Math Bridge: Why a Factory Link Falls to 12 Mbps

← Back to Network Performance Lab
Math BridgeCore NetworkingStruggle-friendly runway

Why can 54 Mbps fall to 12 Mbps inside one factory?

Separate propagation delay from propagation loss and calculate the obstruction loss that consumes one Wi-Fi rate tier.

Pete, the guidePete guides
The one targetConnect path loss to rate fallback.
The chapter casen=3.3 reaches a 14 dB tier gap at 11.9 m.
What it buys youDiagnose throughput without blaming propagation delay.

A field team faces an unresolved physical question: Why can 54 Mbps fall to 12 Mbps inside one factory? They must answer it before changing factory path distance on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is factory path distance. The middle card applies this page's relationship. The green card is free-space loss. 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Factory path distance changes free-space loss An input card leads through the page relationship to the free-space loss result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The access point did not lose advertised bandwidth because the wave took too long to arrive. It used a more robust modulation after the modeled SNR budget lost a tier.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for factory path distance is 20.

  2. 2

    Name the relationship. d=d0·10^(Δtier/[10(n-2)]); delay=d/v

  3. 3

    Substitute the chapter fixture. Set factory path distance to 20. The page ledger gives free-space loss as 66.07 dB.

  4. 4

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

Predict, then change factory path distance

Try Predict the direction of free-space loss. Move one control, calculate, then check your prediction.

20
Chapter baseline
Free-space loss

Observe The access point did not lose advertised bandwidth because the wave took too long to arrive. It used a more robust modulation after the modeled SNR budget lost a tier. Reset the control to 20 and compare free-space loss.

Explain Only factory path distance moves here. The other chapter fixtures remain fixed.

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 factory path distance moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only factory path distance. It replays the chapter fixture; it is not a field prediction.

1. Time and power share one word, not one unit

Propagation delay is distance divided by wave speed and is measured in time. Path loss is a power ratio measured in decibels. A factory can add very little flight time while removing enough SNR to force a robust modulation.

Pete: Keep the units and the assumptions beside every number.

2. Name every algebra move

1

Find the clean lossFSPL=20log10(d)+20log10(f)−147.55.

2

Add the factory excessΔ=10(n−2)log10(d/d0).

3

Compare rate gatesWhen Δ reaches the 14 dB illustrative sensitivity gap, one rate tier can disappear.

3. Solve the tier distance explicitly

d=d0·10^(Δtier/[10(n−2)]); delay=d/v

With n=3.30, d0=1 m, and a 14.0 dB gap, the threshold distance is 10^(14/13)=11.9 m. This is a model boundary, not an 802.11 rate-control guarantee.

4. Try one controlled change

d=d0·10^(Δtier/[10(n−2)]); delay=d/v

TryMove the receiver across the factory floor and compare nanoseconds with obstacle decibels.

Distance
Free-space loss
Obstacle excess
Illustrative rate tier
14 dB tier distance
One-way flight time

ObserveAt 20 m the model adds about 16.9 dB beyond free space and selects the illustrative 12 Mbps tier, while flight time is only about 66.7 ns.

ExplainThe access point did not lose advertised bandwidth because the wave took too long to arrive. It used a more robust modulation after the modeled SNR budget lost a tier.

Technical boundaries.

Real Wi-Fi rate control is a measured, device-specific process.

measured SNR and retries
Link evidence
channel occupancy and interference
Shared-medium evidence
implementation policy and coding
Device behavior
packet size and history
Traffic context

The −65/−79 dBm and n=3.3 values are typical illustrations and require device/site validation.

5. Reproduce the chapter values

At 2.4 GHz and 100 m, FSPL is about 80.1 dB. At 20 m, n=3.3 adds 10(1.3)log10(20)=16.9 dB beyond free space. Solving for a 14.0 dB gap gives 11.9 m.

6. Carry the evidence forward

Log offered load, goodput, latency distribution, jitter, loss, retries, MCS/rate, RSSI/SNR, channel occupancy, path geometry, and timestamps. Compare the same application threshold before and after a controlled path change.

7. Check yourself

Is 66.7 ns the cause of a 12 Mbps fallback?
Answer: No. The illustrative cause is lost SNR margin, not wave flight time.
What does n=3.3 add at 20 m?
Answer: About 16.9 dB above the n=2 free-space model.
Does the widget model a specific rate algorithm?
Answer: No. It exposes a sensitivity-gap boundary; production rate control needs measured device evidence.
Honesty boundary.

These are the worked values and named assumptions for this bridge.

2.4 GHz
Worked carrier
100 m
FSPL distance
80.1 dB
Worked FSPL
20 m
Factory path
16.9 dB
Obstacle excess
14.0 dB
Illustrative tier gap
11.9 m
Solved tier distance
54 Mbps
Illustrative fast tier
12 Mbps
Illustrative robust tier

Real Wi-Fi rate control depends on measured SNR, retries, channel occupancy, interference, implementation policy, coding, packet size, and history. The −65/−79 dBm and n=3.3 values are typical illustrations and require device/site validation.

Return to Network Performance Lab with the maths unpacked →