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.