Math Bridge: What distance can an RSSI tier really mean?

← Back to Ad Hoc Production Framework
Math BridgeEmerging ParadigmsStruggle-friendly runway

What distance can an RSSI tier really mean?

Invert RSSI gaps into distance ratios and expose why the answer changes with the measured environment.

Packet Pete, the guidePacket Pete guides
The one targetTurn dB gaps into distance ratios without pretending RSSI is a ruler.
The chapter case−55.3, −70.2, and −87.8 dBm around a 100 m mesh reference.
What it buys youA threshold tied to field evidence.

A technician must decide whether distance factor at n = 4.95 is safe before changing measured rssi gap on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is measured rssi gap. The middle card applies this page's rule. The green card is distance factor at n = 4.95. 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 measured rssi gap, so the numeric fixture does not switch without explanation.

Measured RSSI gap changes distance factor at n = 4.95 An input card leads through the rule factor = 10^(RSSI gap / 49.5) to the distance factor at n = 4.95 result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A larger RSSI gap maps to a larger distance factor for the fixed environment.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 14.9 dB.

  2. 2

    Name the relationship. factor = 10^(RSSI gap / 49.5)

  3. 3

    Substitute with units. 10^(14.9 / 49.5) = 2.00 times

  4. 4

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

Predict, then change measured rssi gap

Try Predict the direction of factor = 10^(RSSI gap / 49.5). Test another measured rssi gap, then compare distance factor at n = 4.95.

14.9 dB
Chapter baseline
Distance factor at n = 4.95

Observe A larger RSSI gap maps to a larger distance factor for the fixed environment. Reset measured rssi gap to 14.9 and compare distance factor at n = 4.95.

Explain A larger RSSI gap maps to a larger distance factor for the fixed environment.

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 measured rssi gap moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only measured rssi gap. It is not a field prediction.

1. Start with what RSSI can say

RSSI reports received power. Distance, obstruction, antenna orientation, and multipath all spend that power budget, so one reading does not identify one distance.

Packet Pete: A dB gap becomes a distance ratio only after you state the path exponent.

2. Name every algebra move

1

Subtract readingsΔ=RSSIreference−RSSIweaker.

2

Write the modelΔ=10n log10(d/d0).

3

Divide the coefficientlog10(d/d0)=Δ/(10n).

4

Undo the logarithmd=d0×10^(Δ/(10n)).

5

Reverse for nn=Δ/[10 log10(d/d0)].

3. Reproduce the chapter case

Δgood=14.90 dB; Δpoor=32.50 dB; d=d0×10^(Δ/(10n))
At n=2: good=556 m, poor=4,217 m; if good is 2× farther, inferred n=4.95

The free-space distances contradict the chapter's 100 m mesh context. A heavily obstructed exponent is the more honest interpretation.

4. Try the path exponent

TryMove n from open space toward heavy clutter and watch the same RSSI gaps map to different distances.

Path exponent
Excellent→good gap
Excellent→poor gap
Good-link distance
Poor-link distance
Free-space good
Free-space poor
Implied n at 2×
Threshold shift
Distance factor

ObserveAt n=4.95 the good tier sits near 200 m and the poor tier near 453 m, while free space predicts 556 m and 4,217 m. The 2.00 dB retest shift changes the distance factor by about 1.10×.

ExplainA larger n makes received power fall faster, so the same dB gap needs a smaller distance ratio. The field exponent and PDR evidence must travel with the threshold.

Technical boundaries.

This compact engine is a distance-ratio lesson, not a positioning system.

Reference
The 100 m reference is the chapter's nominal mesh scale, not a calibrated anchor
Environment
One exponent compresses shadowing, metal, movement, and multipath into one slope
Quality
RSSI alone does not predict PDR, latency, interference, or route stability

Calibrate against measured distance and delivery evidence in the target site.

5. Turn a tier into a test

Define excellent, good, and poor with RSSI plus packet delivery and stability. Preserve the site, distance, antennas, traffic, and sample count behind each boundary.

6. Keep the threshold record

Record reference RSSI and distance, fitted n, threshold values, PDR, confidence, obstruction state, firmware, antenna placement, owner, and retest trigger.

7. Check yourself

Why does free space put the good reading beyond 500 m?
Answer: A 14.9 dB gap at n=2 gives a 10^(14.9/20)=5.56 distance ratio from 100 m.
What does n≈4.95 mean here?
Answer: It is the exponent implied when a 14.9 dB loss accompanies a doubling of distance; it signals heavy clutter, not a universal factory constant.
Can −70 dBm alone classify a production link?
Answer: No. The chapter also needs PDR, stability, latency, site conditions, and retest evidence.
Honesty boundary.

The readings and threshold shift come directly from the chapter; the distance interpretation is explicitly conditional.

−55.3/−70.2/−87.8 dBm
The chapter's excellent, good, and poor examples
100 m
The chapter's nominal transmission scale used as a teaching reference
−70 to −72 dBm
The chapter's default and factory-retested 70% PDR boundary

Correct, not complete: only calibrated field measurements support a distance claim.

Return to Ad Hoc Production Framework with the maths unpacked →