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I believe hot wire anemometers (HWA, frequently used in wind tunnels to measure flow velocity) or other sensitive techniques could be used to determine the airspeed. Are there specific reasons for why the aircraft industry continues to use pitot-static instruments? Or is it just tradition?
A nice link on HWA's: The hot wire anemometer
The linked article says that an HWA (hot-wire anenometer) is
fragile and requires complex equations to relate the sensed value to the fluid speed as well as correct for inherent, unavoidable nonlinearities as well as external factors such as fluid type, ambient temperature, humidity, and angle between the flow and the sensor.
Conditions in a wind tunnel or other lab equipment are far more predictable, and change much more slowly and much less, than those encountered during an outdoor flight through variable weather.
Although industrial variants of the HWA don't expose the fragile sensing wire to damage or dirt accumulation (the dirt as thermal insulation causes the sensor to report incorrectly; rain or ice would still affect an aircraft-mounted one), they still need to correct for density, humidity, temperature, and flow angle. A four-dimensional lookup table takes a lot of work to create and store. Outside the lab the pitot tube is more reliable, even if it is more "primitive."
HWAs have been flown, but only as test equipment, not as sensors for primary flight instruments. For example, this set of HWAs flew on an F-15B to characterize flows in the boundary layer, sampled many thousands of times per second, far more sensitive than a pitot tube. But between each 30-second measurement interval, the HWAs were retracted inside the airplane for protection.
Hot wire anemometers are great for measuring turbulent fluctuations on a very fine timescale (say kHz). This is really not needed for aircraft speed. The very same wind tunnels that use HWA or LDA (laser Doppler anemometry) or PIV (particle image velocimetry) for detailed measurements themselves usually use Pitot tubes to measure the reference windspeed in the tunnel. It is robust, remains calibrated and will smooth out the fine turbulent fluctuations, which is actually a good thing if you are interested in the speed only.
There are quite a few reasons. First off, as everyone has already mentioned, HWAs are quite fragile and somewhat more complicated to decode (though the latter is a non-issue with modern electronics). More importantly though, a pitot-static measurement offers some distinct advantages specifically as far as aviation is concerned.
On the face of it, a pitot-static system is very simple, both in concept and implementation. A typical integrated pitot-static tube measures total pressure at the pitot port and has a series of equally spaced holes around its circumference (in the cylindrical portion) to measure static pressure. In common use are also pure pitot tubes, wherein a static reference comes from the static port altimeters are connected to.
It is important to note that the tube itself does no measurement. Merely, it provides a reference location for a sensing element to be connected via pipework of some type (usually a mixture of rigid and flexible hose, depending on the application). It is at the sensing element where the magic happens.
When a differential manometer is connected across the total and static references, it is able to directly measure dynamic pressure in that location. This follows from incompressible flow and the Bernoulli equation, namely $P = p + q$, where $P$ is total pressure, $p$ is static pressure and $q$ is dynamic pressure. Upon expansion, $q = 1/2 \rho U_{\mathrm{inf}}^{2}$ where $U_\mathrm{inf}$ is the free stream velocity of the airflow giving rise to $q$, and rho ($\rho$) is the free stream air density.
When we assert a constant rho of 1.225 $kg/m^3$, we can rearrange for free stream velocity: $U_\mathrm{inf} = \sqrt{2 q / \rho}$, or if we factor out $k = \sqrt{2 / \rho}$, $U_\mathrm{inf} = k \sqrt{q}$ - a simple square root relationship which can be implemented mechanically or in software quite easily.
Where this is particularly useful is in aerodynamic calculations during flight. As every important flight parameter (lift, drag, control input, etc.) is directly correlated to $q$, having an indicated airspeed (IAS) also directly correlated to q simplifies a pilot's job drastically. There is now ONE stall speed for each configuration. The feel of the aircraft is exactly the same, no matter the air temperature, the list goes on. The value of this simplification in reducing pilot workload cannot be overstated.
This is why, for any normal flight operations outside navigation, indicated airspeed derived from directly measured dynamic pressure is by far the most useful speed measurement to have. Navigation is secondary and for that there are conversion tables, DME and GPS.
It should be noted, that the raw $q$ measurement from the pitot-static system is almost never left unadjusted for commercial and military applications. Anything from the pitot port's position to compressibility effects must be adjusted for in order to preserve the IAS relationship a pilot expects, which is why modern commercial and military aircraft first convert IAS to calibrated airspeed (CAS), which accounts for the pitot-static system's position error and then into equivalent airspeed (EAS), which further accounts for compressibility as soon as the incompressible flow assumption breaks down (usually at any Mach number above 0.3).
It should further be noted that both Reynolds number (related to true airspeed or TAS) and Mach number will have an effect on aerodynamic forces, but those effects are usually small (during subsonic and low transonic flight) compared to the effect of dynamic pressure and may or may not be accounted for in other ways (i.e. adjustments to the fly by wire system, if present).
Most modern car engines have a computer to balance fuel-air mixture, ignition timing and other factors to give best performance or fuel economy. A hot-wire Mass Air Flow (MAF) sensor is a very common way to supply air flow data, there are also cold-wire versions. Although they are very reliable for that application there are a few issues which would make them less than ideal for aviation:
The electrical airspeed sensors I know of are all pressure transducers, which are accurate and don't have the flaws I listed above.
The thing you also have to be aware of is that hot or cold wire systems need a laminar flow of air to be accurate, you'd still need a pitot system or something similar to direct the flow of air over the sensor for it to give the correct reading.
Of course, the biggest drawback to any computerized sensor system is that they are reliant on electrical power.
