Given that an Airspeed Sensor costs about $12, I though it worth proposing an alternative: 2 temperature sensors and a resistor. Couple the resistor to one temperature sensor, and induce a voltage to generate heat. Place the coupled part in the airstream, now compare the temp of the one sensor against the ambient temperature; the difference is relative to airspeed. Cost $1.20; Weight nearly zilch. Downsides, not as quick to respond, might use more energy, but given the cost and the relative unimportance of airspeed as it input, it might qualify as a reasonable DIY alternative.
Yes, that's called a "hot wire anemometer" and is commonly used in low-speed applications like wind speed and indoor blimps. Not sure how it works at high speeds. See this for background.
eFunda: Introduction to Hot-Wire Anemometers
The Hot-Wire Anemometer is the most well known thermal anemometer, and measures a fluid velocity by noting the heat convected away by the fluid.
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