# The impact of humidity on airspeed measurement

Figure 1 - Meteorological UAV M2AV and meteorological measurement sensors

Article here Five hole MHP, Temperature and Humidity

Reliable measurement of the True Air Speed (TAS) of the aircraft is crucial for flights carried out by autopilot. From the simplest to the most complex, all autopilots installed in fixed-wing airframes require TAS readings, either to use it as a manipulated variable or as a parameter for controller adaptation or reconfiguration. In the following link, for example, airspeed is used as a switching parameter of a gain scheduling scheme .

In order to obtain an accurate TAS measurement $$TAS=\sqrt{\frac{2qc}{\rho}}$$ it is necessary to acquire an accurate value of the air density, $$\rho$$. However, if our airframe is flying across the troposphere the impact of the humidity of the air on our measurements is also not negligible.

We shall use for our further density calculations the well-established CIPM Equation for the Determination of the Density of Moist Air (1981/91). Other density models can be chosen but this is not the main focus in this text.

Using the ISA atmosphere, the air density at 15°C and 101325 Pa is $$\rho_s=1.225\ kg/m^3$$, while the air is assumed to be dry. That value is in accordance with the CIPM equation. Moist air is a mix of dry air and water vapors. The molecular weight of dry air is about 28.96e-3 kg/mol and the molecular weight of water vapor is 18e-3kg/mol. The higher the content of water vapor in the air, the lower the moist air density value is.

Let's assume that the relative humidity value at ground level changes from 45% to 70%. Without modifying any other parameter, the resulting values for the air density are presented in table 1. You can find a density calculator script in the following link. The deviation on last column of the table is referenced to the dry air case.

T=15°C, P=101325 Pa

RH %

Density kg/m3

Airspeed deviation %

0

1.225

0.00

45

1.222

0.12

70

1.22

0.20

It is evident that the reported percentage airspeed variation expression $$100\cdot(1-\sqrt{\frac{\rho_s}{\rho}})$$is not dependent on the $$qc$$ value. The higher the operating temperature, the graver the effect of moist air is on airspeed readings: refer to the following table for numerical values at 35°C and 5°C.

T=15°C, P=101325 Pa

RH %

Density kg/m3

Airspeed deviation %

0

1.252

0.00

45

1.249

0.12

70

1.248

0.16

Extremal values, such as (0,70)RH and (5,35)°C, are plausible but should be carefully treated; in any case, those values are shown here as an example. The precedent tables highlight that air speed deviation increases with the operating temperature. Humidity is often not measured on DIY drones, but as shown here that can have a significant impact on the airspeed measurement. As usual, the overall accuracy of a measurement should be adapted to reflect to the specific application. An additive uncertainty of 1% can be unacceptable for aerodynamic identification tasks, but can be very acceptable for less demanding flight control applications.

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Comment by Gary Mortimer on June 5, 2015 at 12:28pm

Wow an historic airframe!! Nice one Jose

Comment by JLJu on June 5, 2015 at 1:03pm

You make me feel soo old! :-)

Comment by Geoff on June 5, 2015 at 10:17pm

You should not be scheduling gains on true airspeed! The aircraft dynamic scale with dynamic pressure, which is essentially the same as the impact pressure measured by a pitot-static system at the speeds model aircraft / small UAS fly. The only difference is a compressibility factor that is only measurably different than 1 above ~ Mach 0.3. NACA Report 837 is a great reference for calculating the different airspeeds (IAS, EAS, TAS) from pitot, static, temperature measurements.

True airspeed may be useful in contexts other than gain scheduling however, such as when fusing air-data with inertial data, estimating wind speeds in a Kalman filter, or dead reckoning without GPS. In general, more effort should be made to accurately measure the outside air temperature, as differences in this from the standard atmosphere often have a much stronger impact on the density than the relative humidity.

Comment by Georacer on June 6, 2015 at 1:44am

Comment by JLJu on June 6, 2015 at 2:38am

Well, I don't think TAS is central here anyway. TAS can be used to correct to higher than DIY level the sensor readings(i.e. Cl id needs TAS); but i will stop here as that is "another battle".

Your linked pdf looks great. Have a link also to this link http://www.basicairdata.eu/pitot-tube.html Paragraph "Design example". It seems to agree with you "In many pratical cases this term contribution can be safetly neglected as they are small."

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