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Cylindrical-conduction heat-loss method (IEEE 515 practice)9 min read

Worked Example: Pipe Heat-Loss Sizing That Passes — Until a Realistic Cable Resistance Is Added

An 80 m freeze-protection circuit on a 114 mm insulated pipe sizes cleanly for heater output and breaker rating — but adding the heating cable's own resistance reveals a voltage drop that blows past any reasonable limit.

Scenario

Pipe outer diameter / insulation thickness114 mm / 50 mm (k=0.04 W/m·K, mineral wool)
Maintain temperature / minimum ambient10°C / -10°C
Design factor1.3 (IEEE 515 practice margin)
Selected heater output20 W/m
Circuit length / voltage80 m / 230 V
Breaker rating16 A

Step-by-step calculation

Step 1: Compute steady-state radial conduction heat loss through the insulation

Q(W/m) = 2π x k x ΔT / ln(Douter / Dinner)
ΔT = 10-(-10) = 20°C 2π x 0.04 x 20 / ln(214mm/114mm)
heatLossWPerM = 7.98 W/m

Step 2: Apply the design factor to find the required heater output

requiredWPerM = heatLossWPerM x designFactor
7.98 x 1.3
requiredWPerM = 10.38 W/m — the selected 20 W/m heater comfortably covers this. PASS

Step 3: Size the circuit power and current for the full 80 m run

circuitPowerW = heaterOutputWPerM x length circuitCurrentA = circuitPowerW / voltage
20 x 80 = 1600 W 1600 / 230
circuitPowerW = 1600 W, circuitCurrentA = 6.96 A

Step 4: Check the breaker rating

Step 5: Now add the heating cable's own resistance (0.05 Ω/m) and re-check voltage drop

The initial pass above skipped the voltage-drop check because no cable resistance was entered — a self-regulating or constant-wattage cable's real resistance per meter is needed to check whether the far end of an 80 m run still receives enough voltage to deliver its rated output.

totalR = resistancePerM x length Vdrop = current x totalR
0.05 x 80 = 4 Ω 6.96 x 4
voltageDropV = 27.83 V, voltageDropPct = 12.10% of the 230 V supply

Result summary

CheckRequirementActualStatus
Heater output vs. required W/mheaterOutput ≥ requiredWPerM20 W/m ≥ 10.38 W/m✓ PASS
Circuit current vs. breaker rating≤ 16 A6.96 A✓ PASS
Voltage drop (with 0.05 Ω/m cable resistance)typically ≤ 5-10% for heat-tracing circuits12.10%✗ FAIL
The heater output and breaker sizing both pass comfortably for this 80 m circuit. But once the heating cable's own 0.05 Ω/m resistance is factored in, the voltage drop reaches 12.10% of the 230 V supply — well beyond typical acceptable limits — meaning the far end of this run would receive significantly reduced voltage and, for a constant-wattage cable, a correspondingly reduced actual heat output right where freeze protection may matter most.

Key insight: A heat-tracing circuit can pass its power-output sizing and breaker check while still failing on voltage drop, because those are governed by entirely different physics — output sizing depends on the required W/m vs. the heater's rating, while voltage drop depends on cable resistance accumulating over the full run length. Leaving the cable-resistance input at zero silently skips this check altogether, which is exactly why it's worth deliberately entering a manufacturer's real resistance-per-meter figure rather than accepting the default of 0.

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Frequently asked questions

What are the typical fixes for a voltage-drop failure like this one?

The main levers are shortening the circuit run (splitting one long circuit into two shorter ones fed from separate breakers), increasing the supply voltage to the heat-tracing circuit if the installation allows it, or selecting a heating cable with lower resistance per meter for the same output — splitting into shorter circuits is often the simplest fix since it directly reduces the total resistance the current has to travel through.

Does this voltage-drop concern apply the same way to self-regulating heating cables?

Self-regulating cables behave somewhat differently from constant-wattage cables because their output already varies with temperature along the cable's length, but they still rely on adequate voltage reaching every point along the circuit to produce their rated output — a large voltage drop reduces the power delivered at the far end of either cable type, so the voltage-drop check remains relevant regardless of which heating cable technology is used, even though the exact resistance-per-meter figure and its behavior differ.

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