I have a data set that includes TAS, IAS, GPS Lat/Lon, Inertial Lat/Lon, ENU speed, inertial speeds, attitude, and accelerations. I don't need to know the exact wind speed, and I don't think that's even possible to calculate at this point, but I would like to determine whether or not wind speeds were significant at a certain point in the flight. Is this possible?
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2$\begingroup$ If you have TAS and ground speed (compute from GPS) you can get wind speed. If you have heading, you can also calculate direction. See this for more details. $\endgroup$– Ron BeyerCommented Feb 25, 2020 at 14:02
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$\begingroup$ @RonBeyer in other words, if I want to calculate ground speed, I can just take the GPS Lat/Lon and just take the distance that I travelled in the time of interest and divide that by the time, just as I would any other speed calculation? $\endgroup$– synchhCommented Feb 25, 2020 at 14:10
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$\begingroup$ But apparently you do have groundspeed -- is this what "inertial speed" means in this particular context? If so, question could be edited to point that out (and title changed); if not, answer seems invalid. P.S. -- it's may be worth pointing out that the earth-referenced frame is not the only valid inertial reference frame in some aviation questions, but if winds are variable, then it basically is. $\endgroup$– quiet flyerCommented Feb 18, 2023 at 18:43
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1 Answer
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In the inertial (Earth) frame, denoted by subscript $_E$, inertial velocity ($\bf{V^i}$) is related to air velocity ($\bf{V}$) and wind vector ($\bf{W}$) as follows:
$$\bf{W_E}=\bf{V}^i_E-\bf{V_E}$$
Air velocity is more commonly expressed in the body frame (subscript $_B$), and is related to the inertial frame via the rotation matrix, $\bf{L}_{BE}$, as a function of the Euler attitudes ($\phi,\theta,\psi$):
$$\bf{V_B}=\begin{bmatrix}u \\ v \\ w\end{bmatrix}=L_{BE} (\phi,\theta,\psi) \bf{V_E}$$
$\bf{V_E^i}$ can be transformed from the ENU velocity to NED, and you mentioned that attitudes are measured, so that leaves the air velocity components.
If you have AOA ($\alpha$), AOS ($\beta$) and TAS ($V_T$) measurements, they are related to the components as:
$$\alpha = \tan^{-1}\frac{w}{u}$$ $$\beta = \sin^{-1}\frac{v}{V_T}$$ $$V_T=\sqrt{u^2+v^2+w^2}$$
That's three equations with three unknowns. At this point, you have all the information necessary to solve for the wind vector.
Without AOA and AOS measurements, your only hope is to assume some reasonable values of AOA and AOS. For AOS, you can assume 0 if there is no lateral/directional input. For AOA, you may be able to use some offline data (e.g. wind tunnel, CFD) if your weight estimate and aerodynamic data are trustworthy.
An additional note, per your previous question on finding AOA and AOS without sensors, you have a real dilemma here: you cannot obtain both winds and flow angularities without sensors!
