BLDC Thermal Derating Calculator

This calculator models BLDC motor temperature rise using a thermal resistance network to verify that winding temperatures stay within insulation class limits. Motor designers, drone builders, and industrial integrators use it to determine continuous current ratings and required cooling for their operating environment.

The steady-state thermal model follows an electrical analogy: heat flow (watts) through thermal resistance (C/W) produces temperature difference (C). Per Mellor's thermal model (IEE Proc. 1991), the primary path is winding -> stator iron -> case -> ambient, with $T_{winding} = T_{ambient} + P_{total} \times (R_{\theta,wc} + R_{\theta,ca})$, where $R_{\theta,wc}$ is winding-to-case and $R_{\theta,ca}$ is case-to-ambient thermal resistance.

Insulation class defines the maximum allowable winding temperature per IEC 60085: Class B (130C), Class F (155C), and Class H (180C). Most hobby BLDC motors use Class B or F enamel wire. Exceeding the rating by 10C halves insulation life per the Arrhenius rule -- thermal margin is not optional.

Copper resistance increases with temperature: $R(T) = R_{25} \times (1 + \alpha (T - 25))$ where $\alpha = 0.00393$/C for copper. This creates positive thermal feedback: hotter windings have higher resistance, causing more $I^2R$ loss, which further raises temperature. The equilibrium temperature must be solved iteratively or via the closed-form: $T_{eq} = T_{amb} + P_{loss,25} \times R_{\theta,total} / (1 - \alpha \times I^2 R_{25} \times R_{\theta,total})$.

The first-order thermal time constant $\tau = R_{\theta} \times C_{th}$ (where $C_{th}$ is thermal capacitance in J/C) determines how quickly the motor heats. Small drone motors ($\tau$ = 10-30 s) reach 63% of final temperature in under 30 seconds. This means burst current ratings are only safe for durations well below $\tau$.