WP_20170716_012

Dual Sensor Airspeed Measurement

Sometimes we need that our air data system is able to handle airspeed over a wide speed range. Considering small RC planes this kind of measurements are typical when our goal is to study the behavior near the stall. The test flight pattern is usually a simple straight line; the pilot enters into a stall just reducing the throttle and progressively compensating with an increase in the angle of attack. If we are interested in accurate measurements, we may encounter some difficulty in keeping our readings accurate enough at low airspeeds. One possible solution is to use two sensors with different pressure ranges instead of the standard one sensor configuration. That arrangement may reduce by far the impact of the differential pressure uncertainty. Very low airspeed results in a modification of the aerodynamic behavior of the pitot -static probe itself, we will not consider this effects, or any others, here.

Let’s pretend we have an air data system with a differential pressure sensor with a full-scale value FS_{H} of 2500 Pa and an uncertainty expressed in percent of the full-scale value of 0.5% u_s=0.5\cdot FS_{H}/100= 12.5\ Pa. With that range, maximum indicated airspeed IAS_{H}^{M} is about 63.8 m/s or 230 km/h. At the IAS_{30} speed of 30 m/s, the sensor will read q_{c}^{30}=551.2\ Pa . IAS at 3 m/s is IAS_{3} and q_{c}^{3}=5.512 \ Pa. Recalling the IAS Equation we write \frac{q_{c}^{30}}{q_{c}^{3}}=(\frac{IAS_30}{IAS_3})^2. That equation also holds for any arbitrary airspeed tuple. The differential pressure varies between two airspeeds with the square of the airspeed ratios. Accounting for the uncertainty of a pressure sensor u_s the uncertainty of IAS_i measurement is u_{IAS}^i=\sqrt{S_s^2 \cdot u_s^2}, where S_s=0.169\cdot (1/\sqrt{q})
So the ratio between two arbitrary uncertainties, for a single sensor, is u_{IAS}^2/u_{IAS}^1=\sqrt{q_{c}^2 /q_{c}^1}=IAS_{2}/IAS_{1}.

Let’s compare the behavior of two different sensors, for example from the Honeywell HSC series.  

IAS range of example sensors

Type 1 , 16OLD, 160 Pa FS -> 16.1 m/s 58.2 km/h

Type 2, 2-2.5KD, 2500 Pa FS -> 63.8 m/s 229.9 km/h

At 3 ms/s, dynamic pressure 5.512 Pa

Type 1, 160LD, uncertainty  1.75%FS, absolute uncertainty 2.8 Pa, IAS uncertainty 0.2 m/s 6.6 %

Type 2, 2.5KD , uncertainty 0.5%FS,  absolute uncertainty 12.5 Pa, IAS uncertainty 0.9 m/s  30 % 

At 30 m/s, dynamic pressure 551.2 Pa

Type 1, 160LD  Out of measurable range

Type 2, 2.5KD, uncertainty 0.5%FS,  absolute uncertainty 12.5 Pa, IAS uncertainty 0.09 m/s 0.66 %

The first sensor works better at low airspeeds. The ratio between the uncertainties of IAS measurement of the two sensors is equal to u_s^2/u_s^1=12.5/2.8=4.46. We select the sensor measurement from the sensor 1 if the IAS airspeed is less than 16.1 m/s otherwise we use the reading from the sensor 2.
It is evident that our dual sensor configuration is more accurate than a single sensor configuration consisting of a sensor type 2 alone; the use of a single sensor will provide a reduced accuracy of 0.9m/s at 3 m/s.

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