🎉 Free launch period — every calculator, every feature unlocked, no account needed, through mid-November 2026. PDF reports carry a watermark for everyone during this period.
First-principles heat balance (Ohm's law + McAdams convection + linearized radiation)10 min read

Worked Example: Solving a Busbar's Continuous Temperature Rise from First Principles

A 100 x 10 mm copper busbar carrying 1200 A, checked by solving the actual heat balance between I²R loss and convective/radiative cooling — not a table lookup.

Scenario

Busbar1 bar, 100 mm wide x 10 mm thick, copper
MountingOpen, vertical, bare finish (emissivity 0.3)
Ambient temperature35°C
Load current1200 A
Maximum allowed temperature rise65 K

Step-by-step calculation

Step 1: Set up the heat balance

At thermal equilibrium, resistive (I²R) heat generation equals heat lost to convection and radiation — but resistance itself rises with temperature, so this has to be solved iteratively rather than in one step.

I²·Rac(T) = [hconv(ΔT) + hrad(ΔT)] x perimeter x ΔT

Step 2: Iterate to convergence

Starting from an initial guess and refining until the temperature rise stabilizes.

Step 3: Find the resulting surface temperature and check against the limit

Ts = ambient + ΔT
35 + 17.61
Ts = 52.61°C — well under the 65 K rise limit (which would allow up to 100°C)

Step 4: Find the maximum current this busbar could carry at the same rise limit

Solving the same heat balance in reverse, for the current that produces exactly the maximum allowed 65 K rise.

Result summary

CheckRequirementActualStatus
Temperature rise at 1200 A≤ 65 K17.61 K✓ PASS
Maximum continuous current at 65 K risen/a (informational)2478 A✓ PASS
At 1200 A, this busbar runs only 17.6 K above ambient — well inside its 65 K limit — and could actually carry up to about 2478 A continuously before reaching that same limit, meaning it has substantial thermal headroom beyond its current loading.

Key insight: A busbar's continuous ampacity isn't a single number pulled from a manufacturer table — it depends on the specific installation's mounting, orientation, finish (emissivity), ambient temperature and even nearby airflow, all of which change how effectively it sheds heat. This first-principles heat-balance approach recomputes the actual thermal limit for the specific installation rather than relying on a generic published rating that may not match the real conditions.

Try it with your own numbers

Every input in this example is editable in the live calculator — free, no signup.

Open Busbar & Switchgear Rating calculator →

Frequently asked questions

Why does surface finish (bare vs. painted) matter so much for busbar rating?

Radiative heat loss scales with emissivity, and a bare copper bus has a fairly low emissivity (about 0.3) compared to a painted finish (about 0.9) — painting an otherwise-identical busbar black can meaningfully increase its radiative cooling and therefore its continuous ampacity at the same temperature-rise limit, which is why the calculator exposes emissivity as an adjustable input rather than hiding it as a fixed constant.

Is this a substitute for a manufacturer's IEC 60890 type-test rating?

No — this is explicitly a transparent engineering approximation for preliminary sizing, with every coefficient (emissivity, McAdams constant, proximity/skin-effect factors) exposed as an adjustable input rather than hidden. For final equipment specification or formal compliance, a manufacturer's actual IEC 60890 type-test data for the specific busbar configuration should be used.

More in Transformers, CT/VT & Condition Testing

← Back to all worked examples