Winding Temperature Rise
Estimate winding temperature from cold and hot resistance measurements using the resistance method.
Engineering approximation
The resistance method (R2 = R1 · [1 + α·(T2 − T1)]) assumes a constant temperature coefficient α near 20°C. It is a standard, widely used approximation — not a lab-grade thermometry measurement — and accuracy degrades over very wide temperature spans.
Formula
Resistance-method temperature approximation
R2 = R1 · [1 + α · (T2 − T1)]
- R1, R2
- Winding resistance at T1 and T2 [Ω]
- T1, T2
- Reference and target winding temperature [°C]
- α
- Temperature coefficient of resistance (≈0.00393/°C copper, ≈0.00403/°C aluminum) [1/°C]
α is referenced near 20°C and treated as constant — an engineering approximation, not an exact material law. The reverse mode solves the same equation for T2 given a measured hot resistance; it is equally approximate, not a substitute for direct temperature measurement.
Why this is an approximation, not a measurement
The resistance method infers an average winding temperature from a bulk resistance change — it cannot see hot spots, and it assumes the coefficient α stays constant over the full temperature span, which is only exactly true near the 20°C reference it's specified at. Treat the result as a useful estimate for sizing and sanity-checking, not as a substitute for a thermocouple or thermal-imaging measurement in a safety-critical design.
Worked example
A copper winding measures 1.20 Ω at 25°C. After a run, it measures 1.45 Ω:
- Resistance ratio: 1.45 / 1.20 = 1.208
- Estimated hot temperature: 25 + (0.208 / 0.00393) ≈ 78°C