Math Bridge: WirelessHART Obstacle Scale

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Math BridgeWirelessHARTObstacle scale

Can channel hopping route around a physical shadow?

Compare plant obstacle size with wavelength across the 2.4 GHz hop set and a 900 MHz reference before changing a blacklist.

Eddie, the electronics guideEddie guides
The one targetTurn obstacle size into wavelength-scale indicators across two bands.
The chapter caseA 0.30 m beam at IEEE 802.15.4 channels 11 and 26 versus 900 MHz.
What it buys youA bounded diagnostic split between frequency-specific interference and route-scale obstruction.

A field team has a real problem to settle: Can channel hopping route around a physical shadow? They must decide what happens before they change obstacle size on the device. Predict the direction first.

See the relationship first

The figure reads from left to right. The blue card is obstacle size. The middle card uses this page's rule. The green card is obstacle centimetres. Follow the arrows: set the input, use the rule, then read the result and its unit.

The audit later on checks more than one number. Here, the added model uses the baseline named below and holds every other chapter value fixed. That sentence bridges the fixtures, so the numbers do not change without a reason.

Obstacle size changes obstacle centimetres An input card leads through the page rule to the obstacle centimetres result. SET INPUT ONE CONTROL USE RULE predict calculate check units READ RESULT
Follow the arrows. The 2.4 GHz channels change wavelength by only about 3.0%, so a common geometry problem remains common across hops.

Derive the baseline in four moves

  1. 1

    Name the input. The chapter baseline for obstacle size is 0.3.

  2. 2

    Name the rule. λ_2405 = 0.1247 m; λ_2480 = 0.1210 m; λ_900 = 0.3333 m L/λ_2405 = 0.30/0.1247 = 2.405 L/λ_2480 = 2.480; L/λ_900 = 0.900

  3. 3

    Put in the chapter value. Set obstacle size to 0.3. The page rule gives obstacle centimetres as 30.00 cm.

  4. 4

    Read the result. Keep cm next to the value. Use it only within the limits on this page.

Predict, then change obstacle size

Try Predict what happens to obstacle centimetres. Move one control, calculate, then check your idea.

0.3
Chapter baseline
Obstacle centimetres

Observe The 2.4 GHz channels change wavelength by only about 3.0%, so a common geometry problem remains common across hops. Reset to 0.3 and compare obstacle centimetres.

Explain Only obstacle size moves here. The other chapter values stay fixed.

Check yourself

What should you do before you trust the result?
Answer: Predict its direction, use the shown rule, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only obstacle size moves. Field effects named in the page limits stay fixed.

Honesty note. This teaching model changes only obstacle size. It replays the chapter baseline; it is not a field prediction.

1. Start with the physical story

Hopping changes frequency, not geometry. When every channel has nearly the same wavelength, a large structural obstruction stays large on every hop.

Eddie: Wavelength scale is a screening clue, not a diffraction or industrial propagation solver.

2. Name every algebra move

1

Find wavelengthsUse λ = c/f at 2405, 2480, and 900 MHz.

2

Measure hop spreadCompare first and last 2.4 GHz wavelengths.

3

Scale the obstacleDivide obstacle size L by each wavelength.

4

Compare bandsKeep 2.4 GHz and 900 MHz ratios side by side.

5

Choose evidenceUse channel-local retries for interference and route/site tests for common shadows.

3. Reproduce the chapter case

λ_2405 = 0.1247 m; λ_2480 = 0.1210 m; λ_900 = 0.3333 m
L/λ_2405 = 0.30/0.1247 = 2.405
L/λ_2480 = 2.480; L/λ_900 = 0.900

The beam spans about 2.4 wavelengths across the WirelessHART hop set but only 0.9 wavelength at 900 MHz. The 2.4 GHz scale changes little between channel edges.

4. Try one real input

TryMove obstacle size. Its scale on the first hop, last hop, and comparison band recomputes from the same wavelengths.

Obstacle size
Obstacle centimetres
Channel 11 wavelength
Channel 26 wavelength
900 MHz wavelength
Hop-set wavelength spread
Size / channel 11 λ
Size / channel 26 λ
Size / 900 MHz λ
Channel 11 excess over 1 λ
Channel 26 excess over 1 λ
900 MHz excess over 1 λ
Scale spread across hops

ObserveAt 0.30 m, the obstacle is 2.405 to 2.480 wavelengths across the hop-set edges but 0.900 wavelength at 900 MHz.

ExplainThe 2.4 GHz channels change wavelength by only about 3.0%, so a common geometry problem remains common across hops.

Technical boundaries.

This is a wavelength-scale screen, not a diffraction or path-loss model.

Obstacle
Shape, material, thickness, edges, clearance, and Fresnel geometry are omitted.
Band
The 900 MHz row is a comparison, not a WirelessHART channel or migration recommendation.
Network
Interference, schedule, blacklist, graph route, antennas, and measured retries remain operational evidence.

Correct, not complete: this ledger does not diagnose a plant link by itself.

5. Use the result in troubleshooting

If retries cluster on particular channels, inspect interference. If they persist across the hop set and route, test placement, clearance, shielding, and alternate graph paths.

6. Record the evidence state

Keep channel and slot, route edge, retries, RSSI and quality, blacklist, obstacle geometry and material, antenna pose, site state, and retest trigger.

7. Check yourself

Why does a large obstacle remain large across the hop set?
Answer: The first and last channel wavelengths differ by only about 3%, so L/λ changes little.
Does L/λ above one calculate shadow loss?
Answer: No. It is only a regime screen; geometry, material, edges, and Fresnel clearance still matter.
Should this ledger trigger a larger blacklist?
Answer: Not by itself. A common structural shadow calls for route and site evidence, while blacklisting needs channel-specific evidence.
Honesty boundary.

The ledger compares physical scales without claiming propagation loss.

Computed
Wavelength, hop-set spread, and obstacle-to-wavelength ratios are reproducible.
Screened
Ratios suggest which geometry deserves route and placement tests.
Measured
Retries, interference, clearance, material loss, and route service decide the diagnosis.

Correct, not complete: use this to choose the next test, not the final remedy.

Return to WirelessHART TDMA with the obstacle maths unpacked →