I want to simulate the Equations of Motions for F/A-18 Hornet (12 states & 6 DOF) on MATLAB using Simulink. I have the Aerodynamic model, from which I will get CL, CD, CY, Cl, Cn, Cm that are flight conditions dependent.

Now, the forces and moments calculated from these coefficients will be in Wind Axes because these coefficients are defined in that coordinate system only (correct me if I am wrong). For using these Aerodynamic Forces and Moments in Body Axes, do I need to convert them into body axes by multiplying a Direction Cosine Matrix, that converts vectors from Wind Axes to Body Axes? Or should I use the Wind Axes computation?

Assume, I took the first option and converted the forces and moments into Body Frame. But, there are terms like $p$, $q$, and $r$ in the computation of the coefficients mentioned above. These terms are defined in the body frame. So, should I use these values of $p$, $q$, $r$ that are in body axes and compute coefficients in wind axes? Or should I convert them also into wind axes before using them in the computation?

PS: Reference for the Aerodynamic Model of F/A-18 Hornet:


2 Answers 2


It's very prudent of you to be concerned about the axis frames in which different forces/motions are defined. It's a common mistake to ignore the fact that aerodynamic coefficients are normally defined in wind axes.

The standard approach is to calculate Equations of Motions in the body frame; this is how they are usually defined. For this, you'll indeed need a wind-to-body matrix (DCM). This is a simple matrix because it involves only two angles (beta and alpha), and these angles are normally small to be concerned about gimbal lock (the model is probably not defined where they are not small). Then you

  • Calculate the forces/moments that are defined in wind axes and rotate them to body.
  • Likewise, calculate forces and other things that are defined in the ground frame, such as gravity and wind per se, and rotate them to body. (It makes sense to use quaternions for that rather than DCM, but this is another matter).
  • Finally, you'll have forces that are defined directly in the body frame, such as thrust.

Now you can integrate EoM with all the data available in the body frame.

Regarding p, q, r (and such) used in calculation of the aerodynamic forces, these are usually body angular velocities that you can take directly from your EoM. However, you should double check if the aerodynamic model requires something else; this should be explicitly defined. Note that if you do need to rotate angular velocities, you can't use the same DCM but need to use the matrix that preserves the total angular momentum.

  • $\begingroup$ Thanks for clearing my doubts! $\endgroup$
    – Pavan
    Mar 5, 2020 at 4:25
  • $\begingroup$ do you know how to model the Propulsion system of the FA-18 Hornet for the above simulation? Do you just assume that the thurst line passes through CG (no moment) and thrust is only in X direction? Please attach some references, if you have any for thrust modeling. $\endgroup$
    – Pavan
    Mar 5, 2020 at 4:28
  • $\begingroup$ Well, that's an entirely different level. Now you are talking about the physical model itself. It depends on how much accuracy you need and how much data you have. The direction and origin of the thrust vector is part of the aircraft/model data. I don't have it, but I'd guess that for F/A-18 it's pretty close to neutral (along X through CG), as long as you don't simulate single engine operation. For the first approximation it might do, but if you simulate variable mass (ordinance/fuel), the CG may shift laterally, while thrust shouldn't. $\endgroup$
    – Zeus
    Mar 6, 2020 at 1:06
  • $\begingroup$ Thanks for the info! $\endgroup$
    – Pavan
    Mar 6, 2020 at 13:42
  • $\begingroup$ I'd beg to differ and in his particular F18 model, CL CD CY are defined in the stability axes, and Cm Cl Cn are defined in the body axes. The only publicly available source for aerodynamic coefficients is the NASA F18 HARV. $\endgroup$
    – LJQCN101
    Apr 26 at 2:51

It's not true to say that those aerodynamic coefficients are defined in wind axes. To be specific to your F/A-18 model, which usually originates from the NASA F18 HARV model, CL CD CY are defined in the stability axes, and Cm Cl Cn are defined in the body axes.

F18 Axes system

Please refer to the following NASA document for a better description of the Equations of Motion and control schemes used in their simulation: https://ntrs.nasa.gov/api/citations/19920024293/downloads/19920024293.pdf

Here's the NASA F18 HARV wind tunnel data where you can get all the coefficients of force and moment: https://ntrs.nasa.gov/api/citations/19900019262/downloads/19900019262.pdf


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