Hot-Wire Anemometer

What is modelled

A thin metal wire is heated by an electric current and cooled by forced convection. Its resistance rises with temperature, so the same wire is both heater and thermometer.

Equations

• King-type convection h(U) = a + b √U + k (W/K), so at equilibrium P = h(U) (T - Ta).
• Lumped thermal mass C dT/dt = P - h(U)(T - Ta).
• Resistance R = R0[1 + α(T - 20)], P = I2 R.
• CTA holds T at the target with a PI controller; CCA fixes the current.
• Inversion U = ((P/(T - Ta) - a - k)/b)2.

Checks run in the page

• The King inversion returns the true airspeed.
• Steady electrical power equals convective loss.
• The constant-current equilibrium matches a root-finder.
• Resistance and V I power consistency.

Honest simplifications

One lumped temperature (no prong conduction or end losses), constant air properties and bounded random turbulence. The constants are illustrative, not a calibrated probe.

• Raise the airspeed in constant-temperature mode: the power climbs as the square root of speed.
• Switch to constant current and watch the wire cool and slow down: the response is slower than the bridge.
• Use the aggressive loop preset and see the controller overshoot.