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