http://basicairdata.blogspot.it/2014/07/pitot-correction-for-position-and.html

## Friday, June 27, 2014

## Tuesday, June 24, 2014

### Pitot measures correction

In this article I will explore some
corrections that should be applied to the Pitot telemetry measurements. A
numerical example will be presented.

Let's consider a nose mounted Pitot, it's
installed on the fuselage axis of symmetry at a distance \(d=0.5m\) from the
center of gravity.

The Pitot speed is referenced in the wind
frame of reference. So is not possible to use together body speeds and Pitot
speeds. The body frame of reference
origin lies on the COG, the frame of reference for Pitot airspeed has the same
origin but is oriented as the wind direction. So the wind frame of reference with
respect to the body reference is rotated by the angle of attack and the angle
of sideslip.

Refer to the previous figure for the body frame definition. Denoting the three body frame velocity
components axis as \(u,v,w\)
and the airspeed as \(V\) then

\(u=Vcos(\alpha)cos(\beta)\)

\(v=Vsin(\beta)\)

\(w=Vsin(\alpha)cos(\beta)\)

\(|V|=\sqrt{u^2+v^2+w^2}\)

\(u=Vcos(\alpha)cos(\beta)\)

\(v=Vsin(\beta)\)

\(w=Vsin(\alpha)cos(\beta)\)

\(|V|=\sqrt{u^2+v^2+w^2}\)

So if we need the body speed for our
computations we should convert airspeed
in the body reference frame as per previous formulas.

Let's consider an example. The aircraft is
travelling at 100 km/h with \(\alpha=10°\) and \(\beta=0°\) in a level straight
flight path. A planar trajectory is assumed, we're flying on a vertical plane. So
in the body frame of reference \(u=98.4 km/h\) and \(w=17.5 km/h\)

Calculated body speed should match with the speed measured with an IMU.

Body rotation rates impact should be investigated; that topic deserves a
dedicated post so I stop here for now. Important fact to note is that COG position should be know for telemetry data processing

## Tuesday, June 17, 2014

### Alfa Multihole probe

A previous article introduced the multi hole probes. Five holes MHP configuration has been chosen for a probe development. The probe should provide angle of attack AOA, angle of sideslip, static pressure and total pressure. In this post I will expose a multi hole AOA probe.

Refer to the following figure for AOA probe definition

*Figure 48.1 Angle of attack MHP probe layout.*

*Figure 48.2 Symbols graphical definition*

The external part of the probe is composed by a cylindrical body; on the cylinder surface two holes are drilled and the pressure from these openings is routed to the pressure sensors. The two holes are 90° degree apart each other. The two pressures at the taps are named \(P_1\) and \(P_2\).

To simplify the example zero angle of sideslip is assumed; hence the cylinder axis of symmetry lies on a plane perpendicular to the wind vector plane. As we need a closed form solution for the pressure field we adopt also the incompressible and unviscid flow hypothesis. Under those circumstances the pressure field is completely defined by the velocity field. That case is in deep studied in specific literature, qualitatively the higher the speed the lower the pressure. Under our working hypothesis the analytical result will be by far different from the experimental result; in fact have been proved that upstream face of the cylinder follows the predicted pressure profile shape, at the contrary the downstream face predicted values are far from predicted values. This flow is supposed to be symmetrical and attached to the cylinder surface.

*Figure 48.3 Stream lines around the cylinder with our working hypothesis*

A viscid flow will be lead to a flow separation; a notable case is the von Karman street, you find here a numerical simulation.

So under our working hypothesis the pressure will be function only of the angular distance \(\zeta\).

Introducing the dimensionless coefficient of pressure \(c_p=\frac{p_{\zeta} –p_{\infty} }{1/2\rho V^2}\)

For our particular case \(c_p=1-4sin^2(\zeta)\), according to equation 4.117 in this link.

Refer to figure 48.2. Note that pressure distribution is symmetrical and \(c_p=1\) for \(\zeta=0\) . Recalling that the holes are 90° degree apart, to account for AOA \(\alpha\) we define \(\zeta=\alpha+45\) .

