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Approximately, how fast would an aircraft have to travel through freezing air to melt the ice off the wing, propellers, or rotor blades?

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    $\begingroup$ Couple more variables you'll probably need: Altitude (alternatively, air pressure), and dew point. $\endgroup$ – Greg Hewgill Feb 3 at 22:17
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    $\begingroup$ Please confirm you mean "melt" as opposed to just 'get rid of...'. Because ice will sublimate at pretty low speeds if the air is dry. Also, temperature is a key variable. "Freezing air" can be 32F down to absolute zero. $\endgroup$ – Michael Hall Feb 3 at 23:23
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    $\begingroup$ Longer than a minute, less than an hour. That's about as precise an answer as you're going to get with so many variables. $\endgroup$ – John K Feb 4 at 3:22
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As already done in this answer, we can calculate the True Air Temperature (TAT) that the aircraft's skin will feel from the Static Air Temperature (SAT) and the Mach number:

$$ \frac{\text{TAT}}{\text{SAT}} = 1 + \frac{\gamma - 1}{2} M^2 = 1 + \frac{1}{5} M^2 $$

(using $ \gamma = 1.4 $ for air). For different SATs the curves then look like this:

TAT for different SAT

I added a dashed line at a TAT of 10°C because this is the limit defined for icing conditions. At higher TATs, the ice should definitely melt (although it could already start melting before). We can now obtain the intersection Mach number as a function of SAT by inverting the formula above:

$$ M = \sqrt{5 \left( \frac{\text{TAT}}{\text{SAT}} - 1 \right)} $$

The resulting curve looks like this:

Mach required

As you can see, a Mach number between ~0.4 and ~1.3 will be required to melt ice, depending on the SAT.

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