bands.

Explain

Agreement across PDR, RSSI, and latency supports the GOOD tier, but one 50 m observation cannot establish backup-path or battery resilience.

Technical boundaries

For the radio ledger, excluded from this fixed arithmetic are multipath fading, interference, routing churn, queueing, battery ageing, or correlated link failures.

1. The 50 m factory example rounds from the full path-loss calculation. With transmit power 0 dBm and environment factor n = 3:

RSSI = 0 - 10 x 3 x log10(50) = -50.969 dBm, rounded to -51.0 dBm

At 100 m, the same model gives 0 - 30 x log10(100) = -60.0 dBm. Doubling from 50 m to 100 m costs 30 x log10(2) = 9.03 dB, which is the chapter's 9 dB warning.

2. The Excellent and Good distance thresholds come from solving the same equation.

Threshold Arithmetic Distance
Excellent boundary, -70 dBm log10(d) = 70 / 30 = 2.3333 10^2.3333 = 215.4 m
Good boundary, -80 dBm log10(d) = 80 / 30 = 2.6667 10^2.6667 = 464.2 m

3. The routing tier must agree across packet delivery, RSSI, and latency. The practice question's 85% PDR is inside the 70-90% GOOD band, -73 dBm is between -70 and -80 dBm, and 30 ms is inside the stated 20-50 ms latency band. All three checks support GOOD; a production controller should still keep backup-path and battery evidence before trusting that link as a relay.

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