With the given \(c_p\) expression is possible to calculate the pressure in correspondence of each pressure tap, \(P_1,P_2\) for different values of \(\alpha\). To ease the burden please download this excel file.

*Table 48.1 Excel Screen shot*

*Figure 48.4 (P1-P2) Vs \(\alpha\) at two different speeds*

By inspection of table 48.1 and figure 48.4 is evident that the pressure difference between the two ports is airspeed dependant.

It is possible to obtain a calibration coefficient constant with the airspeed, it is called coefficient of \(\alpha\) and is defined as \(k_{\alpha}=\frac{P_1-P_2}{P_t-(\frac{P_1+P_2}{2})}\), where \(P_t\) is the total pressure.

Refer to the below figure for a graphical representation.

*Figure 48.5 \(k_{\alpha}\) Vs \(\alpha\) at two different airspeeds*

We’ve examined the behavior of an ideal probe, the real sensor need to be calibrated. Next posts we will continue to investigate MHP.

## Monday, June 9, 2014

### Alfa beta probe

Sensors of angle of attack and sideslip are
not often seen on DIY setups. I make here some consideration on the existing
measurement methods to evaluate the more suitable for further development. The sensor should be installed on small and
middle sized RC planes; the typical flight envelope does include high angle of
attacks and low speed; high frequency measurements are required.

Wind direction along with the other air
data measurements enable us to estimate aerodynamic parameters and implement
real time control. The real time control includes, but not only, stability
augmentation, fault detection and reconfiguration. Classical stall warning devices are based on angle of
attack. Angle of attack is fundamental for obtaining maximum range and most
economical cruises.

Types and performances of angle of attack
devices is wide, the most common principles of measurement are

-Aerodynamic deflection, the device is
pretty similar to a mechanical weather vane. For instance see BasicAirData
Boom.

*Figure 47.1 AOA, AOS winds vanes mounted on BasicAirData probe*

-Multi hole probes or MHP, the wind angles are
derived from the pressure measured at different pressure taps

*Figure 47.2 Multi hole probe from Aeroprobe*

-Null seeking, the device is
mechanically deflected until zero reading is reached.

*Video 47.1 a null seeking device video*

-Hotwire Anemometers, the wind direction
and speed is derived by temperature measurements

Mechanical wind vane was already considered and built. Main issue is the
dynamic behavior and connected measurement limitations. If the operating
airspeed range is wide than problems at extreme speed values can happen;
problems arise at booth upper speed limit and lowers speed limit. This sensor
can have serious dynamic tracking problems so it will better to use another
sensor type.

Hot wire anemometer design seems too
fragile, because of low section cables exposed to the air.

Null seeking device cons is the
considerable hardware part count, the complexity for a combined AOA and AOS
probe seems rather high for a DIY project.

Multi hole probe technology is suggestive because don’t need for moving parts to operate. Sensor probe is self-contained and robust.

Beside the classical standalone probe there
is also the possibility to use multiple pressure ports on the fuselage as the NCAR
plane

*Figure 47.3 NCAR plane AOA and AOS sensor*

Returning to classical MHP, use of this
last kind of sensors should be investigated. The major advantage seems to be the
robustness, absence of moving parts, extremely fast response and a capacity to
operate at high incidence angles. Typical MHP has five holes facing the airstream;
four holes are in a cruciform pattern and the last at the middle point.

*Figure 47.4 Flow angle sensor, flow angle arrangement*

You can note the static pressure ports on
this probe. In the general case the pressure at frontal the ports is measured
respect to static pressure. With this layout five differential pressure
transducers and one absolute pressure transducer are needed for best
performance. When correctly operated this kind of MHP probes can provide static
pressure and total pressure value for altitude and airspeed calculations.

It's evident that this probe needs a good
amount of electronic to be operated. With the current piezoelectric sensors
dimensions that is not a problem anymore.

On a future post I'll numerically evaluate
some probe parameter, to be sure that measurements can be carried out with DIY
level equipment.

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