## Friday, May 15, 2015

### 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.